id	sid	tid	token	lemma	pos
ap-10605	1	1	acta	acta	PROPN
ap-10605	1	2	polytechnica	polytechnica	PROPN
ap-10605	1	3	https://doi.org/10.14311/ap.2025.65.0554	https://doi.org/10.14311/ap.2025.65.0554	PROPN
ap-10605	1	4	acta	acta	PROPN
ap-10605	1	5	polytechnica	polytechnica	PROPN
ap-10605	1	6	65(5):554–561	65(5):554–561	PROPN
ap-10605	1	7	,	,	PUNCT
ap-10605	1	8	2025	2025	NUM
ap-10605	1	9	©	©	ADP
ap-10605	1	10	2025	2025	NUM
ap-10605	1	11	the	the	DET
ap-10605	1	12	author(s	author(s	NOUN
ap-10605	1	13	)	)	PUNCT
ap-10605	1	14	.	.	PUNCT
ap-10605	2	1	licensed	license	VERB
ap-10605	2	2	under	under	ADP
ap-10605	2	3	a	a	DET
ap-10605	2	4	cc	cc	NOUN
ap-10605	2	5	-	-	PUNCT
ap-10605	2	6	by	by	ADP
ap-10605	2	7	4.0	4.0	NUM
ap-10605	2	8	licence	licence	NOUN
ap-10605	2	9	published	publish	VERB
ap-10605	2	10	by	by	ADP
ap-10605	2	11	the	the	DET
ap-10605	2	12	czech	czech	PROPN
ap-10605	2	13	technical	technical	PROPN
ap-10605	2	14	university	university	PROPN
ap-10605	2	15	in	in	ADP
ap-10605	2	16	prague	prague	NOUN
ap-10605	2	17	on	on	ADP
ap-10605	2	18	realizations	realization	NOUN
ap-10605	2	19	of	of	ADP
ap-10605	2	20	lie	lie	NOUN
ap-10605	2	21	algebras	algebras	PROPN
ap-10605	2	22	maryna	maryna	PROPN
ap-10605	2	23	nesterenkoa	nesterenkoa	PROPN
ap-10605	2	24	,	,	PUNCT
ap-10605	2	25	c	c	PROPN
ap-10605	2	26	,	,	PUNCT
ap-10605	2	27	severin	severin	PROPN
ap-10605	2	28	poštab,∗	poštab,∗	PROPN
ap-10605	2	29	,	,	PUNCT
ap-10605	2	30	mykola	mykola	PROPN
ap-10605	2	31	staryia	staryia	PROPN
ap-10605	2	32	a	a	DET
ap-10605	2	33	institute	institute	NOUN
ap-10605	2	34	of	of	ADP
ap-10605	2	35	mathematics	mathematic	NOUN
ap-10605	2	36	of	of	ADP
ap-10605	2	37	nasciences	nascience	NOUN
ap-10605	2	38	of	of	ADP
ap-10605	2	39	ukraine	ukraine	NOUN
ap-10605	2	40	,	,	PUNCT
ap-10605	2	41	3	3	NUM
ap-10605	2	42	tereshchenkivska	tereshchenkivska	PROPN
ap-10605	2	43	st	st	PROPN
ap-10605	2	44	.	.	PROPN
ap-10605	2	45	,	,	PUNCT
ap-10605	2	46	01004	01004	NUM
ap-10605	2	47	kyiv	kyiv	PROPN
ap-10605	2	48	,	,	PUNCT
ap-10605	2	49	ukraine	ukraine	PROPN
ap-10605	2	50	b	b	PROPN
ap-10605	2	51	czech	czech	PROPN
ap-10605	2	52	technical	technical	PROPN
ap-10605	2	53	university	university	PROPN
ap-10605	2	54	in	in	ADP
ap-10605	2	55	prague	prague	PROPN
ap-10605	2	56	,	,	PUNCT
ap-10605	2	57	faculty	faculty	NOUN
ap-10605	2	58	of	of	ADP
ap-10605	2	59	nuclear	nuclear	ADJ
ap-10605	2	60	sciences	science	NOUN
ap-10605	2	61	and	and	CCONJ
ap-10605	2	62	physical	physical	ADJ
ap-10605	2	63	engineering	engineering	NOUN
ap-10605	2	64	,	,	PUNCT
ap-10605	2	65	trojanova	trojanova	X
ap-10605	2	66	13	13	NUM
ap-10605	2	67	,	,	PUNCT
ap-10605	2	68	120	120	NUM
ap-10605	2	69	00	00	NUM
ap-10605	2	70	prague	prague	PROPN
ap-10605	2	71	,	,	PUNCT
ap-10605	2	72	czech	czech	PROPN
ap-10605	2	73	republic	republic	PROPN
ap-10605	2	74	c	c	PROPN
ap-10605	2	75	kyiv	kyiv	PROPN
ap-10605	2	76	school	school	NOUN
ap-10605	2	77	of	of	ADP
ap-10605	2	78	economics	economic	NOUN
ap-10605	2	79	,	,	PUNCT
ap-10605	2	80	3	3	NUM
ap-10605	2	81	mykoly	mykoly	NOUN
ap-10605	2	82	shpaka	shpaka	PROPN
ap-10605	2	83	st	st	PROPN
ap-10605	2	84	.	.	PROPN
ap-10605	2	85	,	,	PUNCT
ap-10605	2	86	03113	03113	NUM
ap-10605	2	87	kyiv	kyiv	PROPN
ap-10605	2	88	,	,	PUNCT
ap-10605	2	89	ukraine	ukraine	NOUN
ap-10605	2	90	∗	∗	NOUN
ap-10605	2	91	corresponding	correspond	VERB
ap-10605	2	92	author	author	NOUN
ap-10605	2	93	:	:	PUNCT
ap-10605	2	94	severin.posta@fjfi.cvut.cz	severin.posta@fjfi.cvut.cz	NOUN
ap-10605	2	95	abstract	abstract	NOUN
ap-10605	2	96	.	.	PUNCT
ap-10605	3	1	we	we	PRON
ap-10605	3	2	discuss	discuss	VERB
ap-10605	3	3	and	and	CCONJ
ap-10605	3	4	compare	compare	VERB
ap-10605	3	5	the	the	DET
ap-10605	3	6	main	main	ADJ
ap-10605	3	7	methods	method	NOUN
ap-10605	3	8	for	for	ADP
ap-10605	3	9	constructing	construct	VERB
ap-10605	3	10	of	of	ADP
ap-10605	3	11	lie	lie	NOUN
ap-10605	3	12	vector	vector	NOUN
ap-10605	3	13	fields	field	NOUN
ap-10605	3	14	from	from	ADP
ap-10605	3	15	the	the	DET
ap-10605	3	16	given	give	VERB
ap-10605	3	17	lie	lie	NOUN
ap-10605	3	18	algebra	algebra	NOUN
ap-10605	3	19	structure	structure	NOUN
ap-10605	3	20	constants	constant	NOUN
ap-10605	3	21	.	.	PUNCT
ap-10605	4	1	generic	generic	ADJ
ap-10605	4	2	realizations	realization	NOUN
ap-10605	4	3	of	of	ADP
ap-10605	4	4	three	three	NUM
ap-10605	4	5	conformal	conformal	ADJ
ap-10605	4	6	algebras	algebra	NOUN
ap-10605	4	7	are	be	AUX
ap-10605	4	8	obtained	obtain	VERB
ap-10605	4	9	by	by	ADP
ap-10605	4	10	the	the	DET
ap-10605	4	11	algebraic	algebraic	ADJ
ap-10605	4	12	method	method	NOUN
ap-10605	4	13	and	and	CCONJ
ap-10605	4	14	all	all	DET
ap-10605	4	15	realizations	realization	NOUN
ap-10605	4	16	of	of	ADP
ap-10605	4	17	the	the	DET
ap-10605	4	18	three	three	NUM
ap-10605	4	19	-	-	PUNCT
ap-10605	4	20	dimensional	dimensional	ADJ
ap-10605	4	21	complex	complex	ADJ
ap-10605	4	22	special	special	ADJ
ap-10605	4	23	linear	linear	NOUN
ap-10605	4	24	algebra	algebra	NOUN
ap-10605	4	25	are	be	AUX
ap-10605	4	26	obtained	obtain	VERB
ap-10605	4	27	by	by	ADP
ap-10605	4	28	the	the	DET
ap-10605	4	29	general	general	ADJ
ap-10605	4	30	method	method	NOUN
ap-10605	4	31	and	and	CCONJ
ap-10605	4	32	compared	compare	VERB
ap-10605	4	33	with	with	ADP
ap-10605	4	34	the	the	DET
ap-10605	4	35	finite	finite	ADJ
ap-10605	4	36	-	-	ADJ
ap-10605	4	37	dimensional	dimensional	ADJ
ap-10605	4	38	weight	weight	NOUN
ap-10605	4	39	representations	representation	NOUN
ap-10605	4	40	.	.	PUNCT
ap-10605	5	1	keywords	keyword	NOUN
ap-10605	5	2	:	:	PUNCT
ap-10605	5	3	realization	realization	NOUN
ap-10605	5	4	,	,	PUNCT
ap-10605	5	5	representation	representation	NOUN
ap-10605	5	6	,	,	PUNCT
ap-10605	5	7	local	local	ADJ
ap-10605	5	8	group	group	NOUN
ap-10605	5	9	.	.	PUNCT
ap-10605	6	1	1	1	X
ap-10605	6	2	.	.	X
ap-10605	6	3	introduction	introduction	NOUN
ap-10605	6	4	despite	despite	SCONJ
ap-10605	6	5	the	the	DET
ap-10605	6	6	fact	fact	NOUN
ap-10605	6	7	that	that	SCONJ
ap-10605	6	8	sophus	sophu	NOUN
ap-10605	6	9	lie	lie	VERB
ap-10605	6	10	himself	himself	PRON
ap-10605	6	11	began	begin	VERB
ap-10605	6	12	constructing	construct	VERB
ap-10605	6	13	realizations	realization	NOUN
ap-10605	6	14	,	,	PUNCT
ap-10605	6	15	this	this	DET
ap-10605	6	16	problem	problem	NOUN
ap-10605	6	17	still	still	ADV
ap-10605	6	18	remains	remain	VERB
ap-10605	6	19	unsolved	unsolved	ADJ
ap-10605	6	20	for	for	ADP
ap-10605	6	21	many	many	ADJ
ap-10605	6	22	important	important	ADJ
ap-10605	6	23	cases	case	NOUN
ap-10605	6	24	.	.	PUNCT
ap-10605	7	1	the	the	DET
ap-10605	7	2	description	description	NOUN
ap-10605	7	3	of	of	ADP
ap-10605	7	4	lie	lie	NOUN
ap-10605	7	5	algebra	algebra	NOUN
ap-10605	7	6	representations	representation	NOUN
ap-10605	7	7	by	by	ADP
ap-10605	7	8	vector	vector	NOUN
ap-10605	7	9	fields	field	NOUN
ap-10605	7	10	is	be	AUX
ap-10605	7	11	of	of	ADP
ap-10605	7	12	great	great	ADJ
ap-10605	7	13	interest	interest	NOUN
ap-10605	7	14	and	and	CCONJ
ap-10605	7	15	widely	widely	ADV
ap-10605	7	16	applicable	applicable	ADJ
ap-10605	7	17	,	,	PUNCT
ap-10605	7	18	e.g.	e.g.	ADV
ap-10605	7	19	to	to	ADP
ap-10605	7	20	the	the	DET
ap-10605	7	21	integration	integration	NOUN
ap-10605	7	22	of	of	ADP
ap-10605	7	23	ordinary	ordinary	ADJ
ap-10605	7	24	differential	differential	ADJ
ap-10605	7	25	equations	equation	NOUN
ap-10605	7	26	.	.	PUNCT
ap-10605	8	1	some	some	DET
ap-10605	8	2	new	new	ADJ
ap-10605	8	3	trends	trend	NOUN
ap-10605	8	4	in	in	ADP
ap-10605	8	5	this	this	DET
ap-10605	8	6	area	area	NOUN
ap-10605	8	7	are	be	AUX
ap-10605	8	8	indicated	indicate	VERB
ap-10605	8	9	in	in	ADP
ap-10605	8	10	[	[	X
ap-10605	8	11	1	1	NUM
ap-10605	8	12	,	,	PUNCT
ap-10605	8	13	2	2	NUM
ap-10605	8	14	]	]	PUNCT
ap-10605	8	15	.	.	PUNCT
ap-10605	9	1	realizations	realization	NOUN
ap-10605	9	2	are	be	AUX
ap-10605	9	3	also	also	ADV
ap-10605	9	4	used	use	VERB
ap-10605	9	5	in	in	ADP
ap-10605	9	6	the	the	DET
ap-10605	9	7	group	group	NOUN
ap-10605	9	8	classification	classification	NOUN
ap-10605	9	9	of	of	ADP
ap-10605	9	10	partial	partial	ADJ
ap-10605	9	11	differential	differential	ADJ
ap-10605	9	12	equations	equation	NOUN
ap-10605	9	13	and	and	CCONJ
ap-10605	9	14	in	in	ADP
ap-10605	9	15	the	the	DET
ap-10605	9	16	classification	classification	NOUN
ap-10605	9	17	of	of	ADP
ap-10605	9	18	gravity	gravity	NOUN
ap-10605	9	19	fields	field	NOUN
ap-10605	9	20	of	of	ADP
ap-10605	9	21	a	a	DET
ap-10605	9	22	general	general	ADJ
ap-10605	9	23	form	form	NOUN
ap-10605	9	24	under	under	ADP
ap-10605	9	25	the	the	DET
ap-10605	9	26	motion	motion	NOUN
ap-10605	9	27	groups	group	NOUN
ap-10605	9	28	or	or	CCONJ
ap-10605	9	29	groups	group	NOUN
ap-10605	9	30	of	of	ADP
ap-10605	9	31	conformal	conformal	ADJ
ap-10605	9	32	transformations	transformation	NOUN
ap-10605	9	33	[	[	X
ap-10605	9	34	3	3	NUM
ap-10605	9	35	]	]	PUNCT
ap-10605	9	36	.	.	PUNCT
ap-10605	10	1	the	the	DET
ap-10605	10	2	construction	construction	NOUN
ap-10605	10	3	of	of	ADP
ap-10605	10	4	realizations	realization	NOUN
ap-10605	10	5	of	of	ADP
ap-10605	10	6	lie	lie	NOUN
ap-10605	10	7	algebras	algebra	NOUN
ap-10605	10	8	is	be	AUX
ap-10605	10	9	also	also	ADV
ap-10605	10	10	a	a	DET
ap-10605	10	11	necessary	necessary	ADJ
ap-10605	10	12	prerequisite	prerequisite	NOUN
ap-10605	10	13	for	for	ADP
ap-10605	10	14	finding	find	VERB
ap-10605	10	15	differential	differential	ADJ
ap-10605	10	16	invariants	invariant	NOUN
ap-10605	10	17	and	and	CCONJ
ap-10605	10	18	constructing	construct	VERB
ap-10605	10	19	mathematical	mathematical	ADJ
ap-10605	10	20	models	model	NOUN
ap-10605	10	21	with	with	ADP
ap-10605	10	22	nontrivial	nontrivial	ADJ
ap-10605	10	23	symmetry	symmetry	NOUN
ap-10605	10	24	.	.	PUNCT
ap-10605	11	1	an	an	DET
ap-10605	11	2	exhaustive	exhaustive	ADJ
ap-10605	11	3	description	description	NOUN
ap-10605	11	4	of	of	ADP
ap-10605	11	5	nonequivalent	nonequivalent	ADJ
ap-10605	11	6	realizations	realization	NOUN
ap-10605	11	7	of	of	ADP
ap-10605	11	8	given	give	VERB
ap-10605	11	9	lie	lie	NOUN
ap-10605	11	10	algebras	algebra	NOUN
ap-10605	11	11	by	by	ADP
ap-10605	11	12	vector	vector	NOUN
ap-10605	11	13	fields	field	NOUN
ap-10605	11	14	is	be	AUX
ap-10605	11	15	also	also	ADV
ap-10605	11	16	an	an	DET
ap-10605	11	17	independent	independent	ADJ
ap-10605	11	18	fundamental	fundamental	ADJ
ap-10605	11	19	mathematical	mathematical	ADJ
ap-10605	11	20	problem	problem	NOUN
ap-10605	11	21	.	.	PUNCT
ap-10605	12	1	in	in	ADP
ap-10605	12	2	this	this	DET
ap-10605	12	3	work	work	NOUN
ap-10605	12	4	,	,	PUNCT
ap-10605	12	5	we	we	PRON
ap-10605	12	6	review	review	VERB
ap-10605	12	7	the	the	DET
ap-10605	12	8	main	main	ADJ
ap-10605	12	9	methods	method	NOUN
ap-10605	12	10	of	of	ADP
ap-10605	12	11	realization	realization	NOUN
ap-10605	12	12	construction	construction	NOUN
ap-10605	12	13	and	and	CCONJ
ap-10605	12	14	apply	apply	VERB
ap-10605	12	15	them	they	PRON
ap-10605	12	16	to	to	ADP
ap-10605	12	17	special	special	ADJ
ap-10605	12	18	linear	linear	NOUN
ap-10605	12	19	and	and	CCONJ
ap-10605	12	20	conformal	conformal	ADJ
ap-10605	12	21	lie	lie	NOUN
ap-10605	12	22	algebras	algebra	NOUN
ap-10605	12	23	.	.	PUNCT
ap-10605	13	1	in	in	ADP
ap-10605	13	2	particular	particular	ADJ
ap-10605	13	3	,	,	PUNCT
ap-10605	13	4	we	we	PRON
ap-10605	13	5	present	present	VERB
ap-10605	13	6	the	the	DET
ap-10605	13	7	realization	realization	NOUN
ap-10605	13	8	of	of	ADP
ap-10605	13	9	sl(2,c	sl(2,c	NOUN
ap-10605	13	10	)	)	PUNCT
ap-10605	13	11	that	that	PRON
ap-10605	13	12	is	be	AUX
ap-10605	13	13	not	not	PART
ap-10605	13	14	equivalent	equivalent	ADJ
ap-10605	13	15	to	to	ADP
ap-10605	13	16	a	a	DET
ap-10605	13	17	finite	finite	ADJ
ap-10605	13	18	-	-	ADJ
ap-10605	13	19	dimensional	dimensional	ADJ
ap-10605	13	20	representation	representation	NOUN
ap-10605	13	21	.	.	PUNCT
ap-10605	14	1	the	the	DET
ap-10605	14	2	paper	paper	NOUN
ap-10605	14	3	is	be	AUX
ap-10605	14	4	arranged	arrange	VERB
ap-10605	14	5	as	as	SCONJ
ap-10605	14	6	follows	follow	VERB
ap-10605	14	7	.	.	PUNCT
ap-10605	15	1	we	we	PRON
ap-10605	15	2	first	first	ADV
ap-10605	15	3	review	review	VERB
ap-10605	15	4	the	the	DET
ap-10605	15	5	basic	basic	ADJ
ap-10605	15	6	definitions	definition	NOUN
ap-10605	15	7	and	and	CCONJ
ap-10605	15	8	notations	notation	NOUN
ap-10605	15	9	in	in	ADP
ap-10605	15	10	section	section	NOUN
ap-10605	15	11	2	2	NUM
ap-10605	15	12	,	,	PUNCT
ap-10605	15	13	then	then	ADV
ap-10605	15	14	in	in	ADP
ap-10605	15	15	section	section	NOUN
ap-10605	15	16	3	3	NUM
ap-10605	15	17	,	,	PUNCT
ap-10605	15	18	we	we	PRON
ap-10605	15	19	describe	describe	VERB
ap-10605	15	20	and	and	CCONJ
ap-10605	15	21	compare	compare	VERB
ap-10605	15	22	the	the	DET
ap-10605	15	23	main	main	ADJ
ap-10605	15	24	methods	method	NOUN
ap-10605	15	25	representing	represent	VERB
ap-10605	15	26	an	an	DET
ap-10605	15	27	abstract	abstract	ADJ
ap-10605	15	28	lie	lie	NOUN
ap-10605	15	29	algebra	algebra	NOUN
ap-10605	15	30	by	by	ADP
ap-10605	15	31	vector	vector	NOUN
ap-10605	15	32	fields	field	NOUN
ap-10605	15	33	.	.	PUNCT
ap-10605	16	1	in	in	ADP
ap-10605	16	2	section	section	NOUN
ap-10605	16	3	4	4	NUM
ap-10605	16	4	,	,	PUNCT
ap-10605	16	5	we	we	PRON
ap-10605	16	6	compare	compare	VERB
ap-10605	16	7	realizations	realization	NOUN
ap-10605	16	8	of	of	ADP
ap-10605	16	9	sl(2,c	sl(2,c	NOUN
ap-10605	16	10	)	)	PUNCT
ap-10605	16	11	constructed	construct	VERB
ap-10605	16	12	by	by	ADP
ap-10605	16	13	the	the	DET
ap-10605	16	14	direct	direct	ADJ
ap-10605	16	15	method	method	NOUN
ap-10605	16	16	and	and	CCONJ
ap-10605	16	17	from	from	ADP
ap-10605	16	18	the	the	DET
ap-10605	16	19	weight	weight	NOUN
ap-10605	16	20	representations	representation	NOUN
ap-10605	16	21	.	.	PUNCT
ap-10605	17	1	and	and	CCONJ
ap-10605	17	2	,	,	PUNCT
ap-10605	17	3	in	in	ADP
ap-10605	17	4	section	section	NOUN
ap-10605	17	5	5	5	NUM
ap-10605	17	6	,	,	PUNCT
ap-10605	17	7	we	we	PRON
ap-10605	17	8	apply	apply	VERB
ap-10605	17	9	the	the	DET
ap-10605	17	10	shirokov	shirokov	NOUN
ap-10605	17	11	’s	’s	PART
ap-10605	17	12	method	method	NOUN
ap-10605	17	13	to	to	ADP
ap-10605	17	14	three	three	NUM
ap-10605	17	15	conformal	conformal	ADJ
ap-10605	17	16	lie	lie	NOUN
ap-10605	17	17	algebras	algebra	NOUN
ap-10605	17	18	,	,	PUNCT
ap-10605	17	19	with	with	ADP
ap-10605	17	20	the	the	DET
ap-10605	17	21	resulting	result	VERB
ap-10605	17	22	generic	generic	ADJ
ap-10605	17	23	realizations	realization	NOUN
ap-10605	17	24	being	be	AUX
ap-10605	17	25	presented	present	VERB
ap-10605	17	26	in	in	ADP
ap-10605	17	27	appendix	appendix	ADJ
ap-10605	17	28	a.	a.	NOUN
ap-10605	17	29	2	2	NUM
ap-10605	17	30	.	.	PUNCT
ap-10605	17	31	definitions	definition	NOUN
ap-10605	17	32	and	and	CCONJ
ap-10605	17	33	statement	statement	NOUN
ap-10605	17	34	of	of	ADP
ap-10605	17	35	the	the	DET
ap-10605	17	36	problem	problem	NOUN
ap-10605	17	37	consider	consider	VERB
ap-10605	17	38	a	a	DET
ap-10605	17	39	lie	lie	NOUN
ap-10605	17	40	algebra	algebra	NOUN
ap-10605	17	41	g	g	PROPN
ap-10605	17	42	=	=	SYM
ap-10605	17	43	(	(	PUNCT
ap-10605	17	44	v	v	NOUN
ap-10605	17	45	,	,	PUNCT
ap-10605	17	46	[	[	X
ap-10605	17	47	·	·	PUNCT
ap-10605	17	48	,	,	PUNCT
ap-10605	17	49	·	·	PUNCT
ap-10605	17	50	]	]	X
ap-10605	17	51	)	)	PUNCT
ap-10605	17	52	,	,	PUNCT
ap-10605	17	53	where	where	SCONJ
ap-10605	17	54	v	v	NOUN
ap-10605	17	55	is	be	AUX
ap-10605	17	56	an	an	DET
ap-10605	17	57	n	n	ADV
ap-10605	17	58	-	-	PUNCT
ap-10605	17	59	dimensional	dimensional	ADJ
ap-10605	17	60	complex	complex	ADJ
ap-10605	17	61	or	or	CCONJ
ap-10605	17	62	real	real	ADJ
ap-10605	17	63	vector	vector	NOUN
ap-10605	17	64	space	space	NOUN
ap-10605	17	65	with	with	ADP
ap-10605	17	66	a	a	DET
ap-10605	17	67	bilinear	bilinear	NOUN
ap-10605	17	68	antisymmetric	antisymmetric	ADJ
ap-10605	17	69	operation	operation	NOUN
ap-10605	17	70	[	[	X
ap-10605	17	71	·	·	PUNCT
ap-10605	17	72	,	,	PUNCT
ap-10605	17	73	·	·	PUNCT
ap-10605	17	74	]	]	X
ap-10605	17	75	:	:	PUNCT
ap-10605	17	76	v	v	NUM
ap-10605	17	77	×	×	NOUN
ap-10605	17	78	v	v	NOUN
ap-10605	17	79	→	→	SYM
ap-10605	17	80	v	v	NOUN
ap-10605	17	81	that	that	PRON
ap-10605	17	82	satisfies	satisfy	VERB
ap-10605	17	83	the	the	DET
ap-10605	17	84	jacobi	jacobi	PROPN
ap-10605	17	85	identity	identity	NOUN
ap-10605	17	86	,	,	PUNCT
ap-10605	17	87	and	and	CCONJ
ap-10605	17	88	is	be	AUX
ap-10605	17	89	usually	usually	ADV
ap-10605	17	90	called	call	VERB
ap-10605	17	91	a	a	DET
ap-10605	17	92	lie	lie	NOUN
ap-10605	17	93	bracket	bracket	NOUN
ap-10605	17	94	or	or	CCONJ
ap-10605	17	95	a	a	DET
ap-10605	17	96	commutator	commutator	NOUN
ap-10605	17	97	.	.	PUNCT
ap-10605	18	1	fixing	fix	VERB
ap-10605	18	2	the	the	DET
ap-10605	18	3	basis	basis	NOUN
ap-10605	18	4	e1	e1	NOUN
ap-10605	18	5	,	,	PUNCT
ap-10605	18	6	.	.	PUNCT
ap-10605	18	7	.	.	PUNCT
ap-10605	19	1	.	.	PUNCT
ap-10605	20	1	,	,	PUNCT
ap-10605	20	2	en	en	ADP
ap-10605	20	3	of	of	ADP
ap-10605	20	4	v	v	NUM
ap-10605	20	5	,	,	PUNCT
ap-10605	20	6	we	we	PRON
ap-10605	20	7	can	can	AUX
ap-10605	20	8	define	define	VERB
ap-10605	20	9	the	the	DET
ap-10605	20	10	lie	lie	NOUN
ap-10605	20	11	algebra	algebra	NOUN
ap-10605	20	12	g	g	NOUN
ap-10605	20	13	by	by	ADP
ap-10605	20	14	its	its	PRON
ap-10605	20	15	commutation	commutation	NOUN
ap-10605	20	16	relations	relation	NOUN
ap-10605	20	17	:	:	PUNCT
ap-10605	21	1	[	[	X
ap-10605	21	2	ei	ei	X
ap-10605	21	3	,	,	PUNCT
ap-10605	21	4	ej	ej	X
ap-10605	21	5	]	]	X
ap-10605	21	6	=	=	PUNCT
ap-10605	22	1	n∑	n∑	NOUN
ap-10605	22	2	k=1	k=1	PROPN
ap-10605	22	3	ck	ck	PROPN
ap-10605	22	4	ijek	ijek	NOUN
ap-10605	22	5	,	,	PUNCT
ap-10605	22	6	or	or	CCONJ
ap-10605	22	7	by	by	ADP
ap-10605	22	8	the	the	DET
ap-10605	22	9	structure	structure	NOUN
ap-10605	22	10	constant	constant	ADJ
ap-10605	22	11	tensor	tensor	NOUN
ap-10605	22	12	c	c	NOUN
ap-10605	22	13	,	,	PUNCT
ap-10605	22	14	with	with	ADP
ap-10605	22	15	the	the	DET
ap-10605	22	16	components	component	NOUN
ap-10605	22	17	ck	ck	INTJ
ap-10605	22	18	ij	ij	INTJ
ap-10605	22	19	∈	∈	PROPN
ap-10605	22	20	c	c	PROPN
ap-10605	22	21	or	or	CCONJ
ap-10605	22	22	ck	ck	INTJ
ap-10605	22	23	ij	ij	NOUN
ap-10605	22	24	∈	∈	PROPN
ap-10605	22	25	r.	r.	PROPN
ap-10605	22	26	hereafter	hereafter	PROPN
ap-10605	22	27	,	,	PUNCT
ap-10605	22	28	we	we	PRON
ap-10605	22	29	assume	assume	VERB
ap-10605	22	30	that	that	SCONJ
ap-10605	22	31	the	the	DET
ap-10605	22	32	indices	index	NOUN
ap-10605	22	33	i	i	PRON
ap-10605	22	34	,	,	PUNCT
ap-10605	22	35	j	j	PROPN
ap-10605	22	36	,	,	PUNCT
ap-10605	22	37	k	k	PROPN
ap-10605	22	38	,	,	PUNCT
ap-10605	22	39	ĩ	ĩ	PROPN
ap-10605	22	40	,	,	PUNCT
ap-10605	22	41	j̃	j̃	PROPN
ap-10605	22	42	and	and	CCONJ
ap-10605	22	43	k̃	k̃	PROPN
ap-10605	22	44	run	run	VERB
ap-10605	22	45	from	from	ADP
ap-10605	22	46	1	1	NUM
ap-10605	22	47	to	to	ADP
ap-10605	22	48	n	n	CCONJ
ap-10605	22	49	,	,	PUNCT
ap-10605	22	50	and	and	CCONJ
ap-10605	22	51	we	we	PRON
ap-10605	22	52	will	will	AUX
ap-10605	22	53	imply	imply	VERB
ap-10605	22	54	the	the	DET
ap-10605	22	55	summation	summation	NOUN
ap-10605	22	56	over	over	ADP
ap-10605	22	57	the	the	DET
ap-10605	22	58	repeating	repeat	VERB
ap-10605	22	59	indices	index	NOUN
ap-10605	22	60	.	.	PUNCT
ap-10605	23	1	the	the	DET
ap-10605	23	2	general	general	ADJ
ap-10605	23	3	linear	linear	PROPN
ap-10605	23	4	group	group	NOUN
ap-10605	23	5	acts	act	VERB
ap-10605	23	6	on	on	ADP
ap-10605	23	7	the	the	DET
ap-10605	23	8	variety	variety	NOUN
ap-10605	23	9	of	of	ADP
ap-10605	23	10	ndimensional	ndimensional	ADJ
ap-10605	23	11	lie	lie	NOUN
ap-10605	23	12	algebras	algebra	NOUN
ap-10605	23	13	as	as	SCONJ
ap-10605	23	14	follows	follow	VERB
ap-10605	23	15	.	.	PUNCT
ap-10605	24	1	let	let	VERB
ap-10605	24	2	a	a	DET
ap-10605	24	3	∈	∈	NOUN
ap-10605	24	4	gln(v	gln(v	NOUN
ap-10605	24	5	)	)	PUNCT
ap-10605	24	6	and	and	CCONJ
ap-10605	24	7	b	b	X
ap-10605	24	8	=	=	SYM
ap-10605	24	9	a−1	a−1	PROPN
ap-10605	24	10	,	,	PUNCT
ap-10605	24	11	then	then	ADV
ap-10605	24	12	the	the	DET
ap-10605	24	13	components	component	NOUN
ap-10605	24	14	of	of	ADP
ap-10605	24	15	the	the	DET
ap-10605	24	16	initial	initial	ADJ
ap-10605	24	17	structure	structure	NOUN
ap-10605	24	18	constant	constant	ADJ
ap-10605	24	19	tensor	tensor	NOUN
ap-10605	24	20	c	c	NOUN
ap-10605	24	21	and	and	CCONJ
ap-10605	24	22	the	the	DET
ap-10605	24	23	resulting	result	VERB
ap-10605	24	24	tensor	tensor	NOUN
ap-10605	24	25	c̃	c̃	PROPN
ap-10605	24	26	are	be	AUX
ap-10605	24	27	connected	connect	VERB
ap-10605	24	28	by	by	ADP
ap-10605	24	29	the	the	DET
ap-10605	24	30	formula	formula	NOUN
ap-10605	24	31	:	:	PUNCT
ap-10605	24	32	c̃k̃	c̃k̃	PROPN
ap-10605	24	33	ĩj̃	ĩj̃	PROPN
ap-10605	24	34	=	=	PUNCT
ap-10605	24	35	ai	ai	VERB
ap-10605	24	36	ĩ	ĩ	PROPN
ap-10605	24	37	aj	aj	PROPN
ap-10605	24	38	j̃	j̃	PROPN
ap-10605	24	39	bk̃	bk̃	PROPN
ap-10605	24	40	kck	kck	PROPN
ap-10605	24	41	ij	ij	PROPN
ap-10605	24	42	.	.	PUNCT
ap-10605	25	1	denote	denote	VERB
ap-10605	25	2	the	the	DET
ap-10605	25	3	whole	whole	ADJ
ap-10605	25	4	automorphism	automorphism	NOUN
ap-10605	25	5	group	group	NOUN
ap-10605	25	6	of	of	ADP
ap-10605	25	7	g	g	PROPN
ap-10605	25	8	by	by	ADP
ap-10605	25	9	aut(g	aut(g	PROPN
ap-10605	25	10	)	)	PUNCT
ap-10605	25	11	⊆	⊆	NUM
ap-10605	25	12	gln(v	gln(v	NOUN
ap-10605	25	13	)	)	PUNCT
ap-10605	25	14	and	and	CCONJ
ap-10605	25	15	the	the	DET
ap-10605	25	16	group	group	NOUN
ap-10605	25	17	of	of	ADP
ap-10605	25	18	the	the	DET
ap-10605	25	19	inner	inner	ADJ
ap-10605	25	20	automorphisms	automorphism	NOUN
ap-10605	25	21	by	by	ADP
ap-10605	25	22	inn(g	inn(g	PROPN
ap-10605	25	23	)	)	PUNCT
ap-10605	25	24	.	.	PUNCT
ap-10605	26	1	in	in	ADP
ap-10605	26	2	this	this	DET
ap-10605	26	3	work	work	NOUN
ap-10605	26	4	,	,	PUNCT
ap-10605	26	5	we	we	PRON
ap-10605	26	6	mostly	mostly	ADV
ap-10605	26	7	follow	follow	VERB
ap-10605	26	8	the	the	DET
ap-10605	26	9	definitions	definition	NOUN
ap-10605	26	10	proposed	propose	VERB
ap-10605	26	11	in	in	ADP
ap-10605	26	12	[	[	X
ap-10605	26	13	4	4	X
ap-10605	26	14	]	]	PUNCT
ap-10605	26	15	with	with	ADP
ap-10605	26	16	some	some	DET
ap-10605	26	17	minor	minor	ADJ
ap-10605	26	18	modern	modern	ADJ
ap-10605	26	19	modifications	modification	NOUN
ap-10605	26	20	and	and	CCONJ
ap-10605	26	21	generalization	generalization	NOUN
ap-10605	26	22	to	to	ADP
ap-10605	26	23	the	the	DET
ap-10605	26	24	case	case	NOUN
ap-10605	26	25	of	of	ADP
ap-10605	26	26	complex	complex	ADJ
ap-10605	26	27	field	field	NOUN
ap-10605	26	28	.	.	PUNCT
ap-10605	27	1	note	note	VERB
ap-10605	27	2	that	that	SCONJ
ap-10605	27	3	we	we	PRON
ap-10605	27	4	work	work	VERB
ap-10605	27	5	only	only	ADV
ap-10605	27	6	locally	locally	ADV
ap-10605	27	7	.	.	PUNCT
ap-10605	28	1	the	the	DET
ap-10605	28	2	definitions	definition	NOUN
ap-10605	28	3	given	give	VERB
ap-10605	28	4	below	below	ADP
ap-10605	28	5	are	be	AUX
ap-10605	28	6	similar	similar	ADJ
ap-10605	28	7	for	for	ADP
ap-10605	28	8	the	the	DET
ap-10605	28	9	field	field	NOUN
ap-10605	28	10	of	of	ADP
ap-10605	28	11	real	real	ADJ
ap-10605	28	12	and	and	CCONJ
ap-10605	28	13	complex	complex	ADJ
ap-10605	28	14	numbers	number	NOUN
ap-10605	28	15	,	,	PUNCT
ap-10605	28	16	but	but	CCONJ
ap-10605	28	17	differ	differ	VERB
ap-10605	28	18	in	in	ADP
ap-10605	28	19	some	some	DET
ap-10605	28	20	details	detail	NOUN
ap-10605	28	21	.	.	PUNCT
ap-10605	29	1	let	let	AUX
ap-10605	29	2	m	m	PROPN
ap-10605	29	3	⊂	⊂	PROPN
ap-10605	29	4	rm	rm	PROPN
ap-10605	29	5	,	,	PUNCT
ap-10605	29	6	m	m	PROPN
ap-10605	29	7	∈	∈	PROPN
ap-10605	29	8	n	n	PRON
ap-10605	29	9	be	be	VERB
ap-10605	29	10	an	an	DET
ap-10605	29	11	m	m	ADV
ap-10605	29	12	-	-	ADJ
ap-10605	29	13	dimensional	dimensional	ADJ
ap-10605	29	14	smooth	smooth	ADJ
ap-10605	29	15	manifold	manifold	NOUN
ap-10605	29	16	and	and	CCONJ
ap-10605	29	17	vect(m	vect(m	NOUN
ap-10605	29	18	)	)	PUNCT
ap-10605	29	19	denote	denote	VERB
ap-10605	29	20	the	the	DET
ap-10605	29	21	lie	lie	NOUN
ap-10605	29	22	algebra	algebra	NOUN
ap-10605	29	23	of	of	ADP
ap-10605	29	24	smooth	smooth	ADJ
ap-10605	29	25	vector	vector	NOUN
ap-10605	29	26	fields	field	NOUN
ap-10605	29	27	on	on	ADP
ap-10605	29	28	m	m	PROPN
ap-10605	29	29	.	.	PUNCT
ap-10605	30	1	definition	definition	NOUN
ap-10605	30	2	1	1	NUM
ap-10605	30	3	.	.	PUNCT
ap-10605	31	1	a	a	DET
ap-10605	31	2	realization	realization	NOUN
ap-10605	31	3	of	of	ADP
ap-10605	31	4	lie	lie	NOUN
ap-10605	31	5	algebra	algebra	NOUN
ap-10605	31	6	g	g	PROPN
ap-10605	31	7	in	in	ADP
ap-10605	31	8	vector	vector	NOUN
ap-10605	31	9	fields	field	NOUN
ap-10605	31	10	on	on	ADP
ap-10605	31	11	m	m	PROPN
ap-10605	31	12	is	be	AUX
ap-10605	31	13	a	a	DET
ap-10605	31	14	homomorphism	homomorphism	NOUN
ap-10605	31	15	r	r	NOUN
ap-10605	31	16	:	:	PUNCT
ap-10605	31	17	g	g	NOUN
ap-10605	31	18	→	→	SYM
ap-10605	31	19	vect(m	vect(m	NOUN
ap-10605	31	20	)	)	PUNCT
ap-10605	31	21	.	.	PUNCT
ap-10605	32	1	the	the	DET
ap-10605	32	2	realization	realization	NOUN
ap-10605	32	3	is	be	AUX
ap-10605	32	4	called	call	VERB
ap-10605	32	5	faithful	faithful	ADJ
ap-10605	32	6	if	if	SCONJ
ap-10605	32	7	ker	ker	NOUN
ap-10605	32	8	r	r	NOUN
ap-10605	32	9	=	=	PUNCT
ap-10605	32	10	{	{	PUNCT
ap-10605	32	11	0	0	NUM
ap-10605	32	12	}	}	PUNCT
ap-10605	32	13	,	,	PUNCT
ap-10605	32	14	and	and	CCONJ
ap-10605	32	15	unfaithful	unfaithful	ADJ
ap-10605	32	16	otherwise	otherwise	ADV
ap-10605	32	17	.	.	PUNCT
ap-10605	33	1	554	554	NUM
ap-10605	33	2	https://doi.org/10.14311/ap.2025.65.0554	https://doi.org/10.14311/ap.2025.65.0554	PROPN
ap-10605	33	3	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
ap-10605	33	4	https://www.cvut.cz/en	https://www.cvut.cz/en	PROPN
ap-10605	33	5	vol	vol	NOUN
ap-10605	33	6	.	.	PROPN
ap-10605	34	1	65	65	NUM
ap-10605	34	2	no	no	NOUN
ap-10605	34	3	.	.	PUNCT
ap-10605	35	1	5/2025	5/2025	NUM
ap-10605	35	2	on	on	ADP
ap-10605	35	3	realizations	realization	NOUN
ap-10605	35	4	of	of	ADP
ap-10605	35	5	lie	lie	NOUN
ap-10605	35	6	algebras	algebra	VERB
ap-10605	35	7	loosely	loosely	ADV
ap-10605	35	8	speaking	speak	VERB
ap-10605	35	9	,	,	PUNCT
ap-10605	35	10	we	we	PRON
ap-10605	35	11	consider	consider	VERB
ap-10605	35	12	lie	lie	NOUN
ap-10605	35	13	algebras	algebra	NOUN
ap-10605	35	14	of	of	ADP
ap-10605	35	15	homogeneous	homogeneous	ADJ
ap-10605	35	16	first	first	ADJ
ap-10605	35	17	-	-	PUNCT
ap-10605	35	18	order	order	NOUN
ap-10605	35	19	differential	differential	ADJ
ap-10605	35	20	operators	operator	NOUN
ap-10605	35	21	:	:	PUNCT
ap-10605	35	22	ξ1(x	ξ1(x	NOUN
ap-10605	35	23	)	)	PUNCT
ap-10605	35	24	∂	∂	NUM
ap-10605	35	25	∂x1	∂x1	NOUN
ap-10605	35	26	+	+	CCONJ
ap-10605	35	27	ξ2(x	ξ2(x	NOUN
ap-10605	35	28	)	)	PUNCT
ap-10605	35	29	∂	∂	NUM
ap-10605	35	30	∂x2	∂x2	NOUN
ap-10605	35	31	+	+	X
ap-10605	35	32	·	·	PUNCT
ap-10605	35	33	·	·	PUNCT
ap-10605	35	34	·	·	PUNCT
ap-10605	36	1	+	+	NUM
ap-10605	36	2	ξm(x	ξm(x	NUM
ap-10605	36	3	)	)	PUNCT
ap-10605	36	4	∂	∂	NUM
ap-10605	36	5	∂xm	∂xm	NOUN
ap-10605	36	6	,	,	PUNCT
ap-10605	36	7	with	with	SCONJ
ap-10605	36	8	the	the	DET
ap-10605	36	9	coefficients	coefficient	NOUN
ap-10605	36	10	ξα	ξα	VERB
ap-10605	36	11	that	that	PRON
ap-10605	36	12	are	be	AUX
ap-10605	36	13	smooth	smooth	ADJ
ap-10605	36	14	functions	function	NOUN
ap-10605	36	15	on	on	ADP
ap-10605	36	16	m	m	PROPN
ap-10605	36	17	,	,	PUNCT
ap-10605	36	18	hereafter	hereafter	ADJ
ap-10605	36	19	indices	indice	VERB
ap-10605	36	20	α	α	PRON
ap-10605	36	21	,	,	PUNCT
ap-10605	36	22	β	β	X
ap-10605	36	23	and	and	CCONJ
ap-10605	36	24	γ	γ	PROPN
ap-10605	36	25	run	run	VERB
ap-10605	36	26	from	from	ADP
ap-10605	36	27	1	1	NUM
ap-10605	36	28	to	to	ADP
ap-10605	36	29	m	m	PRON
ap-10605	36	30	,	,	PUNCT
ap-10605	36	31	∂α	∂α	PROPN
ap-10605	36	32	=	=	PUNCT
ap-10605	36	33	∂xα	∂xα	PROPN
ap-10605	36	34	=	=	SYM
ap-10605	36	35	∂	∂	NUM
ap-10605	36	36	∂xα	∂xα	PROPN
ap-10605	36	37	and	and	CCONJ
ap-10605	36	38	x	x	SYM
ap-10605	36	39	=	=	SYM
ap-10605	36	40	(	(	PUNCT
ap-10605	36	41	x1	x1	PROPN
ap-10605	36	42	,	,	PUNCT
ap-10605	36	43	x2	x2	PROPN
ap-10605	36	44	,	,	PUNCT
ap-10605	36	45	.	.	PUNCT
ap-10605	36	46	.	.	PUNCT
ap-10605	37	1	.	.	PUNCT
ap-10605	38	1	,	,	PUNCT
ap-10605	38	2	xm	xm	PROPN
ap-10605	38	3	)	)	PUNCT
ap-10605	38	4	.	.	PUNCT
ap-10605	39	1	in	in	ADP
ap-10605	39	2	the	the	DET
ap-10605	39	3	case	case	NOUN
ap-10605	39	4	of	of	ADP
ap-10605	39	5	a	a	DET
ap-10605	39	6	complex	complex	ADJ
ap-10605	39	7	lie	lie	NOUN
ap-10605	39	8	algebra	algebra	NOUN
ap-10605	39	9	,	,	PUNCT
ap-10605	39	10	we	we	PRON
ap-10605	39	11	denote	denote	VERB
ap-10605	39	12	a	a	DET
ap-10605	39	13	domain	domain	NOUN
ap-10605	39	14	of	of	ADP
ap-10605	39	15	cm	cm	PROPN
ap-10605	39	16	as	as	ADP
ap-10605	39	17	m	m	PROPN
ap-10605	39	18	and	and	CCONJ
ap-10605	39	19	vect(m	vect(m	NOUN
ap-10605	39	20	)	)	PUNCT
ap-10605	39	21	are	be	AUX
ap-10605	39	22	the	the	DET
ap-10605	39	23	vector	vector	NOUN
ap-10605	39	24	fields	field	NOUN
ap-10605	39	25	on	on	ADP
ap-10605	39	26	m	m	PROPN
ap-10605	39	27	with	with	ADP
ap-10605	39	28	analytical	analytical	ADJ
ap-10605	39	29	coefficients	coefficient	NOUN
ap-10605	39	30	.	.	PUNCT
ap-10605	40	1	the	the	DET
ap-10605	40	2	formulation	formulation	NOUN
ap-10605	40	3	of	of	ADP
ap-10605	40	4	the	the	DET
ap-10605	40	5	realization	realization	NOUN
ap-10605	40	6	definition	definition	NOUN
ap-10605	40	7	is	be	AUX
ap-10605	40	8	the	the	DET
ap-10605	40	9	same	same	ADJ
ap-10605	40	10	.	.	PUNCT
ap-10605	41	1	the	the	DET
ap-10605	41	2	main	main	ADJ
ap-10605	41	3	problem	problem	NOUN
ap-10605	41	4	considered	consider	VERB
ap-10605	41	5	in	in	ADP
ap-10605	41	6	this	this	DET
ap-10605	41	7	work	work	NOUN
ap-10605	41	8	is	be	AUX
ap-10605	41	9	the	the	DET
ap-10605	41	10	construction	construction	NOUN
ap-10605	41	11	of	of	ADP
ap-10605	41	12	all	all	DET
ap-10605	41	13	possible	possible	ADJ
ap-10605	41	14	realizations	realization	NOUN
ap-10605	41	15	of	of	ADP
ap-10605	41	16	an	an	DET
ap-10605	41	17	abstract	abstract	ADJ
ap-10605	41	18	lie	lie	NOUN
ap-10605	41	19	algebra	algebra	NOUN
ap-10605	41	20	g	g	NOUN
ap-10605	41	21	given	give	VERB
ap-10605	41	22	by	by	ADP
ap-10605	41	23	its	its	PRON
ap-10605	41	24	commutation	commutation	NOUN
ap-10605	41	25	relations	relation	NOUN
ap-10605	41	26	.	.	PUNCT
ap-10605	42	1	note	note	VERB
ap-10605	42	2	that	that	SCONJ
ap-10605	42	3	for	for	ADP
ap-10605	42	4	the	the	DET
ap-10605	42	5	fixed	fix	VERB
ap-10605	42	6	lie	lie	NOUN
ap-10605	42	7	algebra	algebra	NOUN
ap-10605	42	8	g	g	PROPN
ap-10605	42	9	,	,	PUNCT
ap-10605	42	10	it	it	PRON
ap-10605	42	11	is	be	AUX
ap-10605	42	12	reasonable	reasonable	ADJ
ap-10605	42	13	to	to	PART
ap-10605	42	14	look	look	VERB
ap-10605	42	15	for	for	ADP
ap-10605	42	16	the	the	DET
ap-10605	42	17	faithful	faithful	ADJ
ap-10605	42	18	realizations	realization	NOUN
ap-10605	42	19	only	only	ADV
ap-10605	42	20	,	,	PUNCT
ap-10605	42	21	since	since	SCONJ
ap-10605	42	22	all	all	DET
ap-10605	42	23	unfaithful	unfaithful	ADJ
ap-10605	42	24	realizations	realization	NOUN
ap-10605	42	25	can	can	AUX
ap-10605	42	26	be	be	AUX
ap-10605	42	27	investigated	investigate	VERB
ap-10605	42	28	as	as	ADP
ap-10605	42	29	faithful	faithful	ADJ
ap-10605	42	30	realizations	realization	NOUN
ap-10605	42	31	of	of	ADP
ap-10605	42	32	some	some	DET
ap-10605	42	33	lower	lower	ADV
ap-10605	42	34	-	-	PUNCT
ap-10605	42	35	dimensional	dimensional	ADJ
ap-10605	42	36	algebra	algebra	NOUN
ap-10605	42	37	.	.	PUNCT
ap-10605	43	1	as	as	SCONJ
ap-10605	43	2	it	it	PRON
ap-10605	43	3	follows	follow	VERB
ap-10605	43	4	from	from	ADP
ap-10605	43	5	the	the	DET
ap-10605	43	6	definition	definition	NOUN
ap-10605	43	7	,	,	PUNCT
ap-10605	43	8	realization	realization	NOUN
ap-10605	43	9	is	be	AUX
ap-10605	43	10	a	a	DET
ap-10605	43	11	partial	partial	ADJ
ap-10605	43	12	case	case	NOUN
ap-10605	43	13	of	of	ADP
ap-10605	43	14	representations	representation	NOUN
ap-10605	43	15	and	and	CCONJ
ap-10605	43	16	we	we	PRON
ap-10605	43	17	will	will	AUX
ap-10605	43	18	discuss	discuss	VERB
ap-10605	43	19	connections	connection	NOUN
ap-10605	43	20	between	between	ADP
ap-10605	43	21	realizations	realization	NOUN
ap-10605	43	22	and	and	CCONJ
ap-10605	43	23	weight	weight	NOUN
ap-10605	43	24	representations	representation	NOUN
ap-10605	43	25	in	in	ADP
ap-10605	43	26	the	the	DET
ap-10605	43	27	next	next	ADJ
ap-10605	43	28	section	section	NOUN
ap-10605	43	29	.	.	PUNCT
ap-10605	44	1	to	to	PART
ap-10605	44	2	find	find	VERB
ap-10605	44	3	exhaustive	exhaustive	ADJ
ap-10605	44	4	lists	list	NOUN
ap-10605	44	5	,	,	PUNCT
ap-10605	44	6	we	we	PRON
ap-10605	44	7	need	need	VERB
ap-10605	44	8	to	to	PART
ap-10605	44	9	define	define	VERB
ap-10605	44	10	which	which	DET
ap-10605	44	11	realizations	realization	NOUN
ap-10605	44	12	of	of	ADP
ap-10605	44	13	a	a	DET
ap-10605	44	14	given	give	VERB
ap-10605	44	15	lie	lie	NOUN
ap-10605	44	16	algebra	algebra	NOUN
ap-10605	44	17	we	we	PRON
ap-10605	44	18	will	will	AUX
ap-10605	44	19	consider	consider	VERB
ap-10605	44	20	different	different	ADJ
ap-10605	44	21	,	,	PUNCT
ap-10605	44	22	or	or	CCONJ
ap-10605	44	23	,	,	PUNCT
ap-10605	44	24	conversely	conversely	ADV
ap-10605	44	25	,	,	PUNCT
ap-10605	44	26	equivalent	equivalent	ADJ
ap-10605	44	27	.	.	PUNCT
ap-10605	45	1	definition	definition	NOUN
ap-10605	45	2	2	2	NUM
ap-10605	45	3	(	(	PUNCT
ap-10605	45	4	r	r	NOUN
ap-10605	45	5	)	)	PUNCT
ap-10605	45	6	.	.	PUNCT
ap-10605	46	1	the	the	DET
ap-10605	46	2	realizations	realization	NOUN
ap-10605	46	3	r1	r1	NOUN
ap-10605	46	4	:	:	PUNCT
ap-10605	46	5	g	g	NOUN
ap-10605	46	6	→	→	SYM
ap-10605	46	7	vect(m1	vect(m1	NOUN
ap-10605	46	8	)	)	PUNCT
ap-10605	46	9	and	and	CCONJ
ap-10605	46	10	r2	r2	PROPN
ap-10605	46	11	:	:	PUNCT
ap-10605	46	12	g	g	NOUN
ap-10605	46	13	→	→	SYM
ap-10605	46	14	vect(m2	vect(m2	CCONJ
ap-10605	46	15	)	)	PUNCT
ap-10605	46	16	are	be	AUX
ap-10605	46	17	called	call	VERB
ap-10605	46	18	weakly	weakly	ADV
ap-10605	46	19	equivalent	equivalent	ADJ
ap-10605	46	20	if	if	SCONJ
ap-10605	46	21	there	there	PRON
ap-10605	46	22	exist	exist	VERB
ap-10605	46	23	φ	φ	PROPN
ap-10605	46	24	∈	∈	PROPN
ap-10605	46	25	aut(g	aut(g	PROPN
ap-10605	46	26	)	)	PUNCT
ap-10605	46	27	and	and	CCONJ
ap-10605	46	28	a	a	DET
ap-10605	46	29	diffeomorphism	diffeomorphism	NOUN
ap-10605	46	30	f	f	NOUN
ap-10605	46	31	:	:	PUNCT
ap-10605	46	32	m1	m1	PROPN
ap-10605	46	33	→	→	SYM
ap-10605	46	34	m2	m2	PROPN
ap-10605	46	35	such	such	ADJ
ap-10605	46	36	that	that	PRON
ap-10605	46	37	r2(v	r2(v	NOUN
ap-10605	46	38	)	)	PUNCT
ap-10605	46	39	=	=	SYM
ap-10605	46	40	f∗	f∗	NOUN
ap-10605	46	41	r1(φ(v	r1(φ(v	NOUN
ap-10605	46	42	)	)	PUNCT
ap-10605	46	43	)	)	PUNCT
ap-10605	46	44	for	for	ADP
ap-10605	46	45	all	all	PRON
ap-10605	46	46	v	v	ADP
ap-10605	46	47	∈	∈	NOUN
ap-10605	46	48	g.	g.	NOUN
ap-10605	46	49	here	here	ADV
ap-10605	46	50	,	,	PUNCT
ap-10605	46	51	f∗	f∗	PROPN
ap-10605	46	52	is	be	AUX
ap-10605	46	53	the	the	DET
ap-10605	46	54	pushforward	pushforward	NOUN
ap-10605	46	55	from	from	ADP
ap-10605	46	56	vect(m1	vect(m1	NOUN
ap-10605	46	57	)	)	PUNCT
ap-10605	46	58	to	to	PART
ap-10605	46	59	vect(m2	vect(m2	ADV
ap-10605	46	60	)	)	PUNCT
ap-10605	46	61	.	.	PUNCT
ap-10605	47	1	if	if	SCONJ
ap-10605	47	2	φ	φ	PROPN
ap-10605	47	3	is	be	AUX
ap-10605	47	4	the	the	DET
ap-10605	47	5	identical	identical	ADJ
ap-10605	47	6	transformation	transformation	NOUN
ap-10605	47	7	,	,	PUNCT
ap-10605	47	8	the	the	DET
ap-10605	47	9	realizations	realization	NOUN
ap-10605	47	10	are	be	AUX
ap-10605	47	11	called	call	VERB
ap-10605	47	12	strongly	strongly	ADV
ap-10605	47	13	equivalent	equivalent	ADJ
ap-10605	47	14	.	.	PUNCT
ap-10605	48	1	definition	definition	NOUN
ap-10605	48	2	3	3	NUM
ap-10605	48	3	(	(	PUNCT
ap-10605	48	4	c	c	NOUN
ap-10605	48	5	)	)	PUNCT
ap-10605	48	6	.	.	PUNCT
ap-10605	49	1	the	the	DET
ap-10605	49	2	realizations	realization	NOUN
ap-10605	49	3	r1	r1	NOUN
ap-10605	49	4	:	:	PUNCT
ap-10605	49	5	g	g	NOUN
ap-10605	49	6	→	→	SYM
ap-10605	49	7	vect(m1	vect(m1	NOUN
ap-10605	49	8	)	)	PUNCT
ap-10605	49	9	and	and	CCONJ
ap-10605	49	10	r2	r2	PROPN
ap-10605	49	11	:	:	PUNCT
ap-10605	49	12	g	g	NOUN
ap-10605	49	13	→	→	SYM
ap-10605	49	14	vect(m2	vect(m2	CCONJ
ap-10605	49	15	)	)	PUNCT
ap-10605	49	16	are	be	AUX
ap-10605	49	17	called	call	VERB
ap-10605	49	18	weakly	weakly	ADV
ap-10605	49	19	equivalent	equivalent	ADJ
ap-10605	49	20	if	if	SCONJ
ap-10605	49	21	there	there	PRON
ap-10605	49	22	exist	exist	VERB
ap-10605	49	23	φ	φ	PROPN
ap-10605	49	24	∈	∈	PROPN
ap-10605	49	25	aut(g	aut(g	PROPN
ap-10605	49	26	)	)	PUNCT
ap-10605	49	27	and	and	CCONJ
ap-10605	49	28	a	a	DET
ap-10605	49	29	biholomorphic	biholomorphic	ADJ
ap-10605	49	30	mapping	mapping	NOUN
ap-10605	49	31	f	f	NOUN
ap-10605	49	32	:	:	PUNCT
ap-10605	49	33	m1	m1	PROPN
ap-10605	49	34	→	→	SYM
ap-10605	49	35	m2	m2	PROPN
ap-10605	49	36	such	such	ADJ
ap-10605	49	37	that	that	PRON
ap-10605	49	38	r2(v	r2(v	NOUN
ap-10605	49	39	)	)	PUNCT
ap-10605	49	40	=	=	SYM
ap-10605	49	41	f∗	f∗	NOUN
ap-10605	49	42	r1(φ(v	r1(φ(v	NOUN
ap-10605	49	43	)	)	PUNCT
ap-10605	49	44	)	)	PUNCT
ap-10605	49	45	for	for	ADP
ap-10605	49	46	all	all	PRON
ap-10605	49	47	v	v	ADP
ap-10605	49	48	∈	∈	NOUN
ap-10605	49	49	g.	g.	NOUN
ap-10605	49	50	here	here	ADV
ap-10605	49	51	,	,	PUNCT
ap-10605	49	52	f∗	f∗	NOUN
ap-10605	49	53	is	be	AUX
ap-10605	49	54	the	the	DET
ap-10605	49	55	pullback	pullback	NOUN
ap-10605	49	56	from	from	ADP
ap-10605	49	57	vect(m1	vect(m1	NOUN
ap-10605	49	58	)	)	PUNCT
ap-10605	49	59	to	to	PART
ap-10605	49	60	vect(m2	vect(m2	ADV
ap-10605	49	61	)	)	PUNCT
ap-10605	49	62	.	.	PUNCT
ap-10605	50	1	if	if	SCONJ
ap-10605	50	2	φ	φ	PROPN
ap-10605	50	3	is	be	AUX
ap-10605	50	4	the	the	DET
ap-10605	50	5	identical	identical	ADJ
ap-10605	50	6	transformation	transformation	NOUN
ap-10605	50	7	,	,	PUNCT
ap-10605	50	8	the	the	DET
ap-10605	50	9	realizations	realization	NOUN
ap-10605	50	10	are	be	AUX
ap-10605	50	11	called	call	VERB
ap-10605	50	12	strongly	strongly	ADV
ap-10605	50	13	equivalent	equivalent	ADJ
ap-10605	50	14	.	.	PUNCT
ap-10605	51	1	the	the	DET
ap-10605	51	2	strong	strong	ADJ
ap-10605	51	3	equivalence	equivalence	NOUN
ap-10605	51	4	is	be	AUX
ap-10605	51	5	verified	verify	VERB
ap-10605	51	6	in	in	ADP
ap-10605	51	7	a	a	DET
ap-10605	51	8	simpler	simple	ADJ
ap-10605	51	9	way	way	NOUN
ap-10605	51	10	than	than	ADP
ap-10605	51	11	the	the	DET
ap-10605	51	12	weak	weak	ADJ
ap-10605	51	13	one	one	NOUN
ap-10605	51	14	and	and	CCONJ
ap-10605	51	15	it	it	PRON
ap-10605	51	16	can	can	AUX
ap-10605	51	17	be	be	AUX
ap-10605	51	18	used	use	VERB
ap-10605	51	19	for	for	ADP
ap-10605	51	20	construction	construction	NOUN
ap-10605	51	21	of	of	ADP
ap-10605	51	22	realizations	realization	NOUN
ap-10605	51	23	using	use	VERB
ap-10605	51	24	realizations	realization	NOUN
ap-10605	51	25	of	of	ADP
ap-10605	51	26	subalgebras	subalgebra	NOUN
ap-10605	51	27	,	,	PUNCT
ap-10605	51	28	but	but	CCONJ
ap-10605	51	29	in	in	ADP
ap-10605	51	30	general	general	ADJ
ap-10605	51	31	case	case	NOUN
ap-10605	51	32	,	,	PUNCT
ap-10605	51	33	we	we	PRON
ap-10605	51	34	should	should	AUX
ap-10605	51	35	classify	classify	VERB
ap-10605	51	36	all	all	DET
ap-10605	51	37	realizations	realization	NOUN
ap-10605	51	38	of	of	ADP
ap-10605	51	39	the	the	DET
ap-10605	51	40	given	give	VERB
ap-10605	51	41	lie	lie	NOUN
ap-10605	51	42	algebra	algebra	NOUN
ap-10605	51	43	with	with	ADP
ap-10605	51	44	respect	respect	NOUN
ap-10605	51	45	to	to	ADP
ap-10605	51	46	the	the	DET
ap-10605	51	47	weak	weak	ADJ
ap-10605	51	48	equivalence	equivalence	NOUN
ap-10605	51	49	.	.	PUNCT
ap-10605	52	1	however	however	ADV
ap-10605	52	2	,	,	PUNCT
ap-10605	52	3	the	the	DET
ap-10605	52	4	algebraic	algebraic	ADJ
ap-10605	52	5	method	method	NOUN
ap-10605	52	6	of	of	ADP
ap-10605	52	7	constructing	construct	VERB
ap-10605	52	8	realizations	realization	NOUN
ap-10605	52	9	(	(	PUNCT
ap-10605	52	10	shirokov	shirokov	NOUN
ap-10605	52	11	’s	’s	PART
ap-10605	52	12	method	method	NOUN
ap-10605	52	13	)	)	PUNCT
ap-10605	52	14	gives	give	VERB
ap-10605	52	15	grounds	ground	NOUN
ap-10605	52	16	to	to	PART
ap-10605	52	17	consider	consider	VERB
ap-10605	52	18	the	the	DET
ap-10605	52	19	hypothesis	hypothesis	NOUN
ap-10605	52	20	that	that	PRON
ap-10605	52	21	for	for	ADP
ap-10605	52	22	two	two	NUM
ap-10605	52	23	weakly	weakly	ADJ
ap-10605	52	24	equivalent	equivalent	ADJ
ap-10605	52	25	realizations	realization	NOUN
ap-10605	52	26	,	,	PUNCT
ap-10605	52	27	it	it	PRON
ap-10605	52	28	is	be	AUX
ap-10605	52	29	possible	possible	ADJ
ap-10605	52	30	to	to	PART
ap-10605	52	31	construct	construct	VERB
ap-10605	52	32	a	a	DET
ap-10605	52	33	non	non	ADJ
ap-10605	52	34	-	-	ADJ
ap-10605	52	35	degenerate	degenerate	ADJ
ap-10605	52	36	change	change	NOUN
ap-10605	52	37	of	of	ADP
ap-10605	52	38	variables	variable	NOUN
ap-10605	52	39	that	that	PRON
ap-10605	52	40	transforms	transform	VERB
ap-10605	52	41	them	they	PRON
ap-10605	52	42	from	from	ADP
ap-10605	52	43	one	one	NUM
ap-10605	52	44	to	to	ADP
ap-10605	52	45	another	another	PRON
ap-10605	52	46	,	,	PUNCT
ap-10605	52	47	at	at	ADP
ap-10605	52	48	least	least	ADJ
ap-10605	52	49	this	this	DET
ap-10605	52	50	hypothesis	hypothesis	NOUN
ap-10605	52	51	may	may	AUX
ap-10605	52	52	hold	hold	VERB
ap-10605	52	53	when	when	SCONJ
ap-10605	52	54	the	the	DET
ap-10605	52	55	full	full	ADJ
ap-10605	52	56	automorphism	automorphism	NOUN
ap-10605	52	57	group	group	NOUN
ap-10605	52	58	coincides	coincide	VERB
ap-10605	52	59	with	with	ADP
ap-10605	52	60	the	the	DET
ap-10605	52	61	group	group	NOUN
ap-10605	52	62	of	of	ADP
ap-10605	52	63	inner	inner	ADJ
ap-10605	52	64	automorphisms	automorphism	NOUN
ap-10605	52	65	.	.	PUNCT
ap-10605	53	1	3	3	X
ap-10605	53	2	.	.	X
ap-10605	53	3	construction	construction	NOUN
ap-10605	53	4	methods	method	NOUN
ap-10605	53	5	there	there	PRON
ap-10605	53	6	are	be	VERB
ap-10605	53	7	two	two	NUM
ap-10605	53	8	main	main	ADJ
ap-10605	53	9	approaches	approach	NOUN
ap-10605	53	10	to	to	ADP
ap-10605	53	11	the	the	DET
ap-10605	53	12	construction	construction	NOUN
ap-10605	53	13	and	and	CCONJ
ap-10605	53	14	classification	classification	NOUN
ap-10605	53	15	of	of	ADP
ap-10605	53	16	realizations	realization	NOUN
ap-10605	53	17	of	of	ADP
ap-10605	53	18	lie	lie	NOUN
ap-10605	53	19	algebras	algebra	NOUN
ap-10605	53	20	:	:	PUNCT
ap-10605	53	21	(	(	PUNCT
ap-10605	53	22	1	1	NUM
ap-10605	53	23	.	.	NUM
ap-10605	53	24	)	)	PUNCT
ap-10605	54	1	construction	construction	NOUN
ap-10605	54	2	of	of	ADP
ap-10605	54	3	basis	basis	NOUN
ap-10605	54	4	vector	vector	NOUN
ap-10605	54	5	fields	field	NOUN
ap-10605	54	6	that	that	PRON
ap-10605	54	7	satisfy	satisfy	VERB
ap-10605	54	8	the	the	DET
ap-10605	54	9	given	give	VERB
ap-10605	54	10	structure	structure	NOUN
ap-10605	54	11	constants	constant	NOUN
ap-10605	54	12	of	of	ADP
ap-10605	54	13	the	the	DET
ap-10605	54	14	lie	lie	NOUN
ap-10605	54	15	algebra	algebra	NOUN
ap-10605	54	16	;	;	PUNCT
ap-10605	54	17	(	(	PUNCT
ap-10605	54	18	2	2	NUM
ap-10605	54	19	.	.	NUM
ap-10605	54	20	)	)	PUNCT
ap-10605	54	21	construction	construction	NOUN
ap-10605	54	22	of	of	ADP
ap-10605	54	23	finite	finite	ADJ
ap-10605	54	24	-	-	ADJ
ap-10605	54	25	dimensional	dimensional	ADJ
ap-10605	54	26	spaces	space	NOUN
ap-10605	54	27	of	of	ADP
ap-10605	54	28	vector	vector	NOUN
ap-10605	54	29	fields	field	NOUN
ap-10605	54	30	closed	close	VERB
ap-10605	54	31	with	with	ADP
ap-10605	54	32	respect	respect	NOUN
ap-10605	54	33	to	to	ADP
ap-10605	54	34	a	a	DET
ap-10605	54	35	multiplication	multiplication	NOUN
ap-10605	54	36	(	(	PUNCT
ap-10605	54	37	commutation	commutation	NOUN
ap-10605	54	38	)	)	PUNCT
ap-10605	54	39	that	that	PRON
ap-10605	54	40	satisfies	satisfy	VERB
ap-10605	54	41	the	the	DET
ap-10605	54	42	definition	definition	NOUN
ap-10605	54	43	of	of	ADP
ap-10605	54	44	a	a	DET
ap-10605	54	45	lie	lie	NOUN
ap-10605	54	46	bracket	bracket	NOUN
ap-10605	54	47	.	.	PUNCT
ap-10605	55	1	regarding	regard	VERB
ap-10605	55	2	the	the	DET
ap-10605	55	3	second	second	ADJ
ap-10605	55	4	approach	approach	NOUN
ap-10605	55	5	,	,	PUNCT
ap-10605	55	6	the	the	DET
ap-10605	55	7	classification	classification	NOUN
ap-10605	55	8	of	of	ADP
ap-10605	55	9	realizations	realization	NOUN
ap-10605	55	10	was	be	AUX
ap-10605	55	11	started	start	VERB
ap-10605	55	12	by	by	ADP
ap-10605	55	13	sophus	sophu	NOUN
ap-10605	55	14	lie	lie	VERB
ap-10605	55	15	himself	himself	PRON
ap-10605	55	16	and	and	CCONJ
ap-10605	55	17	was	be	AUX
ap-10605	55	18	done	do	VERB
ap-10605	55	19	for	for	ADP
ap-10605	55	20	the	the	DET
ap-10605	55	21	case	case	NOUN
ap-10605	55	22	of	of	ADP
ap-10605	55	23	one	one	NUM
ap-10605	55	24	variable	variable	NOUN
ap-10605	55	25	over	over	ADP
ap-10605	55	26	real	real	ADJ
ap-10605	55	27	and	and	CCONJ
ap-10605	55	28	complex	complex	ADJ
ap-10605	55	29	fields	field	NOUN
ap-10605	55	30	and	and	CCONJ
ap-10605	55	31	for	for	ADP
ap-10605	55	32	two	two	NUM
ap-10605	55	33	variables	variable	NOUN
ap-10605	55	34	in	in	ADP
ap-10605	55	35	the	the	DET
ap-10605	55	36	complex	complex	ADJ
ap-10605	55	37	case	case	NOUN
ap-10605	55	38	.	.	PUNCT
ap-10605	56	1	within	within	ADP
ap-10605	56	2	the	the	DET
ap-10605	56	3	framework	framework	NOUN
ap-10605	56	4	of	of	ADP
ap-10605	56	5	the	the	DET
ap-10605	56	6	second	second	ADJ
ap-10605	56	7	approach	approach	NOUN
ap-10605	56	8	,	,	PUNCT
ap-10605	56	9	there	there	PRON
ap-10605	56	10	are	be	VERB
ap-10605	56	11	several	several	ADJ
ap-10605	56	12	interesting	interesting	ADJ
ap-10605	56	13	methods	method	NOUN
ap-10605	56	14	for	for	ADP
ap-10605	56	15	constructing	construct	VERB
ap-10605	56	16	realizations	realization	NOUN
ap-10605	56	17	,	,	PUNCT
ap-10605	56	18	in	in	ADP
ap-10605	56	19	particular	particular	ADJ
ap-10605	56	20	for	for	ADP
ap-10605	56	21	nilpotent	nilpotent	ADJ
ap-10605	56	22	lie	lie	NOUN
ap-10605	56	23	algebras	algebra	NOUN
ap-10605	56	24	.	.	PUNCT
ap-10605	57	1	certain	certain	ADJ
ap-10605	57	2	results	result	NOUN
ap-10605	57	3	have	have	AUX
ap-10605	57	4	also	also	ADV
ap-10605	57	5	been	be	AUX
ap-10605	57	6	obtained	obtain	VERB
ap-10605	57	7	for	for	ADP
ap-10605	57	8	spaces	space	NOUN
ap-10605	57	9	of	of	ADP
ap-10605	57	10	a	a	DET
ap-10605	57	11	small	small	ADJ
ap-10605	57	12	number	number	NOUN
ap-10605	57	13	of	of	ADP
ap-10605	57	14	variables	variable	NOUN
ap-10605	57	15	,	,	PUNCT
ap-10605	57	16	but	but	CCONJ
ap-10605	57	17	this	this	DET
ap-10605	57	18	approach	approach	NOUN
ap-10605	57	19	is	be	AUX
ap-10605	57	20	not	not	PART
ap-10605	57	21	relevant	relevant	ADJ
ap-10605	57	22	to	to	ADP
ap-10605	57	23	the	the	DET
ap-10605	57	24	problem	problem	NOUN
ap-10605	57	25	we	we	PRON
ap-10605	57	26	are	be	AUX
ap-10605	57	27	considering	consider	VERB
ap-10605	57	28	in	in	ADP
ap-10605	57	29	this	this	DET
ap-10605	57	30	paper	paper	NOUN
ap-10605	57	31	,	,	PUNCT
ap-10605	57	32	so	so	SCONJ
ap-10605	57	33	we	we	PRON
ap-10605	57	34	will	will	AUX
ap-10605	57	35	not	not	PART
ap-10605	57	36	provide	provide	VERB
ap-10605	57	37	a	a	DET
ap-10605	57	38	detailed	detailed	ADJ
ap-10605	57	39	overview	overview	NOUN
ap-10605	57	40	of	of	ADP
ap-10605	57	41	the	the	DET
ap-10605	57	42	methods	method	NOUN
ap-10605	57	43	and	and	CCONJ
ap-10605	57	44	results	result	NOUN
ap-10605	57	45	.	.	PUNCT
ap-10605	58	1	3.1	3.1	NUM
ap-10605	58	2	.	.	PUNCT
ap-10605	59	1	the	the	DET
ap-10605	59	2	direct	direct	ADJ
ap-10605	59	3	method	method	NOUN
ap-10605	59	4	as	as	ADP
ap-10605	59	5	for	for	ADP
ap-10605	59	6	the	the	DET
ap-10605	59	7	first	first	ADJ
ap-10605	59	8	approach	approach	NOUN
ap-10605	59	9	to	to	ADP
ap-10605	59	10	constructing	construct	VERB
ap-10605	59	11	realizations	realization	NOUN
ap-10605	59	12	of	of	ADP
ap-10605	59	13	lie	lie	NOUN
ap-10605	59	14	algebras	algebra	NOUN
ap-10605	59	15	,	,	PUNCT
ap-10605	59	16	the	the	DET
ap-10605	59	17	most	most	ADV
ap-10605	59	18	obvious	obvious	ADJ
ap-10605	59	19	is	be	AUX
ap-10605	59	20	the	the	DET
ap-10605	59	21	direct	direct	ADJ
ap-10605	59	22	method	method	NOUN
ap-10605	59	23	(	(	PUNCT
ap-10605	59	24	which	which	PRON
ap-10605	59	25	is	be	AUX
ap-10605	59	26	technically	technically	ADV
ap-10605	59	27	quite	quite	ADV
ap-10605	59	28	complex	complex	ADJ
ap-10605	59	29	)	)	PUNCT
ap-10605	59	30	.	.	PUNCT
ap-10605	60	1	first	first	ADV
ap-10605	60	2	,	,	PUNCT
ap-10605	60	3	it	it	PRON
ap-10605	60	4	was	be	AUX
ap-10605	60	5	formulated	formulate	VERB
ap-10605	60	6	in	in	ADP
ap-10605	60	7	[	[	X
ap-10605	60	8	4	4	NUM
ap-10605	60	9	]	]	PUNCT
ap-10605	60	10	,	,	PUNCT
ap-10605	60	11	here	here	ADV
ap-10605	60	12	we	we	PRON
ap-10605	60	13	present	present	VERB
ap-10605	60	14	it	it	PRON
ap-10605	60	15	in	in	ADP
ap-10605	60	16	detail	detail	NOUN
ap-10605	60	17	since	since	SCONJ
ap-10605	60	18	this	this	PRON
ap-10605	60	19	is	be	AUX
ap-10605	60	20	the	the	DET
ap-10605	60	21	only	only	ADJ
ap-10605	60	22	general	general	ADJ
ap-10605	60	23	method	method	NOUN
ap-10605	60	24	known	know	VERB
ap-10605	60	25	to	to	ADP
ap-10605	60	26	us	we	PRON
ap-10605	60	27	today	today	NOUN
ap-10605	60	28	.	.	PUNCT
ap-10605	61	1	the	the	DET
ap-10605	61	2	direct	direct	ADJ
ap-10605	61	3	method	method	NOUN
ap-10605	61	4	consists	consist	VERB
ap-10605	61	5	of	of	ADP
ap-10605	61	6	three	three	NUM
ap-10605	61	7	main	main	ADJ
ap-10605	61	8	steps	step	NOUN
ap-10605	61	9	:	:	PUNCT
ap-10605	61	10	(	(	PUNCT
ap-10605	61	11	1	1	NUM
ap-10605	61	12	.	.	PUNCT
ap-10605	61	13	)	)	PUNCT
ap-10605	61	14	take	take	VERB
ap-10605	61	15	n	n	PRON
ap-10605	61	16	linearly	linearly	ADV
ap-10605	61	17	independent	independent	ADJ
ap-10605	61	18	vector	vector	NOUN
ap-10605	61	19	fields	field	NOUN
ap-10605	61	20	of	of	ADP
ap-10605	61	21	the	the	DET
ap-10605	61	22	general	general	ADJ
ap-10605	61	23	form	form	NOUN
ap-10605	61	24	ei	ei	X
ap-10605	61	25	=	=	PUNCT
ap-10605	61	26	ξiα(x)∂α	ξiα(x)∂α	ADV
ap-10605	61	27	,	,	PUNCT
ap-10605	61	28	and	and	CCONJ
ap-10605	61	29	require	require	VERB
ap-10605	61	30	them	they	PRON
ap-10605	61	31	to	to	PART
ap-10605	61	32	satisfy	satisfy	VERB
ap-10605	61	33	the	the	DET
ap-10605	61	34	given	give	VERB
ap-10605	61	35	commutation	commutation	NOUN
ap-10605	61	36	relations	relation	NOUN
ap-10605	61	37	of	of	ADP
ap-10605	61	38	g.	g.	PROPN
ap-10605	61	39	(	(	PUNCT
ap-10605	61	40	2	2	NUM
ap-10605	61	41	.	.	PUNCT
ap-10605	61	42	)	)	PUNCT
ap-10605	61	43	by	by	ADP
ap-10605	61	44	comparing	compare	VERB
ap-10605	61	45	coefficients	coefficient	NOUN
ap-10605	61	46	near	near	ADP
ap-10605	61	47	different	different	ADJ
ap-10605	61	48	partial	partial	ADJ
ap-10605	61	49	differentiation	differentiation	NOUN
ap-10605	61	50	operators	operator	NOUN
ap-10605	61	51	,	,	PUNCT
ap-10605	61	52	we	we	PRON
ap-10605	61	53	obtain	obtain	VERB
ap-10605	61	54	a	a	DET
ap-10605	61	55	system	system	NOUN
ap-10605	61	56	of	of	ADP
ap-10605	61	57	firstorder	firstorder	NOUN
ap-10605	61	58	pdes	pde	NOUN
ap-10605	61	59	for	for	ADP
ap-10605	61	60	the	the	DET
ap-10605	61	61	coefficients	coefficient	NOUN
ap-10605	61	62	ξia	ξia	PROPN
ap-10605	61	63	.	.	PUNCT
ap-10605	62	1	integrate	integrate	VERB
ap-10605	62	2	this	this	DET
ap-10605	62	3	system	system	NOUN
ap-10605	62	4	considering	consider	VERB
ap-10605	62	5	all	all	DET
ap-10605	62	6	the	the	DET
ap-10605	62	7	possible	possible	ADJ
ap-10605	62	8	cases	case	NOUN
ap-10605	62	9	.	.	PUNCT
ap-10605	63	1	(	(	PUNCT
ap-10605	63	2	3	3	NUM
ap-10605	63	3	.	.	PUNCT
ap-10605	63	4	)	)	PUNCT
ap-10605	63	5	transform	transform	VERB
ap-10605	63	6	the	the	DET
ap-10605	63	7	solution	solution	NOUN
ap-10605	63	8	into	into	ADP
ap-10605	63	9	the	the	DET
ap-10605	63	10	simplest	simple	ADJ
ap-10605	63	11	form	form	NOUN
ap-10605	63	12	,	,	PUNCT
ap-10605	63	13	using	use	VERB
ap-10605	63	14	nondegenerate	nondegenerate	ADJ
ap-10605	63	15	transformations	transformation	NOUN
ap-10605	63	16	of	of	ADP
ap-10605	63	17	the	the	DET
ap-10605	63	18	coordinates	coordinate	NOUN
ap-10605	63	19	on	on	ADP
ap-10605	63	20	m	m	NOUN
ap-10605	63	21	and	and	CCONJ
ap-10605	63	22	automorphism	automorphism	NOUN
ap-10605	63	23	transformations	transformation	NOUN
ap-10605	63	24	of	of	ADP
ap-10605	63	25	g.	g.	NOUN
ap-10605	63	26	the	the	DET
ap-10605	63	27	direct	direct	ADJ
ap-10605	63	28	method	method	NOUN
ap-10605	63	29	is	be	AUX
ap-10605	63	30	quite	quite	ADV
ap-10605	63	31	difficult	difficult	ADJ
ap-10605	63	32	to	to	PART
ap-10605	63	33	apply	apply	VERB
ap-10605	63	34	,	,	PUNCT
ap-10605	63	35	primarily	primarily	ADV
ap-10605	63	36	due	due	ADP
ap-10605	63	37	to	to	ADP
ap-10605	63	38	the	the	DET
ap-10605	63	39	need	need	NOUN
ap-10605	63	40	to	to	PART
ap-10605	63	41	solve	solve	VERB
ap-10605	63	42	a	a	DET
ap-10605	63	43	system	system	NOUN
ap-10605	63	44	of	of	ADP
ap-10605	63	45	partial	partial	ADJ
ap-10605	63	46	differential	differential	ADJ
ap-10605	63	47	equations	equation	NOUN
ap-10605	63	48	and	and	CCONJ
ap-10605	63	49	the	the	DET
ap-10605	63	50	requirement	requirement	NOUN
ap-10605	63	51	to	to	PART
ap-10605	63	52	check	check	VERB
ap-10605	63	53	a	a	DET
ap-10605	63	54	large	large	ADJ
ap-10605	63	55	number	number	NOUN
ap-10605	63	56	of	of	ADP
ap-10605	63	57	branching	branch	VERB
ap-10605	63	58	cases	case	NOUN
ap-10605	63	59	.	.	PUNCT
ap-10605	64	1	but	but	CCONJ
ap-10605	64	2	we	we	PRON
ap-10605	64	3	can	can	AUX
ap-10605	64	4	propose	propose	VERB
ap-10605	64	5	several	several	ADJ
ap-10605	64	6	approaches	approach	NOUN
ap-10605	64	7	that	that	PRON
ap-10605	64	8	make	make	VERB
ap-10605	64	9	the	the	DET
ap-10605	64	10	procedure	procedure	NOUN
ap-10605	64	11	less	less	ADV
ap-10605	64	12	cumbersome	cumbersome	ADJ
ap-10605	64	13	.	.	PUNCT
ap-10605	65	1	first	first	ADV
ap-10605	65	2	,	,	PUNCT
ap-10605	65	3	we	we	PRON
ap-10605	65	4	formulate	formulate	VERB
ap-10605	65	5	the	the	DET
ap-10605	65	6	ideas	idea	NOUN
ap-10605	65	7	,	,	PUNCT
ap-10605	65	8	then	then	ADV
ap-10605	65	9	we	we	PRON
ap-10605	65	10	introduce	introduce	VERB
ap-10605	65	11	all	all	DET
ap-10605	65	12	the	the	DET
ap-10605	65	13	definitions	definition	NOUN
ap-10605	65	14	and	and	CCONJ
ap-10605	65	15	formulate	formulate	VERB
ap-10605	65	16	the	the	DET
ap-10605	65	17	necessary	necessary	ADJ
ap-10605	65	18	statements	statement	NOUN
ap-10605	65	19	:	:	PUNCT
ap-10605	65	20	•	•	ADP
ap-10605	65	21	to	to	PART
ap-10605	65	22	transform	transform	VERB
ap-10605	65	23	one	one	NUM
ap-10605	65	24	of	of	ADP
ap-10605	65	25	basis	basis	NOUN
ap-10605	65	26	elements	element	NOUN
ap-10605	65	27	to	to	ADP
ap-10605	65	28	the	the	DET
ap-10605	65	29	shift	shift	NOUN
ap-10605	65	30	operator	operator	NOUN
ap-10605	65	31	,	,	PUNCT
ap-10605	65	32	for	for	ADP
ap-10605	65	33	example	example	NOUN
ap-10605	65	34	,	,	PUNCT
ap-10605	65	35	e1	e1	NOUN
ap-10605	65	36	=	=	SYM
ap-10605	65	37	∂	∂	NUM
ap-10605	65	38	∂x1	∂x1	NOUN
ap-10605	65	39	.	.	PUNCT
ap-10605	66	1	note	note	VERB
ap-10605	66	2	that	that	SCONJ
ap-10605	66	3	the	the	DET
ap-10605	66	4	choice	choice	NOUN
ap-10605	66	5	of	of	ADP
ap-10605	66	6	the	the	DET
ap-10605	66	7	basis	basis	NOUN
ap-10605	66	8	element	element	NOUN
ap-10605	66	9	that	that	PRON
ap-10605	66	10	we	we	PRON
ap-10605	66	11	transform	transform	VERB
ap-10605	66	12	to	to	ADP
ap-10605	66	13	the	the	DET
ap-10605	66	14	shift	shift	NOUN
ap-10605	66	15	operator	operator	NOUN
ap-10605	66	16	significantly	significantly	ADV
ap-10605	66	17	affects	affect	VERB
ap-10605	66	18	the	the	DET
ap-10605	66	19	subsequent	subsequent	ADJ
ap-10605	66	20	complexity	complexity	NOUN
ap-10605	66	21	of	of	ADP
ap-10605	66	22	the	the	DET
ap-10605	66	23	calculations	calculation	NOUN
ap-10605	66	24	and	and	CCONJ
ap-10605	66	25	the	the	DET
ap-10605	66	26	form	form	NOUN
ap-10605	66	27	of	of	ADP
ap-10605	66	28	the	the	DET
ap-10605	66	29	operators	operator	NOUN
ap-10605	66	30	that	that	PRON
ap-10605	66	31	we	we	PRON
ap-10605	66	32	obtain	obtain	VERB
ap-10605	66	33	as	as	ADP
ap-10605	66	34	a	a	DET
ap-10605	66	35	result	result	NOUN
ap-10605	66	36	.	.	PUNCT
ap-10605	67	1	•	•	INTJ
ap-10605	67	2	to	to	PART
ap-10605	67	3	classify	classify	VERB
ap-10605	67	4	sequential	sequential	ADJ
ap-10605	67	5	realizations	realization	NOUN
ap-10605	67	6	of	of	ADP
ap-10605	67	7	a	a	DET
ap-10605	67	8	series	series	NOUN
ap-10605	67	9	of	of	ADP
ap-10605	67	10	nested	nest	VERB
ap-10605	67	11	subalgebras	subalgebra	NOUN
ap-10605	67	12	of	of	ADP
ap-10605	67	13	g	g	PROPN
ap-10605	67	14	,	,	PUNCT
ap-10605	67	15	starting	start	VERB
ap-10605	67	16	with	with	ADP
ap-10605	67	17	a	a	DET
ap-10605	67	18	onedimensional	onedimensional	ADJ
ap-10605	67	19	subalgebra	subalgebra	NOUN
ap-10605	67	20	and	and	CCONJ
ap-10605	67	21	ending	end	VERB
ap-10605	67	22	with	with	ADP
ap-10605	67	23	g.	g.	PROPN
ap-10605	67	24	inequiva555	inequiva555	PROPN
ap-10605	67	25	m.	m.	PROPN
ap-10605	67	26	nesterenko	nesterenko	PROPN
ap-10605	67	27	,	,	PUNCT
ap-10605	67	28	s.	s.	PROPN
ap-10605	67	29	pošta	pošta	PROPN
ap-10605	67	30	,	,	PUNCT
ap-10605	67	31	m.	m.	NOUN
ap-10605	67	32	staryi	staryi	PROPN
ap-10605	67	33	acta	acta	PROPN
ap-10605	67	34	polytechnica	polytechnica	PROPN
ap-10605	67	35	lence	lence	NOUN
ap-10605	67	36	of	of	ADP
ap-10605	67	37	the	the	DET
ap-10605	67	38	obtained	obtain	VERB
ap-10605	67	39	realizations	realization	NOUN
ap-10605	67	40	can	can	AUX
ap-10605	67	41	be	be	AUX
ap-10605	67	42	guaranteed	guarantee	VERB
ap-10605	67	43	if	if	SCONJ
ap-10605	67	44	we	we	PRON
ap-10605	67	45	consider	consider	VERB
ap-10605	67	46	a	a	DET
ap-10605	67	47	chain	chain	NOUN
ap-10605	67	48	of	of	ADP
ap-10605	67	49	megaideals	megaideal	NOUN
ap-10605	67	50	.	.	PUNCT
ap-10605	68	1	•	•	NUM
ap-10605	68	2	to	to	PART
ap-10605	68	3	split	split	VERB
ap-10605	68	4	all	all	DET
ap-10605	68	5	possible	possible	ADJ
ap-10605	68	6	cases	case	NOUN
ap-10605	68	7	into	into	ADP
ap-10605	68	8	the	the	DET
ap-10605	68	9	groups	group	NOUN
ap-10605	68	10	with	with	ADP
ap-10605	68	11	the	the	DET
ap-10605	68	12	different	different	ADJ
ap-10605	68	13	realization	realization	NOUN
ap-10605	68	14	ranks	rank	NOUN
ap-10605	68	15	.	.	PUNCT
ap-10605	69	1	let	let	VERB
ap-10605	69	2	us	we	PRON
ap-10605	69	3	fix	fix	VERB
ap-10605	69	4	x	x	PUNCT
ap-10605	69	5	∈	∈	NOUN
ap-10605	69	6	m	m	NOUN
ap-10605	69	7	and	and	CCONJ
ap-10605	69	8	let	let	VERB
ap-10605	69	9	rx	rx	AUX
ap-10605	69	10	be	be	AUX
ap-10605	69	11	a	a	DET
ap-10605	69	12	realization	realization	NOUN
ap-10605	69	13	of	of	ADP
ap-10605	69	14	g	g	NOUN
ap-10605	69	15	in	in	ADP
ap-10605	69	16	this	this	DET
ap-10605	69	17	point	point	NOUN
ap-10605	69	18	.	.	PUNCT
ap-10605	70	1	consider	consider	VERB
ap-10605	70	2	the	the	DET
ap-10605	70	3	linear	linear	ADJ
ap-10605	70	4	map	map	NOUN
ap-10605	70	5	rx	rx	VERB
ap-10605	70	6	:	:	PUNCT
ap-10605	70	7	g	g	PROPN
ap-10605	70	8	→	→	SYM
ap-10605	70	9	vect(m)(x	vect(m)(x	NOUN
ap-10605	70	10	)	)	PUNCT
ap-10605	70	11	.	.	PUNCT
ap-10605	71	1	the	the	DET
ap-10605	71	2	matrix	matrix	NOUN
ap-10605	71	3	that	that	PRON
ap-10605	71	4	corresponds	correspond	VERB
ap-10605	71	5	to	to	ADP
ap-10605	71	6	this	this	DET
ap-10605	71	7	linear	linear	ADJ
ap-10605	71	8	map	map	NOUN
ap-10605	71	9	is	be	AUX
ap-10605	71	10	the	the	DET
ap-10605	71	11	n	n	NOUN
ap-10605	71	12	by	by	ADP
ap-10605	71	13	m	m	PROPN
ap-10605	71	14	matrix	matrix	NOUN
ap-10605	71	15	ξ	ξ	NOUN
ap-10605	71	16	formed	form	VERB
ap-10605	71	17	by	by	ADP
ap-10605	71	18	the	the	DET
ap-10605	71	19	coefficients	coefficient	NOUN
ap-10605	71	20	of	of	ADP
ap-10605	71	21	the	the	DET
ap-10605	71	22	realization	realization	NOUN
ap-10605	71	23	:	:	PUNCT
ap-10605	71	24	ξ(x	ξ(x	NOUN
ap-10605	71	25	)	)	PUNCT
ap-10605	71	26	=	=	SYM
ap-10605	71	27			ADJ
ap-10605	71	28	ξ11(x	ξ11(x	NOUN
ap-10605	71	29	)	)	PUNCT
ap-10605	71	30	ξ12(x	ξ12(x	NUM
ap-10605	71	31	)	)	PUNCT
ap-10605	71	32	.	.	PUNCT
ap-10605	71	33	.	.	PUNCT
ap-10605	71	34	.	.	PUNCT
ap-10605	72	1	ξ1m(x	ξ1m(x	NUM
ap-10605	72	2	)	)	PUNCT
ap-10605	72	3	ξ21(x	ξ21(x	NOUN
ap-10605	72	4	)	)	PUNCT
ap-10605	72	5	ξ22(x	ξ22(x	NUM
ap-10605	72	6	)	)	PUNCT
ap-10605	72	7	.	.	PUNCT
ap-10605	72	8	.	.	PUNCT
ap-10605	72	9	.	.	PUNCT
ap-10605	73	1	ξ2m(x	ξ2m(x	NUM
ap-10605	73	2	)	)	PUNCT
ap-10605	73	3	...	...	PUNCT
ap-10605	73	4	...	...	PUNCT
ap-10605	73	5	.	.	PUNCT
ap-10605	73	6	.	.	PUNCT
ap-10605	73	7	.	.	PUNCT
ap-10605	74	1	...	...	PUNCT
ap-10605	75	1	ξn1(x	ξn1(x	NOUN
ap-10605	75	2	)	)	PUNCT
ap-10605	75	3	ξn2(x	ξn2(x	PROPN
ap-10605	75	4	)	)	PUNCT
ap-10605	75	5	.	.	PUNCT
ap-10605	75	6	.	.	PUNCT
ap-10605	75	7	.	.	PUNCT
ap-10605	76	1	ξnm(x	ξnm(x	X
ap-10605	76	2	)	)	PUNCT
ap-10605	76	3	.	.	PROPN
ap-10605	76	4	definition	definition	NOUN
ap-10605	76	5	4	4	NUM
ap-10605	76	6	.	.	PUNCT
ap-10605	77	1	the	the	DET
ap-10605	77	2	general	general	ADJ
ap-10605	77	3	(	(	PUNCT
ap-10605	77	4	maximal	maximal	ADJ
ap-10605	77	5	possible	possible	ADJ
ap-10605	77	6	)	)	PUNCT
ap-10605	77	7	rank	rank	NOUN
ap-10605	77	8	of	of	ADP
ap-10605	77	9	the	the	DET
ap-10605	77	10	linear	linear	ADJ
ap-10605	77	11	map	map	NOUN
ap-10605	77	12	rx	rx	VERB
ap-10605	77	13	is	be	AUX
ap-10605	77	14	called	call	VERB
ap-10605	77	15	a	a	DET
ap-10605	77	16	rank	rank	NOUN
ap-10605	77	17	of	of	ADP
ap-10605	77	18	realization	realization	NOUN
ap-10605	77	19	r	r	NOUN
ap-10605	77	20	and	and	CCONJ
ap-10605	77	21	is	be	AUX
ap-10605	77	22	denoted	denote	VERB
ap-10605	77	23	as	as	ADP
ap-10605	77	24	rank	rank	PROPN
ap-10605	77	25	r.	r.	PROPN
ap-10605	77	26	the	the	DET
ap-10605	77	27	realization	realization	NOUN
ap-10605	77	28	rank	rank	NOUN
ap-10605	77	29	value	value	NOUN
ap-10605	77	30	possesses	possess	VERB
ap-10605	77	31	the	the	DET
ap-10605	77	32	obvious	obvious	ADJ
ap-10605	77	33	inequality	inequality	NOUN
ap-10605	77	34	0	0	NUM
ap-10605	77	35	≤	≤	NUM
ap-10605	77	36	rank	rank	NOUN
ap-10605	77	37	rx	rx	VERB
ap-10605	77	38	≤	≤	NUM
ap-10605	77	39	n	n	CCONJ
ap-10605	77	40	,	,	PUNCT
ap-10605	77	41	where	where	SCONJ
ap-10605	77	42	n	n	X
ap-10605	77	43	is	be	AUX
ap-10605	77	44	the	the	DET
ap-10605	77	45	dimension	dimension	NOUN
ap-10605	77	46	of	of	ADP
ap-10605	77	47	the	the	DET
ap-10605	77	48	lie	lie	NOUN
ap-10605	77	49	algebra	algebra	NOUN
ap-10605	77	50	g.	g.	NOUN
ap-10605	78	1	the	the	DET
ap-10605	78	2	second	second	ADJ
ap-10605	78	3	inequality	inequality	NOUN
ap-10605	78	4	is	be	AUX
ap-10605	78	5	dictated	dictate	VERB
ap-10605	78	6	by	by	ADP
ap-10605	78	7	the	the	DET
ap-10605	78	8	number	number	NOUN
ap-10605	78	9	of	of	ADP
ap-10605	78	10	rows	row	NOUN
ap-10605	78	11	in	in	ADP
ap-10605	78	12	matrix	matrix	NOUN
ap-10605	78	13	ξ	ξ	PROPN
ap-10605	78	14	,	,	PUNCT
ap-10605	78	15	which	which	PRON
ap-10605	78	16	is	be	AUX
ap-10605	78	17	equal	equal	ADJ
ap-10605	78	18	to	to	ADP
ap-10605	78	19	the	the	DET
ap-10605	78	20	number	number	NOUN
ap-10605	78	21	of	of	ADP
ap-10605	78	22	basis	basis	NOUN
ap-10605	78	23	vector	vector	NOUN
ap-10605	78	24	fields	field	NOUN
ap-10605	78	25	of	of	ADP
ap-10605	78	26	g.	g.	PROPN
ap-10605	78	27	if	if	SCONJ
ap-10605	78	28	there	there	PRON
ap-10605	78	29	exists	exist	VERB
ap-10605	78	30	a	a	DET
ap-10605	78	31	subset	subset	ADJ
ap-10605	78	32	g0	g0	NOUN
ap-10605	78	33	⊂	⊂	PROPN
ap-10605	78	34	g	g	PROPN
ap-10605	78	35	such	such	ADJ
ap-10605	78	36	that	that	DET
ap-10605	78	37	rank	rank	PROPN
ap-10605	78	38	r1(g0	r1(g0	NOUN
ap-10605	78	39	)	)	PUNCT
ap-10605	78	40	̸=	̸=	PROPN
ap-10605	78	41	rank	rank	NOUN
ap-10605	78	42	r2(g0	r2(g0	PROPN
ap-10605	78	43	)	)	PUNCT
ap-10605	78	44	,	,	PUNCT
ap-10605	78	45	then	then	ADV
ap-10605	78	46	the	the	DET
ap-10605	78	47	realizations	realization	NOUN
ap-10605	78	48	r1	r1	NOUN
ap-10605	78	49	and	and	CCONJ
ap-10605	78	50	r2	r2	PROPN
ap-10605	78	51	are	be	AUX
ap-10605	78	52	strongly	strongly	ADV
ap-10605	78	53	inequivalent	inequivalent	ADJ
ap-10605	78	54	.	.	PUNCT
ap-10605	79	1	definition	definition	NOUN
ap-10605	79	2	5	5	NUM
ap-10605	79	3	.	.	PUNCT
ap-10605	80	1	a	a	DET
ap-10605	80	2	megaideal	megaideal	NOUN
ap-10605	80	3	m	m	NOUN
ap-10605	80	4	of	of	ADP
ap-10605	80	5	g	g	PROPN
ap-10605	80	6	is	be	AUX
ap-10605	80	7	such	such	DET
ap-10605	80	8	a	a	DET
ap-10605	80	9	vector	vector	NOUN
ap-10605	80	10	subspace	subspace	NOUN
ap-10605	80	11	m	m	PROPN
ap-10605	80	12	⊂	⊂	PROPN
ap-10605	80	13	g	g	PROPN
ap-10605	80	14	,	,	PUNCT
ap-10605	80	15	that	that	SCONJ
ap-10605	80	16	it	it	PRON
ap-10605	80	17	is	be	AUX
ap-10605	80	18	invariant	invariant	ADJ
ap-10605	80	19	under	under	ADP
ap-10605	80	20	any	any	DET
ap-10605	80	21	transformation	transformation	NOUN
ap-10605	80	22	from	from	ADP
ap-10605	80	23	aut(a	aut(a	PROPN
ap-10605	80	24	)	)	PUNCT
ap-10605	80	25	.	.	PUNCT
ap-10605	81	1	it	it	PRON
ap-10605	81	2	is	be	AUX
ap-10605	81	3	clear	clear	ADJ
ap-10605	81	4	that	that	SCONJ
ap-10605	81	5	any	any	DET
ap-10605	81	6	megaideal	megaideal	NOUN
ap-10605	81	7	is	be	AUX
ap-10605	81	8	a	a	DET
ap-10605	81	9	subalgebra	subalgebra	NOUN
ap-10605	81	10	and	and	CCONJ
ap-10605	81	11	,	,	PUNCT
ap-10605	81	12	moreover	moreover	ADV
ap-10605	81	13	,	,	PUNCT
ap-10605	81	14	an	an	DET
ap-10605	81	15	ideal	ideal	NOUN
ap-10605	81	16	in	in	ADP
ap-10605	81	17	g.	g.	PROPN
ap-10605	81	18	but	but	CCONJ
ap-10605	81	19	there	there	PRON
ap-10605	81	20	exist	exist	VERB
ap-10605	81	21	ideals	ideal	NOUN
ap-10605	81	22	which	which	PRON
ap-10605	81	23	are	be	AUX
ap-10605	81	24	not	not	PART
ap-10605	81	25	megaideals	megaideal	NOUN
ap-10605	81	26	.	.	PUNCT
ap-10605	82	1	moreover	moreover	ADV
ap-10605	82	2	,	,	PUNCT
ap-10605	82	3	any	any	DET
ap-10605	82	4	megaideal	megaideal	NOUN
ap-10605	82	5	is	be	AUX
ap-10605	82	6	invariant	invariant	ADJ
ap-10605	82	7	with	with	ADP
ap-10605	82	8	respect	respect	NOUN
ap-10605	82	9	to	to	ADP
ap-10605	82	10	all	all	DET
ap-10605	82	11	the	the	DET
ap-10605	82	12	derivations	derivation	NOUN
ap-10605	82	13	,	,	PUNCT
ap-10605	82	14	i.e.	i.e.	X
ap-10605	82	15	it	it	PRON
ap-10605	82	16	is	be	AUX
ap-10605	82	17	a	a	DET
ap-10605	82	18	characteristic	characteristic	ADJ
ap-10605	82	19	subalgebra	subalgebra	NOUN
ap-10605	82	20	.	.	PUNCT
ap-10605	83	1	let	let	VERB
ap-10605	83	2	m	m	PRON
ap-10605	83	3	be	be	AUX
ap-10605	83	4	a	a	DET
ap-10605	83	5	megaideal	megaideal	NOUN
ap-10605	83	6	and	and	CCONJ
ap-10605	83	7	r1	r1	PROPN
ap-10605	83	8	and	and	CCONJ
ap-10605	83	9	r2	r2	PROPN
ap-10605	83	10	be	be	VERB
ap-10605	83	11	realizations	realization	NOUN
ap-10605	83	12	of	of	ADP
ap-10605	83	13	the	the	DET
ap-10605	83	14	algebra	algebra	NOUN
ap-10605	83	15	g.	g.	NOUN
ap-10605	84	1	if	if	SCONJ
ap-10605	84	2	r1	r1	PROPN
ap-10605	84	3	∣∣	∣∣	PUNCT
ap-10605	84	4	m	m	NOUN
ap-10605	84	5	and	and	CCONJ
ap-10605	84	6	r2	r2	PROPN
ap-10605	84	7	∣∣	∣∣	NUM
ap-10605	84	8	m	m	VERB
ap-10605	84	9	are	be	AUX
ap-10605	84	10	inequivalent	inequivalent	ADJ
ap-10605	84	11	,	,	PUNCT
ap-10605	84	12	then	then	ADV
ap-10605	84	13	r1	r1	PROPN
ap-10605	84	14	and	and	CCONJ
ap-10605	84	15	r2	r2	PROPN
ap-10605	84	16	are	be	AUX
ap-10605	84	17	inequivalent	inequivalent	ADJ
ap-10605	84	18	too	too	ADV
ap-10605	84	19	.	.	PUNCT
ap-10605	85	1	moreover	moreover	ADV
ap-10605	85	2	,	,	PUNCT
ap-10605	85	3	if	if	SCONJ
ap-10605	85	4	there	there	PRON
ap-10605	85	5	exists	exist	VERB
ap-10605	85	6	a	a	DET
ap-10605	85	7	megaideal	megaideal	NOUN
ap-10605	85	8	m	m	NOUN
ap-10605	85	9	of	of	ADP
ap-10605	85	10	g	g	PROPN
ap-10605	85	11	such	such	DET
ap-10605	85	12	that	that	DET
ap-10605	85	13	rank	rank	NOUN
ap-10605	85	14	r1(m	r1(m	NOUN
ap-10605	85	15	)	)	PUNCT
ap-10605	85	16	̸=	̸=	PROPN
ap-10605	85	17	rank	rank	NOUN
ap-10605	85	18	r2(m	r2(m	NOUN
ap-10605	85	19	)	)	PUNCT
ap-10605	85	20	then	then	ADV
ap-10605	85	21	the	the	DET
ap-10605	85	22	realizations	realization	NOUN
ap-10605	85	23	r1	r1	NOUN
ap-10605	85	24	and	and	CCONJ
ap-10605	85	25	r2	r2	PROPN
ap-10605	85	26	are	be	AUX
ap-10605	85	27	weakly	weakly	ADJ
ap-10605	85	28	inequivalent	inequivalent	NOUN
ap-10605	85	29	.	.	PUNCT
ap-10605	86	1	the	the	DET
ap-10605	86	2	notion	notion	NOUN
ap-10605	86	3	of	of	ADP
ap-10605	86	4	megaideal	megaideal	NOUN
ap-10605	86	5	allows	allow	VERB
ap-10605	86	6	us	we	PRON
ap-10605	86	7	to	to	PART
ap-10605	86	8	construct	construct	VERB
ap-10605	86	9	realizations	realization	NOUN
ap-10605	86	10	starting	start	VERB
ap-10605	86	11	from	from	ADP
ap-10605	86	12	the	the	DET
ap-10605	86	13	known	know	VERB
ap-10605	86	14	lists	list	NOUN
ap-10605	86	15	of	of	ADP
ap-10605	86	16	realizations	realization	NOUN
ap-10605	86	17	for	for	ADP
ap-10605	86	18	the	the	DET
ap-10605	86	19	low	low	ADJ
ap-10605	86	20	-	-	PUNCT
ap-10605	86	21	dimensional	dimensional	ADJ
ap-10605	86	22	algebras	algebra	NOUN
ap-10605	86	23	,	,	PUNCT
ap-10605	86	24	but	but	CCONJ
ap-10605	86	25	only	only	ADV
ap-10605	86	26	in	in	ADP
ap-10605	86	27	the	the	DET
ap-10605	86	28	case	case	NOUN
ap-10605	86	29	when	when	SCONJ
ap-10605	86	30	we	we	PRON
ap-10605	86	31	can	can	AUX
ap-10605	86	32	find	find	VERB
ap-10605	86	33	a	a	DET
ap-10605	86	34	nested	nested	ADJ
ap-10605	86	35	chain	chain	NOUN
ap-10605	86	36	of	of	ADP
ap-10605	86	37	megaideals	megaideal	NOUN
ap-10605	86	38	.	.	PUNCT
ap-10605	87	1	such	such	DET
ap-10605	87	2	a	a	DET
ap-10605	87	3	chain	chain	NOUN
ap-10605	87	4	of	of	ADP
ap-10605	87	5	megaideals	megaideal	NOUN
ap-10605	87	6	can	can	AUX
ap-10605	87	7	not	not	PART
ap-10605	87	8	be	be	AUX
ap-10605	87	9	constructed	construct	VERB
ap-10605	87	10	for	for	ADP
ap-10605	87	11	simple	simple	ADJ
ap-10605	87	12	lie	lie	NOUN
ap-10605	87	13	algebras	algebra	NOUN
ap-10605	87	14	,	,	PUNCT
ap-10605	87	15	so	so	ADV
ap-10605	87	16	constructing	construct	VERB
ap-10605	87	17	realizations	realization	NOUN
ap-10605	87	18	for	for	ADP
ap-10605	87	19	them	they	PRON
ap-10605	87	20	is	be	AUX
ap-10605	87	21	a	a	DET
ap-10605	87	22	particularly	particularly	ADV
ap-10605	87	23	difficult	difficult	ADJ
ap-10605	87	24	task	task	NOUN
ap-10605	87	25	.	.	PUNCT
ap-10605	88	1	for	for	ADP
ap-10605	88	2	low	low	ADJ
ap-10605	88	3	-	-	PUNCT
ap-10605	88	4	dimensional	dimensional	ADJ
ap-10605	88	5	lie	lie	NOUN
ap-10605	88	6	algebras	algebra	NOUN
ap-10605	88	7	,	,	PUNCT
ap-10605	88	8	the	the	DET
ap-10605	88	9	direct	direct	ADJ
ap-10605	88	10	method	method	NOUN
ap-10605	88	11	is	be	AUX
ap-10605	88	12	quite	quite	ADV
ap-10605	88	13	effective	effective	ADJ
ap-10605	88	14	and	and	CCONJ
ap-10605	88	15	has	have	AUX
ap-10605	88	16	allowed	allow	VERB
ap-10605	88	17	us	we	PRON
ap-10605	88	18	to	to	PART
ap-10605	88	19	describe	describe	VERB
ap-10605	88	20	realizations	realization	NOUN
ap-10605	88	21	of	of	ADP
ap-10605	88	22	real	real	ADJ
ap-10605	88	23	lie	lie	NOUN
ap-10605	88	24	algebras	algebra	NOUN
ap-10605	88	25	of	of	ADP
ap-10605	88	26	dimensions	dimension	NOUN
ap-10605	88	27	no	no	ADV
ap-10605	88	28	higher	high	ADJ
ap-10605	88	29	than	than	ADP
ap-10605	88	30	four	four	NUM
ap-10605	88	31	[	[	NOUN
ap-10605	88	32	4	4	NUM
ap-10605	88	33	]	]	PUNCT
ap-10605	88	34	.	.	PUNCT
ap-10605	89	1	3.2	3.2	NUM
ap-10605	89	2	.	.	PUNCT
ap-10605	90	1	blattner	blattner	NOUN
ap-10605	90	2	’s	’s	PART
ap-10605	90	3	method	method	NOUN
ap-10605	90	4	let	let	VERB
ap-10605	90	5	us	we	PRON
ap-10605	90	6	consider	consider	VERB
ap-10605	90	7	the	the	DET
ap-10605	90	8	method	method	NOUN
ap-10605	90	9	proposed	propose	VERB
ap-10605	90	10	by	by	ADP
ap-10605	90	11	blattner	blattner	NOUN
ap-10605	91	1	[	[	X
ap-10605	91	2	5	5	NUM
ap-10605	91	3	]	]	PUNCT
ap-10605	91	4	in	in	ADP
ap-10605	91	5	1969	1969	NUM
ap-10605	91	6	.	.	PUNCT
ap-10605	92	1	it	it	PRON
ap-10605	92	2	constructs	construct	VERB
ap-10605	92	3	transitive	transitive	ADJ
ap-10605	92	4	realizations	realization	NOUN
ap-10605	92	5	of	of	ADP
ap-10605	92	6	lie	lie	NOUN
ap-10605	92	7	algebras	algebra	NOUN
ap-10605	92	8	starting	start	VERB
ap-10605	92	9	from	from	ADP
ap-10605	92	10	their	their	PRON
ap-10605	92	11	structure	structure	NOUN
ap-10605	92	12	constants	constant	NOUN
ap-10605	92	13	.	.	PUNCT
ap-10605	93	1	for	for	ADP
ap-10605	93	2	further	further	ADJ
ap-10605	93	3	explanation	explanation	NOUN
ap-10605	93	4	,	,	PUNCT
ap-10605	93	5	we	we	PRON
ap-10605	93	6	need	need	VERB
ap-10605	93	7	to	to	PART
ap-10605	93	8	define	define	VERB
ap-10605	93	9	transitive	transitive	ADJ
ap-10605	93	10	realizations	realization	NOUN
ap-10605	93	11	.	.	PUNCT
ap-10605	94	1	by	by	SCONJ
ap-10605	94	2	the	the	DET
ap-10605	94	3	third	third	ADJ
ap-10605	94	4	lie	lie	NOUN
ap-10605	94	5	theorem	theorem	VERB
ap-10605	94	6	,	,	PUNCT
ap-10605	94	7	there	there	PRON
ap-10605	94	8	exists	exist	VERB
ap-10605	94	9	a	a	DET
ap-10605	94	10	local	local	ADJ
ap-10605	94	11	nparametric	nparametric	ADJ
ap-10605	94	12	transformation	transformation	NOUN
ap-10605	94	13	group	group	NOUN
ap-10605	94	14	g	g	PROPN
ap-10605	94	15	corresponding	correspond	VERB
ap-10605	94	16	to	to	ADP
ap-10605	94	17	the	the	DET
ap-10605	94	18	vector	vector	NOUN
ap-10605	94	19	fields	field	NOUN
ap-10605	94	20	ei	ei	X
ap-10605	94	21	,	,	PUNCT
ap-10605	94	22	i.e.	i.e.	X
ap-10605	94	23	ei	ei	X
ap-10605	94	24	are	be	AUX
ap-10605	94	25	infinitesimal	infinitesimal	ADJ
ap-10605	94	26	generators	generator	NOUN
ap-10605	94	27	of	of	ADP
ap-10605	94	28	the	the	DET
ap-10605	94	29	action	action	NOUN
ap-10605	94	30	of	of	ADP
ap-10605	94	31	the	the	DET
ap-10605	94	32	group	group	NOUN
ap-10605	94	33	g	g	PROPN
ap-10605	94	34	on	on	ADP
ap-10605	94	35	m	m	PROPN
ap-10605	94	36	.	.	PUNCT
ap-10605	95	1	note	note	VERB
ap-10605	95	2	that	that	SCONJ
ap-10605	95	3	such	such	DET
ap-10605	95	4	a	a	DET
ap-10605	95	5	correspondence	correspondence	NOUN
ap-10605	95	6	between	between	ADP
ap-10605	95	7	the	the	DET
ap-10605	95	8	group	group	NOUN
ap-10605	95	9	and	and	CCONJ
ap-10605	95	10	the	the	DET
ap-10605	95	11	lie	lie	NOUN
ap-10605	95	12	algebra	algebra	NOUN
ap-10605	95	13	is	be	AUX
ap-10605	95	14	given	give	VERB
ap-10605	95	15	by	by	ADP
ap-10605	95	16	the	the	DET
ap-10605	95	17	tangent	tangent	ADJ
ap-10605	95	18	space	space	NOUN
ap-10605	95	19	at	at	ADP
ap-10605	95	20	the	the	DET
ap-10605	95	21	unit	unit	NOUN
ap-10605	95	22	of	of	ADP
ap-10605	95	23	the	the	DET
ap-10605	95	24	group	group	NOUN
ap-10605	95	25	(	(	PUNCT
ap-10605	95	26	the	the	DET
ap-10605	95	27	zero	zero	NUM
ap-10605	95	28	of	of	ADP
ap-10605	95	29	the	the	DET
ap-10605	95	30	lie	lie	NOUN
ap-10605	95	31	algebra	algebra	PROPN
ap-10605	95	32	)	)	PUNCT
ap-10605	95	33	.	.	PUNCT
ap-10605	96	1	a	a	DET
ap-10605	96	2	lie	lie	NOUN
ap-10605	96	3	group	group	NOUN
ap-10605	96	4	g	g	PROPN
ap-10605	96	5	can	can	AUX
ap-10605	96	6	act	act	VERB
ap-10605	96	7	on	on	ADP
ap-10605	96	8	m	m	PROPN
ap-10605	96	9	in	in	ADP
ap-10605	96	10	several	several	ADJ
ap-10605	96	11	different	different	ADJ
ap-10605	96	12	ways	way	NOUN
ap-10605	96	13	:	:	PUNCT
ap-10605	96	14	primitively	primitively	ADV
ap-10605	96	15	(	(	PUNCT
ap-10605	96	16	only	only	ADV
ap-10605	96	17	one	one	NUM
ap-10605	96	18	orbit	orbit	NOUN
ap-10605	96	19	is	be	AUX
ap-10605	96	20	formed	form	VERB
ap-10605	96	21	when	when	SCONJ
ap-10605	96	22	g	g	PROPN
ap-10605	96	23	acts	act	VERB
ap-10605	96	24	on	on	ADP
ap-10605	96	25	m	m	NOUN
ap-10605	96	26	)	)	PUNCT
ap-10605	96	27	or	or	CCONJ
ap-10605	96	28	imprimitively	imprimitively	ADV
ap-10605	96	29	(	(	PUNCT
ap-10605	96	30	m	m	NOUN
ap-10605	96	31	is	be	AUX
ap-10605	96	32	split	split	VERB
ap-10605	96	33	into	into	ADP
ap-10605	96	34	several	several	ADJ
ap-10605	96	35	orbits	orbit	NOUN
ap-10605	96	36	)	)	PUNCT
ap-10605	96	37	;	;	PUNCT
ap-10605	96	38	transitively	transitively	PROPN
ap-10605	96	39	(	(	PUNCT
ap-10605	96	40	orbits	orbit	NOUN
ap-10605	96	41	may	may	AUX
ap-10605	96	42	exist	exist	VERB
ap-10605	96	43	but	but	CCONJ
ap-10605	96	44	there	there	PRON
ap-10605	96	45	are	be	VERB
ap-10605	96	46	no	no	DET
ap-10605	96	47	stationary	stationary	ADJ
ap-10605	96	48	points	point	NOUN
ap-10605	96	49	)	)	PUNCT
ap-10605	96	50	,	,	PUNCT
ap-10605	96	51	and	and	CCONJ
ap-10605	96	52	intransitively	intransitively	ADV
ap-10605	96	53	(	(	PUNCT
ap-10605	96	54	g	g	PROPN
ap-10605	96	55	decomposes	decompose	VERB
ap-10605	96	56	m	m	VERB
ap-10605	96	57	into	into	ADP
ap-10605	96	58	orbits	orbit	NOUN
ap-10605	96	59	that	that	PRON
ap-10605	96	60	are	be	AUX
ap-10605	96	61	invariant	invariant	ADJ
ap-10605	96	62	under	under	ADP
ap-10605	96	63	the	the	DET
ap-10605	96	64	action	action	NOUN
ap-10605	96	65	of	of	ADP
ap-10605	96	66	g	g	NOUN
ap-10605	96	67	)	)	PUNCT
ap-10605	96	68	.	.	PUNCT
ap-10605	97	1	if	if	SCONJ
ap-10605	97	2	the	the	DET
ap-10605	97	3	local	local	ADJ
ap-10605	97	4	group	group	NOUN
ap-10605	97	5	g	g	NOUN
ap-10605	97	6	corresponding	correspond	VERB
ap-10605	97	7	to	to	ADP
ap-10605	97	8	a	a	DET
ap-10605	97	9	realization	realization	NOUN
ap-10605	97	10	acts	act	VERB
ap-10605	97	11	transitively	transitively	ADV
ap-10605	97	12	on	on	ADP
ap-10605	97	13	m	m	PROPN
ap-10605	97	14	,	,	PUNCT
ap-10605	97	15	then	then	ADV
ap-10605	97	16	the	the	DET
ap-10605	97	17	realization	realization	NOUN
ap-10605	97	18	is	be	AUX
ap-10605	97	19	also	also	ADV
ap-10605	97	20	called	call	VERB
ap-10605	97	21	transitive	transitive	ADJ
ap-10605	97	22	.	.	PUNCT
ap-10605	98	1	let	let	VERB
ap-10605	98	2	{	{	PUNCT
ap-10605	98	3	e1	e1	VERB
ap-10605	98	4	,	,	PUNCT
ap-10605	98	5	.	.	PUNCT
ap-10605	98	6	.	.	PUNCT
ap-10605	99	1	.	.	PUNCT
ap-10605	100	1	,	,	PUNCT
ap-10605	100	2	ek	ek	NOUN
ap-10605	100	3	,	,	PUNCT
ap-10605	100	4	ϵ1	ϵ1	ADJ
ap-10605	100	5	,	,	PUNCT
ap-10605	100	6	.	.	PUNCT
ap-10605	100	7	.	.	PUNCT
ap-10605	101	1	.	.	PUNCT
ap-10605	102	1	,	,	PUNCT
ap-10605	102	2	ϵm	ϵm	AUX
ap-10605	102	3	}	}	PUNCT
ap-10605	102	4	be	be	AUX
ap-10605	102	5	the	the	DET
ap-10605	102	6	basis	basis	NOUN
ap-10605	102	7	of	of	ADP
ap-10605	102	8	a	a	DET
ap-10605	102	9	finitedimensional	finitedimensional	ADJ
ap-10605	102	10	lie	lie	NOUN
ap-10605	102	11	algebra	algebra	NOUN
ap-10605	102	12	g	g	PROPN
ap-10605	102	13	,	,	PUNCT
ap-10605	102	14	where	where	SCONJ
ap-10605	102	15	s	s	VERB
ap-10605	102	16	=	=	SYM
ap-10605	102	17	⟨e1	⟨e1	PROPN
ap-10605	102	18	,	,	PUNCT
ap-10605	102	19	.	.	PUNCT
ap-10605	102	20	.	.	PUNCT
ap-10605	103	1	.	.	PUNCT
ap-10605	103	2	,	,	PUNCT
ap-10605	103	3	ek⟩	ek⟩	VERB
ap-10605	103	4	is	be	AUX
ap-10605	103	5	a	a	DET
ap-10605	103	6	subalgebra	subalgebra	NOUN
ap-10605	103	7	of	of	ADP
ap-10605	103	8	co	co	NOUN
ap-10605	103	9	-	-	NOUN
ap-10605	103	10	dimension	dimension	ADJ
ap-10605	103	11	m	m	NOUN
ap-10605	103	12	,	,	PUNCT
ap-10605	103	13	and	and	CCONJ
ap-10605	103	14	u(g	u(g	PROPN
ap-10605	103	15	)	)	PUNCT
ap-10605	103	16	is	be	AUX
ap-10605	103	17	the	the	DET
ap-10605	103	18	universal	universal	ADJ
ap-10605	103	19	enveloping	enveloping	NOUN
ap-10605	103	20	algebra	algebra	NOUN
ap-10605	103	21	of	of	ADP
ap-10605	103	22	g.	g.	PROPN
ap-10605	103	23	then	then	ADV
ap-10605	103	24	,	,	PUNCT
ap-10605	103	25	using	use	VERB
ap-10605	103	26	the	the	DET
ap-10605	103	27	set	set	NOUN
ap-10605	103	28	of	of	ADP
ap-10605	103	29	vectors	vector	NOUN
ap-10605	103	30	{	{	PUNCT
ap-10605	103	31	ϵ1	ϵ1	ADJ
ap-10605	103	32	,	,	PUNCT
ap-10605	103	33	.	.	PUNCT
ap-10605	103	34	.	.	PUNCT
ap-10605	104	1	.	.	PUNCT
ap-10605	105	1	,	,	PUNCT
ap-10605	105	2	ϵm	ϵm	NOUN
ap-10605	105	3	}	}	PUNCT
ap-10605	105	4	complementary	complementary	ADJ
ap-10605	105	5	to	to	ADP
ap-10605	105	6	the	the	DET
ap-10605	105	7	subalgebra	subalgebra	NOUN
ap-10605	105	8	s	s	PART
ap-10605	105	9	,	,	PUNCT
ap-10605	105	10	we	we	PRON
ap-10605	105	11	can	can	AUX
ap-10605	105	12	construct	construct	VERB
ap-10605	105	13	the	the	DET
ap-10605	105	14	transformation	transformation	NOUN
ap-10605	105	15	φϵ	φϵ	NOUN
ap-10605	105	16	,	,	PUNCT
ap-10605	105	17	defined	define	VERB
ap-10605	105	18	for	for	ADP
ap-10605	105	19	v	v	NOUN
ap-10605	105	20	∈	∈	NOUN
ap-10605	105	21	g	g	NOUN
ap-10605	105	22	,	,	PUNCT
ap-10605	105	23	that	that	PRON
ap-10605	105	24	gives	give	VERB
ap-10605	105	25	a	a	DET
ap-10605	105	26	transitive	transitive	ADJ
ap-10605	105	27	realization	realization	NOUN
ap-10605	105	28	of	of	ADP
ap-10605	105	29	the	the	DET
ap-10605	105	30	algebra	algebra	NOUN
ap-10605	105	31	g	g	NOUN
ap-10605	105	32	by	by	ADP
ap-10605	105	33	the	the	DET
ap-10605	105	34	formula	formula	NOUN
ap-10605	105	35	:	:	PUNCT
ap-10605	105	36	φϵ(v	φϵ(v	X
ap-10605	105	37	)	)	PUNCT
ap-10605	105	38	=	=	PUNCT
ap-10605	106	1	m∑	m∑	INTJ
ap-10605	106	2	i=1	i=1	PROPN
ap-10605	106	3	(	(	PUNCT
ap-10605	106	4	∑	∑	PUNCT
ap-10605	106	5	l∈nm	l∈nm	PROPN
ap-10605	106	6	χi(ϵlv)xl	χi(ϵlv)xl	PROPN
ap-10605	106	7	l	l	NOUN
ap-10605	106	8	!	!	PUNCT
ap-10605	106	9	)	)	PUNCT
ap-10605	107	1	∂i	∂i	PROPN
ap-10605	107	2	,	,	PUNCT
ap-10605	107	3	where	where	SCONJ
ap-10605	107	4	l	l	NOUN
ap-10605	107	5	is	be	AUX
ap-10605	107	6	multi	multi	ADJ
ap-10605	107	7	-	-	NOUN
ap-10605	107	8	index	index	NOUN
ap-10605	107	9	and	and	CCONJ
ap-10605	107	10	l	l	NOUN
ap-10605	107	11	!	!	PUNCT
ap-10605	108	1	:	:	PUNCT
ap-10605	109	1	=	=	PUNCT
ap-10605	109	2	m∏	m∏	PROPN
ap-10605	109	3	i=1	i=1	X
ap-10605	109	4	li	li	PROPN
ap-10605	109	5	!	!	PROPN
ap-10605	109	6	.	.	PUNCT
ap-10605	110	1	here	here	ADV
ap-10605	110	2	ϵlv	ϵlv	X
ap-10605	110	3	∈	∈	PROPN
ap-10605	110	4	u(g	u(g	PROPN
ap-10605	110	5	)	)	PUNCT
ap-10605	110	6	,	,	PUNCT
ap-10605	110	7	and	and	CCONJ
ap-10605	110	8	χi	χi	PROPN
ap-10605	110	9	—	—	PUNCT
ap-10605	110	10	the	the	DET
ap-10605	110	11	poincaré	poincaré	PROPN
ap-10605	110	12	–	–	PUNCT
ap-10605	110	13	birkhoff	birkhoff	NOUN
ap-10605	110	14	–	–	PUNCT
ap-10605	110	15	witt	witt	ADJ
ap-10605	110	16	coefficient	coefficient	NOUN
ap-10605	110	17	before	before	ADP
ap-10605	110	18	the	the	DET
ap-10605	110	19	monomial	monomial	ADJ
ap-10605	110	20	ϵi	ϵi	PROPN
ap-10605	110	21	.	.	PUNCT
ap-10605	111	1	a	a	DET
ap-10605	111	2	poincaré	poincaré	PROPN
ap-10605	111	3	–	–	PUNCT
ap-10605	111	4	birkhoff	birkhoff	NOUN
ap-10605	111	5	–	–	PUNCT
ap-10605	111	6	witt	witt	NUM
ap-10605	111	7	coefficient	coefficient	NOUN
ap-10605	111	8	is	be	AUX
ap-10605	111	9	the	the	DET
ap-10605	111	10	scalar	scalar	NOUN
ap-10605	111	11	that	that	PRON
ap-10605	111	12	appears	appear	VERB
ap-10605	111	13	when	when	SCONJ
ap-10605	111	14	a	a	DET
ap-10605	111	15	product	product	NOUN
ap-10605	111	16	of	of	ADP
ap-10605	111	17	lie	lie	NOUN
ap-10605	111	18	algebra	algebra	NOUN
ap-10605	111	19	generators	generator	NOUN
ap-10605	111	20	is	be	AUX
ap-10605	111	21	rewritten	rewrite	VERB
ap-10605	111	22	in	in	ADP
ap-10605	111	23	terms	term	NOUN
ap-10605	111	24	of	of	ADP
ap-10605	111	25	the	the	DET
ap-10605	111	26	ordered	order	VERB
ap-10605	111	27	pbw	pbw	NOUN
ap-10605	111	28	basis	basis	NOUN
ap-10605	111	29	of	of	ADP
ap-10605	111	30	the	the	DET
ap-10605	111	31	universal	universal	ADJ
ap-10605	111	32	enveloping	enveloping	NOUN
ap-10605	111	33	algebra	algebra	NOUN
ap-10605	111	34	.	.	PUNCT
ap-10605	112	1	it	it	PRON
ap-10605	112	2	is	be	AUX
ap-10605	112	3	the	the	DET
ap-10605	112	4	coefficients	coefficient	NOUN
ap-10605	112	5	χi	χi	NOUN
ap-10605	112	6	that	that	PRON
ap-10605	112	7	significantly	significantly	ADV
ap-10605	112	8	complicate	complicate	VERB
ap-10605	112	9	the	the	DET
ap-10605	112	10	application	application	NOUN
ap-10605	112	11	of	of	ADP
ap-10605	112	12	the	the	DET
ap-10605	112	13	blattner	blattner	NOUN
ap-10605	112	14	’s	’s	PART
ap-10605	112	15	formula	formula	NOUN
ap-10605	112	16	,	,	PUNCT
ap-10605	112	17	since	since	SCONJ
ap-10605	112	18	no	no	DET
ap-10605	112	19	regular	regular	ADJ
ap-10605	112	20	procedure	procedure	NOUN
ap-10605	112	21	has	have	AUX
ap-10605	112	22	been	be	AUX
ap-10605	112	23	found	find	VERB
ap-10605	112	24	for	for	ADP
ap-10605	112	25	their	their	PRON
ap-10605	112	26	calculation	calculation	NOUN
ap-10605	112	27	.	.	PUNCT
ap-10605	113	1	3.3	3.3	NUM
ap-10605	113	2	.	.	PUNCT
ap-10605	114	1	shirokov	shirokov	PROPN
ap-10605	114	2	’s	’s	PART
ap-10605	114	3	method	method	NOUN
ap-10605	114	4	let	let	VERB
ap-10605	114	5	’s	’s	NOUN
ap-10605	114	6	consider	consider	VERB
ap-10605	114	7	another	another	DET
ap-10605	114	8	approach	approach	NOUN
ap-10605	114	9	that	that	PRON
ap-10605	114	10	is	be	AUX
ap-10605	114	11	algebraic	algebraic	ADJ
ap-10605	114	12	and	and	CCONJ
ap-10605	114	13	does	do	AUX
ap-10605	114	14	not	not	PART
ap-10605	114	15	require	require	VERB
ap-10605	114	16	solving	solve	VERB
ap-10605	114	17	differential	differential	ADJ
ap-10605	114	18	equations	equation	NOUN
ap-10605	114	19	.	.	PUNCT
ap-10605	115	1	this	this	DET
ap-10605	115	2	method	method	NOUN
ap-10605	115	3	was	be	AUX
ap-10605	115	4	first	first	ADV
ap-10605	115	5	proposed	propose	VERB
ap-10605	115	6	in	in	ADP
ap-10605	115	7	1997	1997	NUM
ap-10605	115	8	by	by	ADP
ap-10605	115	9	i.	i.	PROPN
ap-10605	115	10	shirokov	shirokov	PROPN
ap-10605	115	11	for	for	ADP
ap-10605	115	12	left	left	ADJ
ap-10605	115	13	-	-	PUNCT
ap-10605	115	14	invariant	invariant	ADJ
ap-10605	115	15	vector	vector	NOUN
ap-10605	115	16	fields	field	NOUN
ap-10605	115	17	,	,	PUNCT
ap-10605	115	18	and	and	CCONJ
ap-10605	115	19	it	it	PRON
ap-10605	115	20	was	be	AUX
ap-10605	115	21	extended	extend	VERB
ap-10605	115	22	to	to	ADP
ap-10605	115	23	the	the	DET
ap-10605	115	24	transitive	transitive	ADJ
ap-10605	115	25	case	case	NOUN
ap-10605	115	26	in	in	ADP
ap-10605	115	27	2013	2013	NUM
ap-10605	115	28	[	[	X
ap-10605	115	29	6	6	NUM
ap-10605	115	30	]	]	PUNCT
ap-10605	115	31	.	.	PUNCT
ap-10605	116	1	the	the	DET
ap-10605	116	2	main	main	ADJ
ap-10605	116	3	ideas	idea	NOUN
ap-10605	116	4	of	of	ADP
ap-10605	116	5	this	this	DET
ap-10605	116	6	method	method	NOUN
ap-10605	116	7	are	be	AUX
ap-10605	116	8	to	to	PART
ap-10605	116	9	construct	construct	VERB
ap-10605	116	10	vector	vector	NOUN
ap-10605	116	11	fields	field	NOUN
ap-10605	116	12	as	as	ADP
ap-10605	116	13	duals	dual	NOUN
ap-10605	116	14	(	(	PUNCT
ap-10605	116	15	inverses	inverse	NOUN
ap-10605	116	16	)	)	PUNCT
ap-10605	116	17	to	to	PART
ap-10605	116	18	differential	differential	VERB
ap-10605	116	19	one	one	NUM
ap-10605	116	20	-	-	PUNCT
ap-10605	116	21	forms	form	NOUN
ap-10605	116	22	,	,	PUNCT
ap-10605	116	23	and	and	CCONJ
ap-10605	116	24	to	to	PART
ap-10605	116	25	construct	construct	VERB
ap-10605	116	26	differential	differential	ADJ
ap-10605	116	27	one	one	NUM
ap-10605	116	28	-	-	PUNCT
ap-10605	116	29	forms	form	NOUN
ap-10605	116	30	using	use	VERB
ap-10605	116	31	adjoint	adjoint	NOUN
ap-10605	116	32	representations	representation	NOUN
ap-10605	116	33	.	.	PUNCT
ap-10605	117	1	let	let	VERB
ap-10605	117	2	the	the	DET
ap-10605	117	3	local	local	ADJ
ap-10605	117	4	lie	lie	NOUN
ap-10605	117	5	group	group	NOUN
ap-10605	117	6	that	that	PRON
ap-10605	117	7	corresponds	correspond	VERB
ap-10605	117	8	to	to	ADP
ap-10605	117	9	g	g	PROPN
ap-10605	117	10	is	be	AUX
ap-10605	117	11	parametrized	parametrize	VERB
ap-10605	117	12	by	by	ADP
ap-10605	117	13	the	the	DET
ap-10605	117	14	canonical	canonical	ADJ
ap-10605	117	15	coordinates	coordinate	NOUN
ap-10605	117	16	of	of	ADP
ap-10605	117	17	the	the	DET
ap-10605	117	18	second	second	ADJ
ap-10605	117	19	kind	kind	NOUN
ap-10605	117	20	,	,	PUNCT
ap-10605	117	21	i.e.	i.e.	X
ap-10605	117	22	,	,	PUNCT
ap-10605	117	23	group	group	NOUN
ap-10605	117	24	elements	element	NOUN
ap-10605	117	25	are	be	AUX
ap-10605	117	26	represented	represent	VERB
ap-10605	117	27	as	as	ADP
ap-10605	117	28	ordered	order	VERB
ap-10605	117	29	products	product	NOUN
ap-10605	117	30	of	of	ADP
ap-10605	117	31	exponentials	exponential	NOUN
ap-10605	117	32	,	,	PUNCT
ap-10605	117	33	each	each	DET
ap-10605	117	34	corresponding	correspond	VERB
ap-10605	117	35	to	to	ADP
ap-10605	117	36	a	a	DET
ap-10605	117	37	separate	separate	ADJ
ap-10605	117	38	basis	basis	NOUN
ap-10605	117	39	element	element	NOUN
ap-10605	117	40	of	of	ADP
ap-10605	117	41	g.	g.	PROPN
ap-10605	117	42	in	in	ADP
ap-10605	117	43	this	this	DET
ap-10605	117	44	case	case	NOUN
ap-10605	117	45	,	,	PUNCT
ap-10605	117	46	we	we	PRON
ap-10605	117	47	can	can	AUX
ap-10605	117	48	construct	construct	VERB
ap-10605	117	49	components	component	NOUN
ap-10605	117	50	ωj	ωj	ADP
ap-10605	117	51	i	i	PRON
ap-10605	117	52	(	(	PUNCT
ap-10605	117	53	x	x	NOUN
ap-10605	117	54	)	)	PUNCT
ap-10605	117	55	of	of	ADP
ap-10605	117	56	differential	differential	ADJ
ap-10605	117	57	one	one	NUM
ap-10605	117	58	-	-	PUNCT
ap-10605	117	59	forms	form	NOUN
ap-10605	117	60	by	by	ADP
ap-10605	117	61	the	the	DET
ap-10605	117	62	formula	formula	NOUN
ap-10605	117	63	:	:	PUNCT
ap-10605	117	64	ωj	ωj	ADP
ap-10605	117	65	i	i	PRON
ap-10605	117	66	(	(	PUNCT
ap-10605	117	67	x	x	X
ap-10605	117	68	)	)	PUNCT
ap-10605	117	69	=	=	SYM
ap-10605	117	70	(	(	PUNCT
ap-10605	117	71	exp(−x1ade1	exp(−x1ade1	NOUN
ap-10605	117	72	)	)	PUNCT
ap-10605	117	73	·	·	PUNCT
ap-10605	117	74	·	·	PUNCT
ap-10605	117	75	·	·	PUNCT
ap-10605	117	76	exp(−xiadei	exp(−xiadei	NUM
ap-10605	117	77	)	)	PUNCT
ap-10605	117	78	)	)	PUNCT
ap-10605	118	1	j	j	PROPN
ap-10605	118	2	i	i	PRON
ap-10605	118	3	.	.	PUNCT
ap-10605	119	1	556	556	NUM
ap-10605	119	2	vol	vol	NOUN
ap-10605	119	3	.	.	PUNCT
ap-10605	120	1	65	65	NUM
ap-10605	120	2	no	no	NOUN
ap-10605	120	3	.	.	PUNCT
ap-10605	121	1	5/2025	5/2025	NUM
ap-10605	121	2	on	on	ADP
ap-10605	121	3	realizations	realization	NOUN
ap-10605	121	4	of	of	ADP
ap-10605	121	5	lie	lie	NOUN
ap-10605	121	6	algebras	algebra	VERB
ap-10605	121	7	now	now	ADV
ap-10605	121	8	the	the	DET
ap-10605	121	9	problem	problem	NOUN
ap-10605	121	10	of	of	ADP
ap-10605	121	11	constructing	construct	VERB
ap-10605	121	12	left	left	ADJ
ap-10605	121	13	-	-	PUNCT
ap-10605	121	14	invariant	invariant	ADJ
ap-10605	121	15	vector	vector	NOUN
ap-10605	121	16	fields	field	NOUN
ap-10605	121	17	reduces	reduce	VERB
ap-10605	121	18	to	to	ADP
ap-10605	121	19	finding	find	VERB
ap-10605	121	20	the	the	DET
ap-10605	121	21	inverse	inverse	NOUN
ap-10605	121	22	transformation	transformation	NOUN
ap-10605	121	23	ξi	ξi	PROPN
ap-10605	121	24	k(x	k(x	PROPN
ap-10605	121	25	)	)	PUNCT
ap-10605	122	1	=	=	PRON
ap-10605	122	2	(	(	PUNCT
ap-10605	122	3	(	(	PUNCT
ap-10605	122	4	ωj	ωj	ADP
ap-10605	122	5	l	l	NOUN
ap-10605	122	6	(	(	PUNCT
ap-10605	122	7	x))−1)i	x))−1)i	PROPN
ap-10605	122	8	k	k	X
ap-10605	122	9	.	.	PUNCT
ap-10605	123	1	note	note	VERB
ap-10605	123	2	that	that	SCONJ
ap-10605	123	3	this	this	DET
ap-10605	123	4	construction	construction	NOUN
ap-10605	123	5	of	of	ADP
ap-10605	123	6	realization	realization	NOUN
ap-10605	123	7	corresponds	correspond	VERB
ap-10605	123	8	to	to	ADP
ap-10605	123	9	the	the	DET
ap-10605	123	10	primitive	primitive	ADJ
ap-10605	123	11	action	action	NOUN
ap-10605	123	12	of	of	ADP
ap-10605	123	13	the	the	DET
ap-10605	123	14	local	local	ADJ
ap-10605	123	15	group	group	NOUN
ap-10605	123	16	,	,	PUNCT
ap-10605	123	17	we	we	PRON
ap-10605	123	18	will	will	AUX
ap-10605	123	19	call	call	VERB
ap-10605	123	20	such	such	DET
ap-10605	123	21	a	a	DET
ap-10605	123	22	realization	realization	NOUN
ap-10605	123	23	generic	generic	ADJ
ap-10605	123	24	.	.	PUNCT
ap-10605	124	1	all	all	DET
ap-10605	124	2	other	other	ADJ
ap-10605	124	3	realizations	realization	NOUN
ap-10605	124	4	that	that	PRON
ap-10605	124	5	correspond	correspond	VERB
ap-10605	124	6	to	to	ADP
ap-10605	124	7	the	the	DET
ap-10605	124	8	transitive	transitive	ADJ
ap-10605	124	9	group	group	NOUN
ap-10605	124	10	action	action	NOUN
ap-10605	124	11	can	can	AUX
ap-10605	124	12	be	be	AUX
ap-10605	124	13	obtained	obtain	VERB
ap-10605	124	14	as	as	ADP
ap-10605	124	15	projections	projection	NOUN
ap-10605	124	16	of	of	ADP
ap-10605	124	17	the	the	DET
ap-10605	124	18	generic	generic	ADJ
ap-10605	124	19	realizations	realization	NOUN
ap-10605	124	20	to	to	ADP
ap-10605	124	21	the	the	DET
ap-10605	124	22	spaces	space	NOUN
ap-10605	124	23	of	of	ADP
ap-10605	124	24	variables	variable	NOUN
ap-10605	124	25	complementary	complementary	ADJ
ap-10605	124	26	to	to	ADP
ap-10605	124	27	subalgebras	subalgebras	PROPN
ap-10605	124	28	.	.	PUNCT
ap-10605	125	1	in	in	ADP
ap-10605	125	2	the	the	DET
ap-10605	125	3	case	case	NOUN
ap-10605	125	4	of	of	ADP
ap-10605	125	5	a	a	DET
ap-10605	125	6	nontransitive	nontransitive	ADJ
ap-10605	125	7	action	action	NOUN
ap-10605	125	8	of	of	ADP
ap-10605	125	9	the	the	DET
ap-10605	125	10	corresponding	corresponding	ADJ
ap-10605	125	11	local	local	ADJ
ap-10605	125	12	group	group	NOUN
ap-10605	125	13	,	,	PUNCT
ap-10605	125	14	the	the	DET
ap-10605	125	15	method	method	NOUN
ap-10605	125	16	becomes	become	VERB
ap-10605	125	17	more	more	ADV
ap-10605	125	18	complicated	complicated	ADJ
ap-10605	125	19	.	.	PUNCT
ap-10605	126	1	it	it	PRON
ap-10605	126	2	was	be	AUX
ap-10605	126	3	discussed	discuss	VERB
ap-10605	126	4	in	in	ADP
ap-10605	126	5	the	the	DET
ap-10605	126	6	thesis	thesis	NOUN
ap-10605	127	1	[	[	X
ap-10605	127	2	7	7	NUM
ap-10605	127	3	]	]	PUNCT
ap-10605	127	4	of	of	ADP
ap-10605	127	5	d.	d.	PROPN
ap-10605	127	6	gromada	gromada	PROPN
ap-10605	127	7	,	,	PUNCT
ap-10605	127	8	but	but	CCONJ
ap-10605	127	9	,	,	PUNCT
ap-10605	127	10	for	for	ADP
ap-10605	127	11	practical	practical	ADJ
ap-10605	127	12	application	application	NOUN
ap-10605	127	13	,	,	PUNCT
ap-10605	127	14	it	it	PRON
ap-10605	127	15	is	be	AUX
ap-10605	127	16	necessary	necessary	ADJ
ap-10605	127	17	to	to	PART
ap-10605	127	18	find	find	VERB
ap-10605	127	19	the	the	DET
ap-10605	127	20	classification	classification	NOUN
ap-10605	127	21	of	of	ADP
ap-10605	127	22	subalgebras	subalgebra	NOUN
ap-10605	127	23	that	that	PRON
ap-10605	127	24	satisfies	satisfy	VERB
ap-10605	127	25	certain	certain	ADJ
ap-10605	127	26	conditions	condition	NOUN
ap-10605	127	27	.	.	PUNCT
ap-10605	128	1	this	this	DET
ap-10605	128	2	subtask	subtask	NOUN
ap-10605	128	3	is	be	AUX
ap-10605	128	4	rather	rather	ADV
ap-10605	128	5	complicated	complicated	ADJ
ap-10605	128	6	itself	itself	PRON
ap-10605	128	7	.	.	PUNCT
ap-10605	129	1	nevertheless	nevertheless	ADV
ap-10605	129	2	,	,	PUNCT
ap-10605	129	3	this	this	DET
ap-10605	129	4	algorithm	algorithm	NOUN
ap-10605	129	5	is	be	AUX
ap-10605	129	6	extremely	extremely	ADV
ap-10605	129	7	efficient	efficient	ADJ
ap-10605	129	8	in	in	ADP
ap-10605	129	9	constructing	construct	VERB
ap-10605	129	10	generic	generic	ADJ
ap-10605	129	11	realizations	realization	NOUN
ap-10605	129	12	and	and	CCONJ
ap-10605	129	13	can	can	AUX
ap-10605	129	14	be	be	AUX
ap-10605	129	15	successfully	successfully	ADV
ap-10605	129	16	applied	apply	VERB
ap-10605	129	17	to	to	ADP
ap-10605	129	18	physically	physically	ADV
ap-10605	129	19	interesting	interesting	ADJ
ap-10605	129	20	high	high	ADJ
ap-10605	129	21	-	-	PUNCT
ap-10605	129	22	dimensional	dimensional	ADJ
ap-10605	129	23	algebras	algebra	NOUN
ap-10605	129	24	.	.	PUNCT
ap-10605	130	1	appendix	appendix	VERB
ap-10605	130	2	a	a	DET
ap-10605	130	3	contains	contain	VERB
ap-10605	130	4	generic	generic	ADJ
ap-10605	130	5	realizations	realization	NOUN
ap-10605	130	6	of	of	ADP
ap-10605	130	7	three	three	NUM
ap-10605	130	8	important	important	ADJ
ap-10605	130	9	conformal	conformal	ADJ
ap-10605	130	10	lie	lie	NOUN
ap-10605	130	11	algebras	algebras	PROPN
ap-10605	130	12	c(3	c(3	PROPN
ap-10605	130	13	,	,	PUNCT
ap-10605	130	14	1	1	NUM
ap-10605	130	15	)	)	PUNCT
ap-10605	130	16	,	,	PUNCT
ap-10605	130	17	c(3	c(3	ADJ
ap-10605	130	18	,	,	PUNCT
ap-10605	130	19	0	0	NUM
ap-10605	130	20	)	)	PUNCT
ap-10605	130	21	and	and	CCONJ
ap-10605	130	22	c(2	c(2	PROPN
ap-10605	130	23	,	,	PUNCT
ap-10605	130	24	1	1	NUM
ap-10605	130	25	)	)	PUNCT
ap-10605	130	26	,	,	PUNCT
ap-10605	130	27	which	which	PRON
ap-10605	130	28	are	be	AUX
ap-10605	130	29	constructed	construct	VERB
ap-10605	130	30	using	use	VERB
ap-10605	130	31	the	the	DET
ap-10605	130	32	algebraic	algebraic	ADJ
ap-10605	130	33	method	method	NOUN
ap-10605	130	34	.	.	PUNCT
ap-10605	131	1	3.4	3.4	NUM
ap-10605	131	2	.	.	PUNCT
ap-10605	131	3	representations	representation	NOUN
ap-10605	131	4	and	and	CCONJ
ap-10605	131	5	realizations	realization	NOUN
ap-10605	131	6	with	with	ADP
ap-10605	131	7	linear	linear	ADJ
ap-10605	131	8	coefficients	coefficient	NOUN
ap-10605	131	9	for	for	ADP
ap-10605	131	10	each	each	DET
ap-10605	131	11	lie	lie	NOUN
ap-10605	131	12	algebra	algebra	NOUN
ap-10605	131	13	,	,	PUNCT
ap-10605	131	14	there	there	PRON
ap-10605	131	15	are	be	VERB
ap-10605	131	16	always	always	ADV
ap-10605	131	17	two	two	NUM
ap-10605	131	18	representations	representation	NOUN
ap-10605	131	19	:	:	PUNCT
ap-10605	131	20	trivial	trivial	ADJ
ap-10605	131	21	and	and	CCONJ
ap-10605	131	22	adjoint	adjoint	NOUN
ap-10605	131	23	.	.	PUNCT
ap-10605	132	1	trivial	trivial	ADJ
ap-10605	132	2	representation	representation	NOUN
ap-10605	132	3	has	have	VERB
ap-10605	132	4	no	no	DET
ap-10605	132	5	essential	essential	ADJ
ap-10605	132	6	applications	application	NOUN
ap-10605	132	7	but	but	CCONJ
ap-10605	132	8	adjoint	adjoint	NOUN
ap-10605	132	9	representation	representation	NOUN
ap-10605	132	10	can	can	AUX
ap-10605	132	11	always	always	ADV
ap-10605	132	12	give	give	VERB
ap-10605	132	13	us	we	PRON
ap-10605	132	14	the	the	DET
ap-10605	132	15	realization	realization	NOUN
ap-10605	132	16	with	with	ADP
ap-10605	132	17	linear	linear	ADJ
ap-10605	132	18	coefficients	coefficient	NOUN
ap-10605	132	19	.	.	PUNCT
ap-10605	133	1	indeed	indeed	ADV
ap-10605	133	2	,	,	PUNCT
ap-10605	133	3	if	if	SCONJ
ap-10605	133	4	the	the	DET
ap-10605	133	5	lie	lie	NOUN
ap-10605	133	6	algebra	algebra	NOUN
ap-10605	133	7	g	g	NOUN
ap-10605	133	8	has	have	VERB
ap-10605	133	9	a	a	DET
ap-10605	133	10	representation	representation	NOUN
ap-10605	133	11	φ	φ	NOUN
ap-10605	133	12	with	with	ADP
ap-10605	133	13	the	the	DET
ap-10605	133	14	corresponding	correspond	VERB
ap-10605	133	15	(	(	PUNCT
ap-10605	133	16	m	m	PROPN
ap-10605	133	17	×	×	NOUN
ap-10605	133	18	m)-matrices	m)-matrice	NOUN
ap-10605	133	19	φi	φi	ADV
ap-10605	133	20	,	,	PUNCT
ap-10605	133	21	then	then	ADV
ap-10605	133	22	the	the	DET
ap-10605	133	23	set	set	NOUN
ap-10605	133	24	of	of	ADP
ap-10605	133	25	operators	operator	NOUN
ap-10605	133	26	:	:	PUNCT
ap-10605	133	27	ei	ei	X
ap-10605	133	28	=	=	PUNCT
ap-10605	133	29	m∑	m∑	PROPN
ap-10605	133	30	α=1	α=1	SYM
ap-10605	133	31			PROPN
ap-10605	133	32	m∑	m∑	ADV
ap-10605	133	33	β=1	β=1	SYM
ap-10605	133	34	(	(	PUNCT
ap-10605	133	35	φi)β	φi)β	PROPN
ap-10605	133	36	αxβ	αxβ	NOUN
ap-10605	133	37	∂α	∂α	NOUN
ap-10605	133	38	generates	generate	VERB
ap-10605	133	39	the	the	DET
ap-10605	133	40	realization	realization	NOUN
ap-10605	133	41	g	g	NOUN
ap-10605	133	42	and	and	CCONJ
ap-10605	133	43	vice	vice	ADV
ap-10605	133	44	versa	versa	ADV
ap-10605	133	45	:	:	PUNCT
ap-10605	133	46	any	any	DET
ap-10605	133	47	realization	realization	NOUN
ap-10605	133	48	with	with	ADP
ap-10605	133	49	linear	linear	ADJ
ap-10605	133	50	homogeneous	homogeneous	ADJ
ap-10605	133	51	coefficients	coefficient	NOUN
ap-10605	133	52	generates	generate	VERB
ap-10605	133	53	the	the	DET
ap-10605	133	54	matrix	matrix	NOUN
ap-10605	133	55	representation	representation	NOUN
ap-10605	133	56	of	of	ADP
ap-10605	133	57	the	the	DET
ap-10605	133	58	lie	lie	NOUN
ap-10605	133	59	algebra	algebra	NOUN
ap-10605	133	60	.	.	PUNCT
ap-10605	134	1	this	this	DET
ap-10605	134	2	method	method	NOUN
ap-10605	134	3	of	of	ADP
ap-10605	134	4	constructing	construct	VERB
ap-10605	134	5	realizations	realization	NOUN
ap-10605	134	6	is	be	AUX
ap-10605	134	7	particularly	particularly	ADV
ap-10605	134	8	interesting	interesting	ADJ
ap-10605	134	9	for	for	ADP
ap-10605	134	10	the	the	DET
ap-10605	134	11	case	case	NOUN
ap-10605	134	12	of	of	ADP
ap-10605	134	13	simple	simple	ADJ
ap-10605	134	14	and	and	CCONJ
ap-10605	134	15	semisimple	semisimple	ADJ
ap-10605	134	16	lie	lie	NOUN
ap-10605	134	17	algebras	algebra	NOUN
ap-10605	134	18	,	,	PUNCT
ap-10605	134	19	since	since	SCONJ
ap-10605	134	20	it	it	PRON
ap-10605	134	21	is	be	AUX
ap-10605	134	22	difficult	difficult	ADJ
ap-10605	134	23	to	to	PART
ap-10605	134	24	apply	apply	VERB
ap-10605	134	25	the	the	DET
ap-10605	134	26	direct	direct	ADJ
ap-10605	134	27	method	method	NOUN
ap-10605	134	28	to	to	ADP
ap-10605	134	29	them	they	PRON
ap-10605	134	30	due	due	ADP
ap-10605	134	31	to	to	ADP
ap-10605	134	32	the	the	DET
ap-10605	134	33	lack	lack	NOUN
ap-10605	134	34	of	of	ADP
ap-10605	134	35	megaideals	megaideal	NOUN
ap-10605	134	36	.	.	PUNCT
ap-10605	135	1	it	it	PRON
ap-10605	135	2	is	be	AUX
ap-10605	135	3	also	also	ADV
ap-10605	135	4	difficult	difficult	ADJ
ap-10605	135	5	to	to	PART
ap-10605	135	6	classify	classify	VERB
ap-10605	135	7	subalgebras	subalgebra	NOUN
ap-10605	135	8	of	of	ADP
ap-10605	135	9	simple	simple	ADJ
ap-10605	135	10	algebras	algebra	NOUN
ap-10605	135	11	for	for	ADP
ap-10605	135	12	the	the	DET
ap-10605	135	13	application	application	NOUN
ap-10605	135	14	of	of	ADP
ap-10605	135	15	the	the	DET
ap-10605	135	16	shirokov	shirokov	NOUN
ap-10605	135	17	method	method	NOUN
ap-10605	135	18	,	,	PUNCT
ap-10605	135	19	but	but	CCONJ
ap-10605	135	20	,	,	PUNCT
ap-10605	135	21	at	at	ADP
ap-10605	135	22	the	the	DET
ap-10605	135	23	same	same	ADJ
ap-10605	135	24	time	time	NOUN
ap-10605	135	25	,	,	PUNCT
ap-10605	135	26	weighted	weight	VERB
ap-10605	135	27	representations	representation	NOUN
ap-10605	135	28	are	be	AUX
ap-10605	135	29	known	know	VERB
ap-10605	135	30	for	for	ADP
ap-10605	135	31	simple	simple	ADJ
ap-10605	135	32	lie	lie	NOUN
ap-10605	135	33	algebras	algebra	NOUN
ap-10605	135	34	.	.	PUNCT
ap-10605	136	1	it	it	PRON
ap-10605	136	2	is	be	AUX
ap-10605	136	3	clear	clear	ADJ
ap-10605	136	4	that	that	SCONJ
ap-10605	136	5	some	some	DET
ap-10605	136	6	realizations	realization	NOUN
ap-10605	136	7	with	with	ADP
ap-10605	136	8	non	non	ADJ
ap-10605	136	9	-	-	ADJ
ap-10605	136	10	linear	linear	ADJ
ap-10605	136	11	coefficients	coefficient	NOUN
ap-10605	136	12	will	will	AUX
ap-10605	136	13	be	be	AUX
ap-10605	136	14	equivalent	equivalent	ADJ
ap-10605	136	15	to	to	ADP
ap-10605	136	16	those	those	PRON
ap-10605	136	17	obtained	obtain	VERB
ap-10605	136	18	from	from	ADP
ap-10605	136	19	representations	representation	NOUN
ap-10605	136	20	,	,	PUNCT
ap-10605	136	21	but	but	CCONJ
ap-10605	136	22	the	the	DET
ap-10605	136	23	more	more	ADV
ap-10605	136	24	interesting	interesting	ADJ
ap-10605	136	25	question	question	NOUN
ap-10605	136	26	is	be	AUX
ap-10605	136	27	whether	whether	SCONJ
ap-10605	136	28	all	all	DET
ap-10605	136	29	realizations	realization	NOUN
ap-10605	136	30	can	can	AUX
ap-10605	136	31	be	be	AUX
ap-10605	136	32	obtained	obtain	VERB
ap-10605	136	33	from	from	ADP
ap-10605	136	34	the	the	DET
ap-10605	136	35	representations	representation	NOUN
ap-10605	136	36	.	.	PUNCT
ap-10605	137	1	to	to	PART
ap-10605	137	2	investigate	investigate	VERB
ap-10605	137	3	this	this	DET
ap-10605	137	4	connections	connection	NOUN
ap-10605	137	5	between	between	ADP
ap-10605	137	6	realizations	realization	NOUN
ap-10605	137	7	and	and	CCONJ
ap-10605	137	8	representations	representation	NOUN
ap-10605	137	9	,	,	PUNCT
ap-10605	137	10	we	we	PRON
ap-10605	137	11	considered	consider	VERB
ap-10605	137	12	the	the	DET
ap-10605	137	13	smallest	small	ADJ
ap-10605	137	14	simple	simple	ADJ
ap-10605	137	15	lie	lie	NOUN
ap-10605	137	16	algebra	algebra	PROPN
ap-10605	137	17	sl(2,c	sl(2,c	ADV
ap-10605	137	18	)	)	PUNCT
ap-10605	137	19	in	in	ADP
ap-10605	137	20	section	section	NOUN
ap-10605	137	21	4	4	NUM
ap-10605	137	22	.	.	PUNCT
ap-10605	137	23	note	note	VERB
ap-10605	137	24	that	that	SCONJ
ap-10605	137	25	this	this	DET
ap-10605	137	26	case	case	NOUN
ap-10605	137	27	has	have	AUX
ap-10605	137	28	been	be	AUX
ap-10605	137	29	studied	study	VERB
ap-10605	137	30	by	by	ADP
ap-10605	137	31	many	many	ADJ
ap-10605	137	32	authors	author	NOUN
ap-10605	137	33	in	in	ADP
ap-10605	137	34	the	the	DET
ap-10605	137	35	past	past	NOUN
ap-10605	137	36	,	,	PUNCT
ap-10605	137	37	for	for	ADP
ap-10605	137	38	example	example	NOUN
ap-10605	138	1	[	[	X
ap-10605	138	2	8	8	NUM
ap-10605	138	3	]	]	PUNCT
ap-10605	138	4	.	.	PUNCT
ap-10605	139	1	4	4	X
ap-10605	139	2	.	.	X
ap-10605	139	3	realizations	realization	NOUN
ap-10605	139	4	and	and	CCONJ
ap-10605	139	5	representations	representation	NOUN
ap-10605	139	6	of	of	ADP
ap-10605	139	7	sl(2,c	sl(2,c	NOUN
ap-10605	139	8	)	)	PUNCT
ap-10605	139	9	consider	consider	VERB
ap-10605	139	10	the	the	DET
ap-10605	139	11	lie	lie	NOUN
ap-10605	139	12	algebra	algebra	PROPN
ap-10605	139	13	sl(2,c	sl(2,c	NOUN
ap-10605	139	14	)	)	PUNCT
ap-10605	139	15	of	of	ADP
ap-10605	139	16	2	2	NUM
ap-10605	139	17	×	×	NOUN
ap-10605	139	18	2	2	NUM
ap-10605	139	19	traceless	traceless	NOUN
ap-10605	139	20	complex	complex	ADJ
ap-10605	139	21	matrices	matrix	NOUN
ap-10605	139	22	,	,	PUNCT
ap-10605	139	23	the	the	DET
ap-10605	139	24	standard	standard	ADJ
ap-10605	139	25	choice	choice	NOUN
ap-10605	139	26	of	of	ADP
ap-10605	139	27	basis	basis	NOUN
ap-10605	139	28	is	be	AUX
ap-10605	139	29	:	:	PUNCT
ap-10605	139	30	e	e	X
ap-10605	139	31	=	=	SYM
ap-10605	139	32	(	(	PUNCT
ap-10605	139	33	0	0	NUM
ap-10605	139	34	1	1	NUM
ap-10605	139	35	0	0	NUM
ap-10605	139	36	0	0	NUM
ap-10605	139	37	)	)	PUNCT
ap-10605	139	38	,	,	PUNCT
ap-10605	140	1	f	f	X
ap-10605	140	2	=	=	PRON
ap-10605	140	3	(	(	PUNCT
ap-10605	140	4	0	0	NUM
ap-10605	140	5	0	0	NUM
ap-10605	140	6	1	1	NUM
ap-10605	140	7	0	0	NUM
ap-10605	140	8	)	)	PUNCT
ap-10605	140	9	,	,	PUNCT
ap-10605	140	10	h	h	NOUN
ap-10605	140	11	=	=	PUNCT
ap-10605	140	12	(	(	PUNCT
ap-10605	140	13	1	1	NUM
ap-10605	140	14	0	0	NUM
ap-10605	140	15	0	0	NUM
ap-10605	140	16	−1	−1	NOUN
ap-10605	140	17	)	)	PUNCT
ap-10605	140	18	,	,	PUNCT
ap-10605	140	19	(	(	PUNCT
ap-10605	140	20	1	1	X
ap-10605	140	21	)	)	PUNCT
ap-10605	141	1	[	[	X
ap-10605	141	2	e	e	X
ap-10605	141	3	,	,	PUNCT
ap-10605	141	4	f	f	X
ap-10605	141	5	]	]	X
ap-10605	141	6	=	=	SYM
ap-10605	141	7	h	h	NOUN
ap-10605	141	8	,	,	PUNCT
ap-10605	142	1	[	[	X
ap-10605	142	2	h	h	X
ap-10605	142	3	,	,	PUNCT
ap-10605	142	4	e	e	X
ap-10605	142	5	]	]	X
ap-10605	142	6	=	=	SYM
ap-10605	142	7	2e	2e	NOUN
ap-10605	142	8	,	,	PUNCT
ap-10605	142	9	[	[	X
ap-10605	142	10	f	f	X
ap-10605	142	11	,	,	PUNCT
ap-10605	142	12	h	h	NOUN
ap-10605	142	13	]	]	X
ap-10605	142	14	=	=	SYM
ap-10605	142	15	2f	2f	NUM
ap-10605	142	16	.	.	PUNCT
ap-10605	143	1	(	(	PUNCT
ap-10605	143	2	2	2	X
ap-10605	143	3	)	)	PUNCT
ap-10605	143	4	let	let	VERB
ap-10605	143	5	us	we	PRON
ap-10605	143	6	also	also	ADV
ap-10605	143	7	consider	consider	VERB
ap-10605	143	8	the	the	DET
ap-10605	143	9	basis	basis	NOUN
ap-10605	143	10	e1	e1	NOUN
ap-10605	143	11	,	,	PUNCT
ap-10605	143	12	e2	e2	PROPN
ap-10605	143	13	,	,	PUNCT
ap-10605	143	14	e3	e3	NOUN
ap-10605	143	15	,	,	PUNCT
ap-10605	143	16	where	where	SCONJ
ap-10605	143	17	:	:	PUNCT
ap-10605	143	18	e	e	X
ap-10605	143	19	=	=	SYM
ap-10605	143	20	e1	e1	PROPN
ap-10605	143	21	,	,	PUNCT
ap-10605	143	22	h	h	NOUN
ap-10605	143	23	=	=	SYM
ap-10605	143	24	−2e2	−2e2	PROPN
ap-10605	143	25	,	,	PUNCT
ap-10605	143	26	f	f	PROPN
ap-10605	143	27	=	=	SYM
ap-10605	143	28	−e3	−e3	PROPN
ap-10605	143	29	,	,	PUNCT
ap-10605	143	30	and	and	CCONJ
ap-10605	143	31	commutation	commutation	NOUN
ap-10605	143	32	relations	relation	NOUN
ap-10605	143	33	have	have	VERB
ap-10605	143	34	the	the	DET
ap-10605	143	35	form	form	NOUN
ap-10605	143	36	:	:	PUNCT
ap-10605	144	1	[	[	X
ap-10605	144	2	e1	e1	NOUN
ap-10605	144	3	,	,	PUNCT
ap-10605	144	4	e2	e2	X
ap-10605	144	5	]	]	PUNCT
ap-10605	144	6	=	=	SYM
ap-10605	144	7	e1	e1	PROPN
ap-10605	144	8	,	,	PUNCT
ap-10605	144	9	[	[	X
ap-10605	144	10	e2	e2	NOUN
ap-10605	144	11	,	,	PUNCT
ap-10605	144	12	e3	e3	NOUN
ap-10605	144	13	]	]	PUNCT
ap-10605	144	14	=	=	PUNCT
ap-10605	144	15	e3	e3	NOUN
ap-10605	144	16	,	,	PUNCT
ap-10605	144	17	[	[	X
ap-10605	144	18	e1	e1	NOUN
ap-10605	144	19	,	,	PUNCT
ap-10605	144	20	e3	e3	NOUN
ap-10605	144	21	]	]	PUNCT
ap-10605	144	22	=	=	SYM
ap-10605	144	23	2e2	2e2	PROPN
ap-10605	144	24	.	.	PUNCT
ap-10605	144	25	(	(	PUNCT
ap-10605	144	26	3	3	X
ap-10605	144	27	)	)	PUNCT
ap-10605	144	28	irreducible	irreducible	ADJ
ap-10605	144	29	finite	finite	ADJ
ap-10605	144	30	-	-	ADJ
ap-10605	144	31	dimensional	dimensional	ADJ
ap-10605	144	32	weight	weight	NOUN
ap-10605	144	33	representations	representation	NOUN
ap-10605	144	34	of	of	ADP
ap-10605	144	35	sl(2,c	sl(2,c	NOUN
ap-10605	144	36	)	)	PUNCT
ap-10605	144	37	in	in	ADP
ap-10605	144	38	the	the	DET
ap-10605	144	39	basis	basis	NOUN
ap-10605	144	40	e	e	NOUN
ap-10605	144	41	,	,	PUNCT
ap-10605	144	42	f	f	X
ap-10605	144	43	,	,	PUNCT
ap-10605	144	44	h	h	NOUN
ap-10605	144	45	are	be	AUX
ap-10605	144	46	:	:	PUNCT
ap-10605	144	47	φ1	φ1	PROPN
ap-10605	144	48	=	=	SYM
ap-10605	145	1			PROPN
ap-10605	145	2	0	0	NUM
ap-10605	145	3	1	1	NUM
ap-10605	145	4	0	0	NUM
ap-10605	145	5	·	·	PUNCT
ap-10605	145	6	·	·	PUNCT
ap-10605	145	7	·	·	PUNCT
ap-10605	145	8	0	0	NUM
ap-10605	145	9	0	0	NUM
ap-10605	145	10	0	0	NUM
ap-10605	145	11	2	2	NUM
ap-10605	145	12	·	·	PUNCT
ap-10605	145	13	·	·	PUNCT
ap-10605	145	14	·	·	PUNCT
ap-10605	145	15	0	0	NUM
ap-10605	145	16	...	...	PUNCT
ap-10605	145	17	...	...	PUNCT
ap-10605	145	18	.	.	PUNCT
ap-10605	145	19	.	.	PUNCT
ap-10605	145	20	.	.	PUNCT
ap-10605	145	21	.	.	PUNCT
ap-10605	145	22	.	.	PUNCT
ap-10605	145	23	.	.	PUNCT
ap-10605	146	1	...	...	PUNCT
ap-10605	147	1	0	0	NUM
ap-10605	147	2	0	0	NUM
ap-10605	147	3	·	·	PUNCT
ap-10605	147	4	·	·	PUNCT
ap-10605	147	5	·	·	PUNCT
ap-10605	147	6	0	0	PUNCT
ap-10605	148	1	d	d	NOUN
ap-10605	148	2	0	0	NUM
ap-10605	148	3	0	0	NUM
ap-10605	148	4	·	·	PUNCT
ap-10605	148	5	·	·	PUNCT
ap-10605	148	6	·	·	SYM
ap-10605	148	7	0	0	NUM
ap-10605	148	8	0	0	NUM
ap-10605	149	1			PROPN
ap-10605	149	2	,	,	PUNCT
ap-10605	149	3	φ2	φ2	NOUN
ap-10605	149	4	=	=	NOUN
ap-10605	149	5	1	1	NUM
ap-10605	149	6	2	2	NUM
ap-10605	149	7	−d	−d	NOUN
ap-10605	149	8	0	0	NUM
ap-10605	149	9	...	...	SYM
ap-10605	149	10	0	0	NUM
ap-10605	149	11	0	0	X
ap-10605	149	12	−d+2	−d+2	PROPN
ap-10605	149	13	...	...	PUNCT
ap-10605	149	14	0	0	NUM
ap-10605	149	15	...	...	PUNCT
ap-10605	149	16	...	...	PUNCT
ap-10605	149	17	.	.	PUNCT
ap-10605	149	18	.	.	PUNCT
ap-10605	149	19	.	.	PUNCT
ap-10605	149	20	.	.	PUNCT
ap-10605	149	21	.	.	PUNCT
ap-10605	150	1	.	.	PUNCT
ap-10605	151	1	0	0	NUM
ap-10605	151	2	0	0	NUM
ap-10605	151	3	...	...	PUNCT
ap-10605	152	1	d	d	X
ap-10605	152	2			PROPN
ap-10605	152	3	,	,	PUNCT
ap-10605	152	4	φ3	φ3	NOUN
ap-10605	152	5	=	=	PUNCT
ap-10605	152	6			X
ap-10605	152	7	0	0	NUM
ap-10605	152	8	0	0	NUM
ap-10605	152	9	·	·	PUNCT
ap-10605	152	10	·	·	PUNCT
ap-10605	152	11	·	·	SYM
ap-10605	152	12	0	0	SYM
ap-10605	152	13	0	0	NUM
ap-10605	152	14	−d	−d	ADJ
ap-10605	152	15	0	0	NUM
ap-10605	152	16	·	·	PUNCT
ap-10605	152	17	·	·	PUNCT
ap-10605	152	18	·	·	PUNCT
ap-10605	152	19	0	0	NUM
ap-10605	152	20	0	0	NUM
ap-10605	152	21	0	0	NUM
ap-10605	152	22	−d+1	−d+1	PROPN
ap-10605	152	23	·	·	PUNCT
ap-10605	152	24	·	·	PUNCT
ap-10605	152	25	·	·	PUNCT
ap-10605	152	26	0	0	NUM
ap-10605	152	27	0	0	NUM
ap-10605	152	28	...	...	PUNCT
ap-10605	152	29	...	...	PUNCT
ap-10605	152	30	.	.	PUNCT
ap-10605	152	31	.	.	PUNCT
ap-10605	152	32	.	.	PUNCT
ap-10605	152	33	...	...	PUNCT
ap-10605	152	34	...	...	PUNCT
ap-10605	153	1	0	0	NUM
ap-10605	153	2	0	0	NUM
ap-10605	153	3	·	·	PUNCT
ap-10605	153	4	·	·	PUNCT
ap-10605	153	5	·	·	PUNCT
ap-10605	153	6	−1	−1	NOUN
ap-10605	153	7	0	0	PUNCT
ap-10605	154	1	.	.	VERB
ap-10605	154	2	the	the	DET
ap-10605	154	3	realizations	realization	NOUN
ap-10605	154	4	that	that	PRON
ap-10605	154	5	correspond	correspond	VERB
ap-10605	154	6	to	to	ADP
ap-10605	154	7	these	these	DET
ap-10605	154	8	representations	representation	NOUN
ap-10605	154	9	are	be	AUX
ap-10605	154	10	(	(	PUNCT
ap-10605	154	11	d	d	PROPN
ap-10605	154	12	∈	∈	PROPN
ap-10605	154	13	n	n	CCONJ
ap-10605	154	14	):	):	PUNCT
ap-10605	154	15	e1	e1	NOUN
ap-10605	154	16	=	=	SYM
ap-10605	154	17	d+1∑	d+1∑	PROPN
ap-10605	154	18	α=2	α=2	X
ap-10605	154	19	(	(	PUNCT
ap-10605	154	20	α	α	NOUN
ap-10605	154	21	−	−	PROPN
ap-10605	154	22	1)xα−1∂α	1)xα−1∂α	NUM
ap-10605	154	23	,	,	PUNCT
ap-10605	154	24	e2	e2	PROPN
ap-10605	154	25	=	=	PUNCT
ap-10605	154	26	d+1∑	d+1∑	PROPN
ap-10605	154	27	α=1	α=1	X
ap-10605	154	28	(	(	PUNCT
ap-10605	154	29	−d	−d	VERB
ap-10605	154	30	2	2	NUM
ap-10605	154	31	−	−	NOUN
ap-10605	154	32	1	1	NUM
ap-10605	154	33	+	+	NUM
ap-10605	154	34	α	α	NOUN
ap-10605	154	35	)	)	PUNCT
ap-10605	154	36	xα∂α	xα∂α	ADV
ap-10605	154	37	,	,	PUNCT
ap-10605	154	38	e3	e3	VERB
ap-10605	154	39	=	=	SYM
ap-10605	154	40	d∑	d∑	PROPN
ap-10605	154	41	α=1	α=1	X
ap-10605	154	42	(	(	PUNCT
ap-10605	154	43	−d	−d	PROPN
ap-10605	154	44	+	+	CCONJ
ap-10605	154	45	α	α	PROPN
ap-10605	154	46	−	−	PROPN
ap-10605	154	47	1)xα+1∂α	1)xα+1∂α	NUM
ap-10605	154	48	.	.	PUNCT
ap-10605	155	1	applying	apply	VERB
ap-10605	155	2	the	the	DET
ap-10605	155	3	direct	direct	ADJ
ap-10605	155	4	method	method	NOUN
ap-10605	155	5	we	we	PRON
ap-10605	155	6	obtain	obtain	VERB
ap-10605	155	7	the	the	DET
ap-10605	155	8	exhaustive	exhaustive	ADJ
ap-10605	155	9	list	list	NOUN
ap-10605	155	10	of	of	ADP
ap-10605	155	11	inequivalent	inequivalent	ADJ
ap-10605	155	12	realizations	realization	NOUN
ap-10605	155	13	of	of	ADP
ap-10605	155	14	sl(2,c	sl(2,c	NOUN
ap-10605	155	15	):	):	PUNCT
ap-10605	155	16	(	(	PUNCT
ap-10605	155	17	1	1	NUM
ap-10605	155	18	.	.	PUNCT
ap-10605	155	19	)	)	PUNCT
ap-10605	155	20	∂1	∂1	ADJ
ap-10605	155	21	,	,	PUNCT
ap-10605	156	1	x1∂1	x1∂1	PROPN
ap-10605	156	2	+	+	PROPN
ap-10605	157	1	x2∂2	x2∂2	ADV
ap-10605	157	2	,	,	PUNCT
ap-10605	157	3	x2	x2	PROPN
ap-10605	157	4	1∂1	1∂1	NUM
ap-10605	157	5	+	+	CCONJ
ap-10605	157	6	2x1x2∂2	2x1x2∂2	PROPN
ap-10605	157	7	+	+	CCONJ
ap-10605	157	8	x2∂3	x2∂3	PROPN
ap-10605	157	9	,	,	PUNCT
ap-10605	157	10	(	(	PUNCT
ap-10605	157	11	2	2	NUM
ap-10605	157	12	.	.	NUM
ap-10605	157	13	)	)	PUNCT
ap-10605	157	14	∂1	∂1	ADJ
ap-10605	157	15	,	,	PUNCT
ap-10605	157	16	x1∂1	x1∂1	PROPN
ap-10605	158	1	+	+	PROPN
ap-10605	158	2	x2∂2	x2∂2	ADV
ap-10605	158	3	,	,	PUNCT
ap-10605	158	4	(	(	PUNCT
ap-10605	158	5	x2	x2	NOUN
ap-10605	158	6	1	1	NUM
ap-10605	158	7	+	+	NUM
ap-10605	158	8	x2	x2	PROPN
ap-10605	158	9	2)∂1	2)∂1	NUM
ap-10605	158	10	+	+	CCONJ
ap-10605	158	11	2x1x2∂2	2x1x2∂2	NOUN
ap-10605	158	12	,	,	PUNCT
ap-10605	158	13	(	(	PUNCT
ap-10605	158	14	3	3	NUM
ap-10605	158	15	.	.	PUNCT
ap-10605	158	16	)	)	PUNCT
ap-10605	158	17	∂1	∂1	ADJ
ap-10605	158	18	,	,	PUNCT
ap-10605	158	19	x1∂1	x1∂1	PROPN
ap-10605	159	1	+	+	PROPN
ap-10605	159	2	x2∂2	x2∂2	ADV
ap-10605	159	3	,	,	PUNCT
ap-10605	159	4	x2	x2	PROPN
ap-10605	159	5	1∂1	1∂1	NUM
ap-10605	159	6	+	+	CCONJ
ap-10605	159	7	2x1x2∂2	2x1x2∂2	PROPN
ap-10605	159	8	,	,	PUNCT
ap-10605	159	9	(	(	PUNCT
ap-10605	159	10	4	4	NUM
ap-10605	159	11	.	.	PUNCT
ap-10605	159	12	)	)	PUNCT
ap-10605	160	1	∂1	∂1	ADJ
ap-10605	160	2	,	,	PUNCT
ap-10605	160	3	x1∂1	x1∂1	PROPN
ap-10605	160	4	,	,	PUNCT
ap-10605	160	5	x2	x2	PROPN
ap-10605	160	6	1∂1	1∂1	NUM
ap-10605	160	7	.	.	PUNCT
ap-10605	161	1	note	note	VERB
ap-10605	161	2	that	that	SCONJ
ap-10605	161	3	this	this	DET
ap-10605	161	4	list	list	NOUN
ap-10605	161	5	contains	contain	VERB
ap-10605	161	6	one	one	NUM
ap-10605	161	7	less	less	ADJ
ap-10605	161	8	realization	realization	NOUN
ap-10605	161	9	than	than	ADP
ap-10605	161	10	the	the	DET
ap-10605	161	11	similar	similar	ADJ
ap-10605	161	12	list	list	NOUN
ap-10605	161	13	obtained	obtain	VERB
ap-10605	161	14	for	for	ADP
ap-10605	161	15	the	the	DET
ap-10605	161	16	case	case	NOUN
ap-10605	161	17	of	of	ADP
ap-10605	161	18	real	real	ADJ
ap-10605	161	19	numbers	number	NOUN
ap-10605	161	20	[	[	X
ap-10605	161	21	4	4	NUM
ap-10605	161	22	]	]	PUNCT
ap-10605	161	23	.	.	PUNCT
ap-10605	162	1	to	to	PART
ap-10605	162	2	establish	establish	VERB
ap-10605	162	3	the	the	DET
ap-10605	162	4	correspondence	correspondence	NOUN
ap-10605	162	5	between	between	ADP
ap-10605	162	6	the	the	DET
ap-10605	162	7	realizations	realization	NOUN
ap-10605	162	8	and	and	CCONJ
ap-10605	162	9	representations	representation	NOUN
ap-10605	162	10	,	,	PUNCT
ap-10605	162	11	we	we	PRON
ap-10605	162	12	consider	consider	VERB
ap-10605	162	13	different	different	ADJ
ap-10605	162	14	values	value	NOUN
ap-10605	162	15	of	of	ADP
ap-10605	162	16	d	d	PROPN
ap-10605	162	17	=	=	SYM
ap-10605	162	18	1	1	NUM
ap-10605	162	19	,	,	PUNCT
ap-10605	162	20	d	d	NOUN
ap-10605	162	21	=	=	SYM
ap-10605	162	22	2	2	NUM
ap-10605	162	23	,	,	PUNCT
ap-10605	162	24	d	d	NOUN
ap-10605	162	25	=	=	SYM
ap-10605	162	26	3	3	NUM
ap-10605	162	27	,	,	PUNCT
ap-10605	162	28	.	.	PUNCT
ap-10605	162	29	.	.	PUNCT
ap-10605	163	1	.	.	PUNCT
ap-10605	164	1	transform	transform	VERB
ap-10605	164	2	one	one	NUM
ap-10605	164	3	of	of	ADP
ap-10605	164	4	the	the	DET
ap-10605	164	5	operators	operator	NOUN
ap-10605	164	6	to	to	ADP
ap-10605	164	7	the	the	DET
ap-10605	164	8	form	form	NOUN
ap-10605	164	9	∂x1	∂x1	NOUN
ap-10605	164	10	and	and	CCONJ
ap-10605	164	11	look	look	VERB
ap-10605	164	12	for	for	ADP
ap-10605	164	13	the	the	DET
ap-10605	164	14	locally	locally	ADV
ap-10605	164	15	invertible	invertible	ADJ
ap-10605	164	16	transformations	transformation	NOUN
ap-10605	164	17	for	for	ADP
ap-10605	164	18	the	the	DET
ap-10605	164	19	rest	rest	NOUN
ap-10605	164	20	of	of	ADP
ap-10605	164	21	the	the	DET
ap-10605	164	22	variables	variable	NOUN
ap-10605	164	23	.	.	PUNCT
ap-10605	165	1	we	we	PRON
ap-10605	165	2	also	also	ADV
ap-10605	165	3	compare	compare	VERB
ap-10605	165	4	the	the	DET
ap-10605	165	5	ranks	rank	NOUN
ap-10605	165	6	of	of	ADP
ap-10605	165	7	the	the	DET
ap-10605	165	8	realizations	realization	NOUN
ap-10605	165	9	.	.	PUNCT
ap-10605	166	1	in	in	ADP
ap-10605	166	2	this	this	DET
ap-10605	166	3	way	way	NOUN
ap-10605	166	4	we	we	PRON
ap-10605	166	5	have	have	AUX
ap-10605	166	6	shown	show	VERB
ap-10605	166	7	that	that	SCONJ
ap-10605	166	8	the	the	DET
ap-10605	166	9	case	case	NOUN
ap-10605	166	10	d	d	NOUN
ap-10605	166	11	=	=	SYM
ap-10605	166	12	1	1	NUM
ap-10605	166	13	is	be	AUX
ap-10605	166	14	transformed	transform	VERB
ap-10605	166	15	to	to	ADP
ap-10605	166	16	the	the	DET
ap-10605	166	17	realization	realization	NOUN
ap-10605	166	18	(	(	PUNCT
ap-10605	166	19	3	3	NUM
ap-10605	166	20	.	.	PUNCT
ap-10605	166	21	)	)	PUNCT
ap-10605	166	22	by	by	ADP
ap-10605	166	23	the	the	DET
ap-10605	166	24	change	change	NOUN
ap-10605	166	25	of	of	ADP
ap-10605	166	26	variables	variable	NOUN
ap-10605	166	27	x̃1	x̃1	PROPN
ap-10605	167	1	=	=	PUNCT
ap-10605	167	2	x1	x1	PROPN
ap-10605	168	1	x2	x2	PROPN
ap-10605	168	2	,	,	PUNCT
ap-10605	168	3	x̃2	x̃2	PROPN
ap-10605	168	4	=	=	NOUN
ap-10605	168	5	1	1	NUM
ap-10605	168	6	x2	x2	NOUN
ap-10605	168	7	1	1	NUM
ap-10605	168	8	.	.	PUNCT
ap-10605	168	9	557	557	NUM
ap-10605	168	10	m.	m.	NOUN
ap-10605	168	11	nesterenko	nesterenko	PROPN
ap-10605	168	12	,	,	PUNCT
ap-10605	168	13	s.	s.	PROPN
ap-10605	168	14	pošta	pošta	PROPN
ap-10605	168	15	,	,	PUNCT
ap-10605	168	16	m.	m.	NOUN
ap-10605	168	17	staryi	staryi	PROPN
ap-10605	168	18	acta	acta	PROPN
ap-10605	168	19	polytechnica	polytechnica	PROPN
ap-10605	168	20	and	and	CCONJ
ap-10605	168	21	the	the	DET
ap-10605	168	22	case	case	NOUN
ap-10605	168	23	d	d	NOUN
ap-10605	168	24	=	=	SYM
ap-10605	168	25	2	2	NUM
ap-10605	168	26	is	be	AUX
ap-10605	168	27	transformed	transform	VERB
ap-10605	168	28	to	to	ADP
ap-10605	168	29	the	the	DET
ap-10605	168	30	realization	realization	NOUN
ap-10605	168	31	(	(	PUNCT
ap-10605	168	32	2	2	NUM
ap-10605	168	33	.	.	PUNCT
ap-10605	168	34	)	)	PUNCT
ap-10605	168	35	by	by	ADP
ap-10605	168	36	the	the	DET
ap-10605	168	37	change	change	NOUN
ap-10605	168	38	of	of	ADP
ap-10605	168	39	variables	variable	NOUN
ap-10605	168	40	x̃1	x̃1	PROPN
ap-10605	169	1	=	=	PUNCT
ap-10605	169	2	x2	x2	PROPN
ap-10605	169	3	+	+	PROPN
ap-10605	169	4	1	1	NUM
ap-10605	169	5	x1	x1	NOUN
ap-10605	169	6	−	−	NOUN
ap-10605	169	7	x2	x2	NOUN
ap-10605	169	8	2	2	NUM
ap-10605	169	9	+	+	SYM
ap-10605	169	10	x1x3	x1x3	X
ap-10605	169	11	,	,	PUNCT
ap-10605	169	12	x̃2	x̃2	PROPN
ap-10605	169	13	=	=	PUNCT
ap-10605	170	1	x	x	PUNCT
ap-10605	170	2	−	−	NOUN
ap-10605	170	3	1	1	NUM
ap-10605	170	4	2	2	NUM
ap-10605	170	5	1	1	NUM
ap-10605	170	6	(	(	PUNCT
ap-10605	170	7	x2	x2	NOUN
ap-10605	170	8	2	2	NUM
ap-10605	170	9	−	−	NOUN
ap-10605	170	10	x1x3	x1x3	PROPN
ap-10605	170	11	)	)	PUNCT
ap-10605	170	12	,	,	PUNCT
ap-10605	170	13	x̃3	x̃3	PROPN
ap-10605	171	1	=	=	NOUN
ap-10605	171	2	1	1	NUM
ap-10605	171	3	x1	x1	NOUN
ap-10605	171	4	.	.	PUNCT
ap-10605	172	1	the	the	DET
ap-10605	172	2	cases	case	NOUN
ap-10605	172	3	d	d	X
ap-10605	172	4	≥	≥	NUM
ap-10605	172	5	3	3	NUM
ap-10605	172	6	are	be	AUX
ap-10605	172	7	equivalent	equivalent	ADJ
ap-10605	172	8	to	to	ADP
ap-10605	172	9	the	the	DET
ap-10605	172	10	realization	realization	NOUN
ap-10605	172	11	(	(	PUNCT
ap-10605	172	12	1	1	NUM
ap-10605	172	13	.	.	PUNCT
ap-10605	172	14	)	)	PUNCT
ap-10605	173	1	since	since	SCONJ
ap-10605	173	2	all	all	PRON
ap-10605	173	3	of	of	ADP
ap-10605	173	4	them	they	PRON
ap-10605	173	5	are	be	AUX
ap-10605	173	6	of	of	ADP
ap-10605	173	7	the	the	DET
ap-10605	173	8	rank	rank	NOUN
ap-10605	173	9	three	three	NUM
ap-10605	173	10	.	.	PUNCT
ap-10605	174	1	the	the	DET
ap-10605	174	2	only	only	ADJ
ap-10605	174	3	realization	realization	NOUN
ap-10605	174	4	that	that	PRON
ap-10605	174	5	was	be	AUX
ap-10605	174	6	not	not	PART
ap-10605	174	7	obtained	obtain	VERB
ap-10605	174	8	from	from	ADP
ap-10605	174	9	the	the	DET
ap-10605	174	10	irreducible	irreducible	ADJ
ap-10605	174	11	weight	weight	NOUN
ap-10605	174	12	representations	representation	NOUN
ap-10605	174	13	is	be	AUX
ap-10605	174	14	the	the	DET
ap-10605	174	15	realization	realization	NOUN
ap-10605	174	16	of	of	ADP
ap-10605	174	17	the	the	DET
ap-10605	174	18	rank	rank	NOUN
ap-10605	174	19	one	one	NUM
ap-10605	174	20	(	(	PUNCT
ap-10605	174	21	4	4	NUM
ap-10605	174	22	.	.	PUNCT
ap-10605	174	23	)	)	PUNCT
ap-10605	174	24	.	.	PUNCT
ap-10605	175	1	to	to	PART
ap-10605	175	2	investigate	investigate	VERB
ap-10605	175	3	whether	whether	SCONJ
ap-10605	175	4	it	it	PRON
ap-10605	175	5	is	be	AUX
ap-10605	175	6	possible	possible	ADJ
ap-10605	175	7	to	to	PART
ap-10605	175	8	linearize	linearize	VERB
ap-10605	175	9	this	this	DET
ap-10605	175	10	realization	realization	NOUN
ap-10605	175	11	we	we	PRON
ap-10605	175	12	look	look	VERB
ap-10605	175	13	for	for	ADP
ap-10605	175	14	non	non	ADJ
ap-10605	175	15	-	-	ADJ
ap-10605	175	16	degenerate	degenerate	ADJ
ap-10605	175	17	transformations	transformation	NOUN
ap-10605	175	18	x̃α	x̃α	NOUN
ap-10605	175	19	=	=	X
ap-10605	175	20	fα(x	fα(x	NOUN
ap-10605	175	21	)	)	PUNCT
ap-10605	175	22	,	,	PUNCT
ap-10605	175	23	α	α	NOUN
ap-10605	175	24	=	=	SYM
ap-10605	175	25	1	1	NUM
ap-10605	175	26	,	,	PUNCT
ap-10605	175	27	.	.	PUNCT
ap-10605	176	1	.	.	PUNCT
ap-10605	176	2	.	.	PUNCT
ap-10605	177	1	,	,	PUNCT
ap-10605	177	2	m	m	PROPN
ap-10605	177	3	,	,	PUNCT
ap-10605	177	4	x	x	SYM
ap-10605	177	5	=	=	SYM
ap-10605	177	6	(	(	PUNCT
ap-10605	177	7	x1	x1	PROPN
ap-10605	177	8	,	,	PUNCT
ap-10605	177	9	x2	x2	PROPN
ap-10605	177	10	,	,	PUNCT
ap-10605	177	11	.	.	PUNCT
ap-10605	177	12	.	.	PUNCT
ap-10605	178	1	.	.	PUNCT
ap-10605	179	1	,	,	PUNCT
ap-10605	179	2	xm	xm	PROPN
ap-10605	179	3	)	)	PUNCT
ap-10605	179	4	such	such	ADJ
ap-10605	179	5	that	that	PRON
ap-10605	179	6	for	for	ADP
ap-10605	179	7	some	some	DET
ap-10605	179	8	complex	complex	ADJ
ap-10605	179	9	matrices	matrix	NOUN
ap-10605	179	10	a	a	DET
ap-10605	179	11	,	,	PUNCT
ap-10605	179	12	b	b	NOUN
ap-10605	179	13	and	and	CCONJ
ap-10605	179	14	c	c	NOUN
ap-10605	179	15	:	:	PUNCT
ap-10605	180	1	ẽ1	ẽ1	NOUN
ap-10605	180	2	=	=	SYM
ap-10605	180	3	(	(	PUNCT
ap-10605	180	4	aα1x̃1	aα1x̃1	ADJ
ap-10605	180	5	+	+	X
ap-10605	180	6	·	·	PUNCT
ap-10605	180	7	·	·	PUNCT
ap-10605	180	8	·	·	PUNCT
ap-10605	181	1	+	+	CCONJ
ap-10605	181	2	aαmx̃m)∂x̃α	aαmx̃m)∂x̃α	NOUN
ap-10605	181	3	,	,	PUNCT
ap-10605	181	4	ẽ2	ẽ2	PROPN
ap-10605	181	5	=	=	PRON
ap-10605	181	6	(	(	PUNCT
ap-10605	181	7	bα1x̃1	bα1x̃1	NOUN
ap-10605	181	8	+	+	X
ap-10605	181	9	·	·	PUNCT
ap-10605	181	10	·	·	PUNCT
ap-10605	181	11	·	·	PUNCT
ap-10605	182	1	+	+	NUM
ap-10605	182	2	bαmx̃m)∂x̃α	bαmx̃m)∂x̃α	NOUN
ap-10605	182	3	,	,	PUNCT
ap-10605	182	4	ẽ3	ẽ3	PROPN
ap-10605	182	5	=	=	SYM
ap-10605	182	6	(	(	PUNCT
ap-10605	182	7	cα1x̃1	cα1x̃1	NOUN
ap-10605	182	8	+	+	X
ap-10605	182	9	·	·	PUNCT
ap-10605	182	10	·	·	PUNCT
ap-10605	182	11	·	·	PUNCT
ap-10605	183	1	+	+	NUM
ap-10605	183	2	cαmx̃m)∂x̃α	cαmx̃m)∂x̃α	X
ap-10605	183	3	.	.	PUNCT
ap-10605	184	1	solving	solve	VERB
ap-10605	184	2	the	the	DET
ap-10605	184	3	obtained	obtain	VERB
ap-10605	184	4	system	system	NOUN
ap-10605	184	5	of	of	ADP
ap-10605	184	6	pdes	pde	NOUN
ap-10605	184	7	,	,	PUNCT
ap-10605	184	8	we	we	PRON
ap-10605	184	9	come	come	VERB
ap-10605	184	10	to	to	ADP
ap-10605	184	11	the	the	DET
ap-10605	184	12	functional	functional	ADJ
ap-10605	184	13	system	system	NOUN
ap-10605	184	14	that	that	PRON
ap-10605	184	15	is	be	AUX
ap-10605	184	16	linear	linear	ADJ
ap-10605	184	17	and	and	CCONJ
ap-10605	184	18	homogeneous	homogeneous	ADJ
ap-10605	184	19	with	with	ADP
ap-10605	184	20	respect	respect	NOUN
ap-10605	184	21	to	to	ADP
ap-10605	184	22	the	the	DET
ap-10605	184	23	functions	function	NOUN
ap-10605	184	24	fα(x	fα(x	NOUN
ap-10605	184	25	)	)	PUNCT
ap-10605	184	26	,	,	PUNCT
ap-10605	184	27	therefore	therefore	ADV
ap-10605	184	28	,	,	PUNCT
ap-10605	184	29	the	the	DET
ap-10605	184	30	jacobian	jacobian	ADJ
ap-10605	184	31	determinant	determinant	NOUN
ap-10605	184	32	is	be	AUX
ap-10605	184	33	zero	zero	NUM
ap-10605	184	34	and	and	CCONJ
ap-10605	184	35	non	non	ADJ
ap-10605	184	36	-	-	ADJ
ap-10605	184	37	degenerate	degenerate	ADJ
ap-10605	184	38	transformations	transformation	NOUN
ap-10605	184	39	do	do	AUX
ap-10605	184	40	not	not	PART
ap-10605	184	41	exist	exist	VERB
ap-10605	184	42	.	.	PUNCT
ap-10605	185	1	this	this	DET
ap-10605	185	2	simple	simple	ADJ
ap-10605	185	3	example	example	NOUN
ap-10605	185	4	allows	allow	VERB
ap-10605	185	5	us	we	PRON
ap-10605	185	6	to	to	PART
ap-10605	185	7	draw	draw	VERB
ap-10605	185	8	an	an	DET
ap-10605	185	9	important	important	ADJ
ap-10605	185	10	conclusion	conclusion	NOUN
ap-10605	185	11	that	that	SCONJ
ap-10605	185	12	irreducible	irreducible	ADJ
ap-10605	185	13	representations	representation	NOUN
ap-10605	185	14	do	do	AUX
ap-10605	185	15	not	not	PART
ap-10605	185	16	allow	allow	VERB
ap-10605	185	17	us	we	PRON
ap-10605	185	18	to	to	PART
ap-10605	185	19	obtain	obtain	VERB
ap-10605	185	20	all	all	DET
ap-10605	185	21	differential	differential	ADJ
ap-10605	185	22	equations	equation	NOUN
ap-10605	185	23	that	that	PRON
ap-10605	185	24	are	be	AUX
ap-10605	185	25	invariant	invariant	ADJ
ap-10605	185	26	under	under	ADP
ap-10605	185	27	a	a	DET
ap-10605	185	28	given	give	VERB
ap-10605	185	29	group	group	NOUN
ap-10605	185	30	or	or	CCONJ
ap-10605	185	31	lie	lie	NOUN
ap-10605	185	32	algebra	algebra	NOUN
ap-10605	185	33	.	.	PUNCT
ap-10605	186	1	5	5	X
ap-10605	186	2	.	.	X
ap-10605	186	3	realizations	realization	NOUN
ap-10605	186	4	of	of	ADP
ap-10605	186	5	conformal	conformal	NOUN
ap-10605	186	6	algebras	algebra	NOUN
ap-10605	186	7	consider	consider	VERB
ap-10605	186	8	three	three	NUM
ap-10605	186	9	important	important	ADJ
ap-10605	186	10	conformal	conformal	ADJ
ap-10605	186	11	groups	group	NOUN
ap-10605	186	12	:	:	PUNCT
ap-10605	186	13	the	the	DET
ap-10605	186	14	standard	standard	ADJ
ap-10605	186	15	conformal	conformal	NOUN
ap-10605	186	16	group	group	NOUN
ap-10605	186	17	c(3	c(3	PROPN
ap-10605	186	18	,	,	PUNCT
ap-10605	186	19	1	1	NUM
ap-10605	186	20	)	)	PUNCT
ap-10605	186	21	and	and	CCONJ
ap-10605	186	22	two	two	NUM
ap-10605	186	23	conformal	conformal	ADJ
ap-10605	186	24	groups	group	NOUN
ap-10605	186	25	of	of	ADP
ap-10605	186	26	pseudo	pseudo	NOUN
ap-10605	186	27	-	-	ADJ
ap-10605	186	28	euclidean	euclidean	ADJ
ap-10605	186	29	spaces	space	NOUN
ap-10605	186	30	c(3	c(3	ADV
ap-10605	186	31	,	,	PUNCT
ap-10605	186	32	0	0	NUM
ap-10605	186	33	)	)	PUNCT
ap-10605	186	34	and	and	CCONJ
ap-10605	186	35	c(2	c(2	PROPN
ap-10605	186	36	,	,	PUNCT
ap-10605	186	37	1	1	NUM
ap-10605	186	38	)	)	PUNCT
ap-10605	186	39	.	.	PUNCT
ap-10605	187	1	their	their	PRON
ap-10605	187	2	lie	lie	NOUN
ap-10605	187	3	algebras	algebra	NOUN
ap-10605	187	4	are	be	AUX
ap-10605	187	5	denoted	denote	VERB
ap-10605	187	6	c(3	c(3	PROPN
ap-10605	187	7	,	,	PUNCT
ap-10605	187	8	1	1	NUM
ap-10605	187	9	)	)	PUNCT
ap-10605	187	10	,	,	PUNCT
ap-10605	187	11	c(3	c(3	ADJ
ap-10605	187	12	,	,	PUNCT
ap-10605	187	13	0	0	NUM
ap-10605	187	14	)	)	PUNCT
ap-10605	187	15	and	and	CCONJ
ap-10605	187	16	c(2	c(2	PROPN
ap-10605	187	17	,	,	PUNCT
ap-10605	187	18	1	1	NUM
ap-10605	187	19	)	)	PUNCT
ap-10605	187	20	,	,	PUNCT
ap-10605	187	21	respectively	respectively	ADV
ap-10605	187	22	.	.	PUNCT
ap-10605	188	1	some	some	DET
ap-10605	188	2	covariant	covariant	ADJ
ap-10605	188	3	realizations	realization	NOUN
ap-10605	188	4	of	of	ADP
ap-10605	188	5	conformal	conformal	NOUN
ap-10605	188	6	algebras	algebra	NOUN
ap-10605	188	7	and	and	CCONJ
ap-10605	188	8	de	de	PROPN
ap-10605	188	9	sitter	sitter	NOUN
ap-10605	188	10	algebras	algebra	NOUN
ap-10605	188	11	are	be	AUX
ap-10605	188	12	already	already	ADV
ap-10605	188	13	known	know	VERB
ap-10605	188	14	,	,	PUNCT
ap-10605	188	15	but	but	CCONJ
ap-10605	188	16	we	we	PRON
ap-10605	188	17	constructed	construct	VERB
ap-10605	188	18	realizations	realization	NOUN
ap-10605	188	19	in	in	ADP
ap-10605	188	20	spaces	space	NOUN
ap-10605	188	21	of	of	ADP
ap-10605	188	22	fifteen	fifteen	NUM
ap-10605	188	23	and	and	CCONJ
ap-10605	188	24	ten	ten	NUM
ap-10605	188	25	variables	variable	NOUN
ap-10605	188	26	,	,	PUNCT
ap-10605	188	27	respectively	respectively	ADV
ap-10605	188	28	.	.	PUNCT
ap-10605	189	1	this	this	PRON
ap-10605	189	2	is	be	AUX
ap-10605	189	3	the	the	DET
ap-10605	189	4	highest	high	ADJ
ap-10605	189	5	possible	possible	ADJ
ap-10605	189	6	dimensions	dimension	NOUN
ap-10605	189	7	of	of	ADP
ap-10605	189	8	spaces	space	NOUN
ap-10605	189	9	of	of	ADP
ap-10605	189	10	essential	essential	ADJ
ap-10605	189	11	variables	variable	NOUN
ap-10605	189	12	for	for	ADP
ap-10605	189	13	these	these	DET
ap-10605	189	14	algebras	algebra	NOUN
ap-10605	189	15	.	.	PUNCT
ap-10605	190	1	by	by	ADP
ap-10605	190	2	essential	essential	ADJ
ap-10605	190	3	variables	variable	NOUN
ap-10605	190	4	we	we	PRON
ap-10605	190	5	mean	mean	VERB
ap-10605	190	6	variables	variable	NOUN
ap-10605	190	7	that	that	PRON
ap-10605	190	8	can	can	AUX
ap-10605	190	9	not	not	PART
ap-10605	190	10	be	be	AUX
ap-10605	190	11	eliminated	eliminate	VERB
ap-10605	190	12	through	through	ADP
ap-10605	190	13	a	a	DET
ap-10605	190	14	nondegenerate	nondegenerate	ADJ
ap-10605	190	15	change	change	NOUN
ap-10605	190	16	of	of	ADP
ap-10605	190	17	variables	variable	NOUN
ap-10605	190	18	,	,	PUNCT
ap-10605	190	19	i.e.	i.e.	X
ap-10605	190	20	,	,	PUNCT
ap-10605	190	21	they	they	PRON
ap-10605	190	22	can	can	AUX
ap-10605	190	23	not	not	PART
ap-10605	190	24	be	be	AUX
ap-10605	190	25	replaced	replace	VERB
ap-10605	190	26	by	by	ADP
ap-10605	190	27	invariants	invariant	NOUN
ap-10605	190	28	of	of	ADP
ap-10605	190	29	vector	vector	NOUN
ap-10605	190	30	fields	field	NOUN
ap-10605	190	31	.	.	PUNCT
ap-10605	191	1	realizations	realization	NOUN
ap-10605	191	2	with	with	ADP
ap-10605	191	3	fewer	few	ADJ
ap-10605	191	4	variables	variable	NOUN
ap-10605	191	5	,	,	PUNCT
ap-10605	191	6	in	in	ADP
ap-10605	191	7	particular	particular	ADJ
ap-10605	191	8	“	"	PUNCT
ap-10605	191	9	classical	classical	ADJ
ap-10605	191	10	”	"	PUNCT
ap-10605	191	11	realizations	realization	NOUN
ap-10605	191	12	,	,	PUNCT
ap-10605	191	13	can	can	AUX
ap-10605	191	14	be	be	AUX
ap-10605	191	15	obtained	obtain	VERB
ap-10605	191	16	from	from	ADP
ap-10605	191	17	the	the	DET
ap-10605	191	18	presented	present	VERB
ap-10605	191	19	realizations	realization	NOUN
ap-10605	191	20	by	by	ADP
ap-10605	191	21	a	a	DET
ap-10605	191	22	projection	projection	NOUN
ap-10605	191	23	to	to	ADP
ap-10605	191	24	the	the	DET
ap-10605	191	25	spaces	space	NOUN
ap-10605	191	26	of	of	ADP
ap-10605	191	27	lower	low	ADJ
ap-10605	191	28	dimensions	dimension	NOUN
ap-10605	191	29	.	.	PUNCT
ap-10605	192	1	the	the	DET
ap-10605	192	2	15	15	NUM
ap-10605	192	3	-	-	PUNCT
ap-10605	192	4	dimensional	dimensional	ADJ
ap-10605	192	5	lie	lie	NOUN
ap-10605	192	6	algebra	algebra	NOUN
ap-10605	192	7	c(3	c(3	VERB
ap-10605	192	8	,	,	PUNCT
ap-10605	192	9	1	1	NUM
ap-10605	192	10	)	)	PUNCT
ap-10605	192	11	of	of	ADP
ap-10605	192	12	the	the	DET
ap-10605	192	13	conformal	conformal	NOUN
ap-10605	192	14	group	group	NOUN
ap-10605	192	15	is	be	AUX
ap-10605	192	16	the	the	DET
ap-10605	192	17	lie	lie	NOUN
ap-10605	192	18	algebra	algebra	NOUN
ap-10605	192	19	of	of	ADP
ap-10605	192	20	the	the	DET
ap-10605	192	21	maximal	maximal	ADJ
ap-10605	192	22	invariance	invariance	NOUN
ap-10605	192	23	group	group	NOUN
ap-10605	192	24	of	of	ADP
ap-10605	192	25	the	the	DET
ap-10605	192	26	maxwell	maxwell	PROPN
ap-10605	192	27	’s	’s	PART
ap-10605	192	28	equations	equation	NOUN
ap-10605	192	29	in	in	ADP
ap-10605	192	30	flat	flat	ADJ
ap-10605	192	31	space	space	NOUN
ap-10605	192	32	-	-	PUNCT
ap-10605	192	33	time	time	NOUN
ap-10605	192	34	.	.	PUNCT
ap-10605	193	1	this	this	DET
ap-10605	193	2	group	group	NOUN
ap-10605	193	3	,	,	PUNCT
ap-10605	193	4	from	from	ADP
ap-10605	193	5	many	many	ADJ
ap-10605	193	6	points	point	NOUN
ap-10605	193	7	of	of	ADP
ap-10605	193	8	view	view	NOUN
ap-10605	193	9	,	,	PUNCT
ap-10605	193	10	unites	unite	VERB
ap-10605	193	11	all	all	DET
ap-10605	193	12	physical	physical	ADJ
ap-10605	193	13	groups	group	NOUN
ap-10605	193	14	(	(	PUNCT
ap-10605	193	15	lorentz	lorentz	PROPN
ap-10605	193	16	,	,	PUNCT
ap-10605	193	17	poincaré	poincaré	PROPN
ap-10605	193	18	,	,	PUNCT
ap-10605	193	19	de	de	PROPN
ap-10605	193	20	sitter	sitter	NOUN
ap-10605	193	21	,	,	PUNCT
ap-10605	193	22	orthogonal	orthogonal	NOUN
ap-10605	193	23	,	,	PUNCT
ap-10605	193	24	etc	etc	X
ap-10605	193	25	.	.	X
ap-10605	193	26	)	)	PUNCT
ap-10605	193	27	.	.	PUNCT
ap-10605	194	1	it	it	PRON
ap-10605	194	2	is	be	AUX
ap-10605	194	3	generated	generate	VERB
ap-10605	194	4	by	by	ADP
ap-10605	194	5	ten	ten	NUM
ap-10605	194	6	poincaré	poincaré	PROPN
ap-10605	194	7	operators	operators	PROPN
ap-10605	194	8	pµ	pµ	PROPN
ap-10605	194	9	,	,	PUNCT
ap-10605	194	10	jµν	jµν	VERB
ap-10605	194	11	,	,	PUNCT
ap-10605	194	12	dilation	dilation	NOUN
ap-10605	194	13	operator	operator	NOUN
ap-10605	194	14	d	d	NOUN
ap-10605	194	15	and	and	CCONJ
ap-10605	194	16	special	special	ADJ
ap-10605	194	17	conformal	conformal	ADJ
ap-10605	194	18	transformation	transformation	NOUN
ap-10605	194	19	operators	operator	NOUN
ap-10605	194	20	kµ	kµ	PROPN
ap-10605	194	21	,	,	PUNCT
ap-10605	194	22	where	where	SCONJ
ap-10605	194	23	µ	µ	X
ap-10605	194	24	,	,	PUNCT
ap-10605	194	25	ν	ν	X
ap-10605	194	26	=	=	SYM
ap-10605	194	27	1	1	NUM
ap-10605	194	28	,	,	PUNCT
ap-10605	194	29	2	2	NUM
ap-10605	194	30	,	,	PUNCT
ap-10605	194	31	3	3	NUM
ap-10605	194	32	,	,	PUNCT
ap-10605	194	33	4	4	NUM
ap-10605	194	34	.	.	PUNCT
ap-10605	195	1	the	the	DET
ap-10605	195	2	nonzero	nonzero	PROPN
ap-10605	195	3	commutation	commutation	NOUN
ap-10605	195	4	relations	relation	NOUN
ap-10605	195	5	of	of	ADP
ap-10605	195	6	the	the	DET
ap-10605	195	7	lie	lie	NOUN
ap-10605	195	8	algebra	algebra	NOUN
ap-10605	195	9	have	have	VERB
ap-10605	195	10	the	the	DET
ap-10605	195	11	form	form	NOUN
ap-10605	195	12	:	:	PUNCT
ap-10605	195	13	[	[	X
ap-10605	195	14	jµν	jµν	NOUN
ap-10605	195	15	,	,	PUNCT
ap-10605	195	16	jρσ	jρσ	VERB
ap-10605	195	17	]	]	X
ap-10605	195	18	=	=	SYM
ap-10605	195	19	gµρjνσ	gµρjνσ	ADJ
ap-10605	195	20	−	−	PROPN
ap-10605	195	21	gνρjµσ	gνρjµσ	PROPN
ap-10605	195	22	+	+	CCONJ
ap-10605	195	23	gµσjρν	gµσjρν	NOUN
ap-10605	195	24	−	−	NOUN
ap-10605	195	25	gνσjρµ	gνσjρµ	NOUN
ap-10605	195	26	,	,	PUNCT
ap-10605	195	27	(	(	PUNCT
ap-10605	195	28	4	4	X
ap-10605	195	29	)	)	PUNCT
ap-10605	196	1	[	[	X
ap-10605	196	2	jµν	jµν	NOUN
ap-10605	196	3	,	,	PUNCT
ap-10605	196	4	pρ	pρ	ADP
ap-10605	196	5	]	]	X
ap-10605	196	6	=	=	SYM
ap-10605	196	7	gµρpν	gµρpν	NOUN
ap-10605	196	8	−	−	PROPN
ap-10605	196	9	gνρpµ	gνρpµ	NOUN
ap-10605	196	10	,	,	PUNCT
ap-10605	196	11	(	(	PUNCT
ap-10605	196	12	5	5	X
ap-10605	196	13	)	)	PUNCT
ap-10605	196	14	[	[	X
ap-10605	196	15	jµν	jµν	NOUN
ap-10605	196	16	,	,	PUNCT
ap-10605	196	17	kρ	kρ	INTJ
ap-10605	196	18	]	]	PUNCT
ap-10605	196	19	=	=	PUNCT
ap-10605	196	20	gµρkν	gµρkν	PROPN
ap-10605	196	21	−	−	PROPN
ap-10605	196	22	gνρkµ	gνρkµ	NOUN
ap-10605	196	23	,	,	PUNCT
ap-10605	196	24	(	(	PUNCT
ap-10605	196	25	6	6	NUM
ap-10605	196	26	)	)	PUNCT
ap-10605	197	1	[	[	X
ap-10605	197	2	pµ	pµ	X
ap-10605	197	3	,	,	PUNCT
ap-10605	197	4	kν	kν	PROPN
ap-10605	197	5	]	]	PUNCT
ap-10605	197	6	=	=	SYM
ap-10605	197	7	2(gµνd	2(gµνd	NUM
ap-10605	197	8	+	+	CCONJ
ap-10605	197	9	jµν	jµν	NOUN
ap-10605	197	10	)	)	PUNCT
ap-10605	197	11	,	,	PUNCT
ap-10605	197	12	(	(	PUNCT
ap-10605	197	13	7	7	X
ap-10605	197	14	)	)	PUNCT
ap-10605	197	15	[	[	X
ap-10605	197	16	pµ	pµ	X
ap-10605	197	17	,	,	PUNCT
ap-10605	197	18	d	d	X
ap-10605	197	19	]	]	X
ap-10605	197	20	=	=	SYM
ap-10605	197	21	pµ	pµ	PROPN
ap-10605	197	22	,	,	PUNCT
ap-10605	197	23	(	(	PUNCT
ap-10605	197	24	8)	8)	NUM
ap-10605	197	25	[	[	X
ap-10605	197	26	kµ	kµ	PROPN
ap-10605	197	27	,	,	PUNCT
ap-10605	197	28	d	d	X
ap-10605	197	29	]	]	X
ap-10605	197	30	=	=	PUNCT
ap-10605	197	31	−kµ.	−kµ.	PROPN
ap-10605	197	32	(	(	PUNCT
ap-10605	197	33	9	9	NUM
ap-10605	197	34	)	)	PUNCT
ap-10605	197	35	here	here	ADV
ap-10605	197	36	gµν	gµν	NOUN
ap-10605	197	37	is	be	AUX
ap-10605	197	38	the	the	DET
ap-10605	197	39	metric	metric	ADJ
ap-10605	197	40	tensor	tensor	NOUN
ap-10605	197	41	of	of	ADP
ap-10605	197	42	minkowski	minkowski	ADJ
ap-10605	197	43	space	space	NOUN
ap-10605	197	44	g11	g11	NOUN
ap-10605	197	45	=	=	SYM
ap-10605	197	46	g22	g22	PROPN
ap-10605	197	47	=	=	SYM
ap-10605	197	48	g33	g33	PROPN
ap-10605	197	49	=	=	SYM
ap-10605	197	50	−g44	−g44	X
ap-10605	197	51	=	=	NOUN
ap-10605	197	52	1	1	X
ap-10605	197	53	.	.	PUNCT
ap-10605	198	1	if	if	SCONJ
ap-10605	198	2	we	we	PRON
ap-10605	198	3	consider	consider	VERB
ap-10605	198	4	the	the	DET
ap-10605	198	5	well	well	ADV
ap-10605	198	6	-	-	PUNCT
ap-10605	198	7	known	know	VERB
ap-10605	198	8	realization	realization	NOUN
ap-10605	198	9	(	(	PUNCT
ap-10605	198	10	10	10	NUM
ap-10605	198	11	)	)	PUNCT
ap-10605	198	12	of	of	ADP
ap-10605	198	13	the	the	DET
ap-10605	198	14	conformal	conformal	ADJ
ap-10605	198	15	lie	lie	NOUN
ap-10605	198	16	algebra	algebra	NOUN
ap-10605	198	17	,	,	PUNCT
ap-10605	198	18	we	we	PRON
ap-10605	198	19	can	can	AUX
ap-10605	198	20	see	see	VERB
ap-10605	198	21	that	that	SCONJ
ap-10605	198	22	it	it	PRON
ap-10605	198	23	is	be	AUX
ap-10605	198	24	the	the	DET
ap-10605	198	25	projection	projection	NOUN
ap-10605	198	26	of	of	ADP
ap-10605	198	27	the	the	DET
ap-10605	198	28	generic	generic	ADJ
ap-10605	198	29	realization	realization	NOUN
ap-10605	198	30	that	that	PRON
ap-10605	198	31	corresponds	correspond	VERB
ap-10605	198	32	to	to	ADP
ap-10605	198	33	the	the	DET
ap-10605	198	34	subalgebra	subalgebra	NOUN
ap-10605	198	35	span{jµν	span{jµν	PROPN
ap-10605	198	36	,	,	PUNCT
ap-10605	198	37	d	d	PROPN
ap-10605	198	38	,	,	PUNCT
ap-10605	198	39	kµ	kµ	PROPN
ap-10605	198	40	}	}	PUNCT
ap-10605	198	41	with	with	ADP
ap-10605	198	42	the	the	DET
ap-10605	198	43	complementary	complementary	ADJ
ap-10605	198	44	part	part	NOUN
ap-10605	198	45	{	{	PUNCT
ap-10605	198	46	pµ	pµ	NOUN
ap-10605	198	47	,	,	PUNCT
ap-10605	198	48	jµν	jµν	NOUN
ap-10605	198	49	,	,	PUNCT
ap-10605	198	50	kµ	kµ	PROPN
ap-10605	198	51	,	,	PUNCT
ap-10605	198	52	d	d	PROPN
ap-10605	198	53	}	}	PUNCT
ap-10605	198	54	:	:	PUNCT
ap-10605	198	55	pµ	pµ	PROPN
ap-10605	198	56	=	=	PROPN
ap-10605	198	57	∂µ	∂µ	PROPN
ap-10605	198	58	,	,	PUNCT
ap-10605	198	59	jµν	jµν	NOUN
ap-10605	198	60	=	=	SYM
ap-10605	199	1	xν∂µ	xν∂µ	PROPN
ap-10605	199	2	−	−	PROPN
ap-10605	200	1	xµ∂ν	xµ∂ν	PROPN
ap-10605	200	2	,	,	PUNCT
ap-10605	201	1	d	d	X
ap-10605	201	2	=	=	PUNCT
ap-10605	201	3	xν∂ν	xν∂ν	NOUN
ap-10605	201	4	,	,	PUNCT
ap-10605	201	5	kµ	kµ	NOUN
ap-10605	201	6	=	=	NUM
ap-10605	201	7	2xµxν∂ν	2xµxν∂ν	NUM
ap-10605	201	8	−	−	PROPN
ap-10605	201	9	x2∂µ	x2∂µ	PROPN
ap-10605	201	10	;	;	PUNCT
ap-10605	201	11	(	(	PUNCT
ap-10605	201	12	10	10	NUM
ap-10605	201	13	)	)	PUNCT
ap-10605	202	1	where	where	SCONJ
ap-10605	202	2	x2	x2	NOUN
ap-10605	202	3	=	=	SYM
ap-10605	202	4	x2	x2	PROPN
ap-10605	202	5	1	1	NUM
ap-10605	202	6	+	+	CCONJ
ap-10605	202	7	·	·	PUNCT
ap-10605	202	8	·	·	PUNCT
ap-10605	202	9	·	·	PUNCT
ap-10605	203	1	+	+	CCONJ
ap-10605	203	2	x2	x2	PROPN
ap-10605	203	3	n.	n.	NOUN
ap-10605	203	4	we	we	PRON
ap-10605	203	5	also	also	ADV
ap-10605	203	6	consider	consider	VERB
ap-10605	203	7	de	de	NOUN
ap-10605	203	8	sitter	sitter	NOUN
ap-10605	203	9	algebras	algebra	VERB
ap-10605	203	10	that	that	PRON
ap-10605	203	11	correspond	correspond	VERB
ap-10605	203	12	to	to	ADP
ap-10605	203	13	the	the	DET
ap-10605	203	14	transformation	transformation	NOUN
ap-10605	203	15	groups	group	NOUN
ap-10605	203	16	of	of	ADP
ap-10605	203	17	isometry	isometry	NOUN
ap-10605	203	18	of	of	ADP
ap-10605	203	19	pseudoeuclidean	pseudoeuclidean	ADJ
ap-10605	203	20	spaces	space	NOUN
ap-10605	203	21	with	with	ADP
ap-10605	203	22	the	the	DET
ap-10605	203	23	metric	metric	ADJ
ap-10605	203	24	forms	form	NOUN
ap-10605	203	25	x2	x2	NOUN
ap-10605	203	26	1	1	NUM
ap-10605	204	1	+	+	NOUN
ap-10605	204	2	x2	x2	PROPN
ap-10605	204	3	2	2	NUM
ap-10605	204	4	+	+	NOUN
ap-10605	204	5	x2	x2	PROPN
ap-10605	204	6	3	3	NUM
ap-10605	204	7	−	−	NOUN
ap-10605	204	8	x2	x2	NOUN
ap-10605	204	9	4	4	NUM
ap-10605	205	1	+	+	CCONJ
ap-10605	205	2	x2	x2	PROPN
ap-10605	205	3	5	5	NUM
ap-10605	205	4	and	and	CCONJ
ap-10605	205	5	x2	x2	NOUN
ap-10605	205	6	1	1	NUM
ap-10605	206	1	+	+	NUM
ap-10605	206	2	x2	x2	PROPN
ap-10605	206	3	2	2	NUM
ap-10605	207	1	+	+	NUM
ap-10605	207	2	x2	x2	PROPN
ap-10605	207	3	3	3	NUM
ap-10605	207	4	−	−	NOUN
ap-10605	207	5	x2	x2	INTJ
ap-10605	207	6	4	4	NUM
ap-10605	207	7	−	−	NOUN
ap-10605	207	8	x2	x2	INTJ
ap-10605	207	9	5	5	X
ap-10605	207	10	.	.	PUNCT
ap-10605	208	1	they	they	PRON
ap-10605	208	2	are	be	AUX
ap-10605	208	3	the	the	DET
ap-10605	208	4	groups	group	NOUN
ap-10605	208	5	of	of	ADP
ap-10605	208	6	motion	motion	NOUN
ap-10605	208	7	of	of	ADP
ap-10605	208	8	4	4	NUM
ap-10605	208	9	-	-	PUNCT
ap-10605	208	10	dimensional	dimensional	ADJ
ap-10605	208	11	riemannian	riemannian	ADJ
ap-10605	208	12	spaces	space	NOUN
ap-10605	208	13	of	of	ADP
ap-10605	208	14	constant	constant	ADJ
ap-10605	208	15	curvature	curvature	NOUN
ap-10605	208	16	(	(	PUNCT
ap-10605	208	17	de	de	X
ap-10605	208	18	sitter	sitter	NOUN
ap-10605	208	19	spaces	space	NOUN
ap-10605	208	20	)	)	PUNCT
ap-10605	208	21	.	.	PUNCT
ap-10605	209	1	both	both	DET
ap-10605	209	2	de	de	PROPN
ap-10605	209	3	sitter	sitter	NOUN
ap-10605	209	4	spaces	space	NOUN
ap-10605	209	5	describe	describe	VERB
ap-10605	209	6	an	an	DET
ap-10605	209	7	expanding	expand	VERB
ap-10605	209	8	universe	universe	NOUN
ap-10605	209	9	where	where	SCONJ
ap-10605	209	10	the	the	DET
ap-10605	209	11	radial	radial	ADJ
ap-10605	209	12	velocities	velocity	NOUN
ap-10605	209	13	of	of	ADP
ap-10605	209	14	galaxies	galaxy	NOUN
ap-10605	209	15	are	be	AUX
ap-10605	209	16	proportional	proportional	ADJ
ap-10605	209	17	to	to	ADP
ap-10605	209	18	the	the	DET
ap-10605	209	19	distances	distance	NOUN
ap-10605	209	20	to	to	ADP
ap-10605	209	21	points	point	NOUN
ap-10605	209	22	in	in	ADP
ap-10605	209	23	space	space	NOUN
ap-10605	209	24	.	.	PUNCT
ap-10605	210	1	for	for	ADP
ap-10605	210	2	de	de	PROPN
ap-10605	210	3	sitter	sitter	NOUN
ap-10605	210	4	algebras	algebras	PROPN
ap-10605	210	5	,	,	PUNCT
ap-10605	210	6	we	we	PRON
ap-10605	210	7	can	can	AUX
ap-10605	210	8	use	use	VERB
ap-10605	210	9	isomorphisms	isomorphism	NOUN
ap-10605	210	10	c(3	c(3	PROPN
ap-10605	210	11	,	,	PUNCT
ap-10605	210	12	0	0	X
ap-10605	210	13	)	)	PUNCT
ap-10605	210	14	∼	∼	NOUN
ap-10605	210	15	so(4	so(4	PROPN
ap-10605	210	16	,	,	PUNCT
ap-10605	210	17	1	1	NUM
ap-10605	210	18	)	)	PUNCT
ap-10605	210	19	and	and	CCONJ
ap-10605	210	20	c(2	c(2	PROPN
ap-10605	210	21	,	,	PUNCT
ap-10605	210	22	1	1	X
ap-10605	210	23	)	)	PUNCT
ap-10605	210	24	∼	∼	NOUN
ap-10605	210	25	so(3	so(3	NOUN
ap-10605	210	26	,	,	PUNCT
ap-10605	210	27	2	2	NUM
ap-10605	210	28	)	)	PUNCT
ap-10605	210	29	with	with	ADP
ap-10605	210	30	conformal	conformal	ADJ
ap-10605	210	31	commutation	commutation	NOUN
ap-10605	210	32	relations	relation	NOUN
ap-10605	210	33	(	(	PUNCT
ap-10605	210	34	4)–(9	4)–(9	NOUN
ap-10605	210	35	)	)	PUNCT
ap-10605	210	36	for	for	ADP
ap-10605	210	37	µ	µ	NOUN
ap-10605	210	38	,	,	PUNCT
ap-10605	210	39	ν	ν	X
ap-10605	210	40	=	=	SYM
ap-10605	210	41	1	1	NUM
ap-10605	210	42	,	,	PUNCT
ap-10605	210	43	2	2	NUM
ap-10605	210	44	,	,	PUNCT
ap-10605	210	45	3	3	NUM
ap-10605	210	46	and	and	CCONJ
ap-10605	210	47	metric	metric	ADJ
ap-10605	210	48	tensors	tensor	NOUN
ap-10605	210	49	g11	g11	X
ap-10605	210	50	=	=	SYM
ap-10605	210	51	g22	g22	PROPN
ap-10605	210	52	=	=	SYM
ap-10605	210	53	g33	g33	PROPN
ap-10605	210	54	=	=	SYM
ap-10605	210	55	1	1	NUM
ap-10605	210	56	and	and	CCONJ
ap-10605	210	57	g11	g11	NOUN
ap-10605	210	58	=	=	SYM
ap-10605	210	59	g22	g22	NOUN
ap-10605	210	60	=	=	SYM
ap-10605	210	61	−g33	−g33	SYM
ap-10605	210	62	=	=	SYM
ap-10605	210	63	1	1	NUM
ap-10605	210	64	,	,	PUNCT
ap-10605	210	65	respectively	respectively	ADV
ap-10605	210	66	.	.	PUNCT
ap-10605	211	1	below	below	ADV
ap-10605	211	2	,	,	PUNCT
ap-10605	211	3	we	we	PRON
ap-10605	211	4	present	present	VERB
ap-10605	211	5	all	all	DET
ap-10605	211	6	their	their	PRON
ap-10605	211	7	generic	generic	ADJ
ap-10605	211	8	realizations	realization	NOUN
ap-10605	211	9	that	that	PRON
ap-10605	211	10	we	we	PRON
ap-10605	211	11	obtained	obtain	VERB
ap-10605	211	12	by	by	ADP
ap-10605	211	13	the	the	DET
ap-10605	211	14	shirokov	shirokov	NOUN
ap-10605	211	15	’s	’s	PART
ap-10605	211	16	method	method	NOUN
ap-10605	211	17	with	with	ADP
ap-10605	211	18	the	the	DET
ap-10605	211	19	complementary	complementary	ADJ
ap-10605	211	20	part	part	NOUN
ap-10605	211	21	{	{	PUNCT
ap-10605	211	22	pµ	pµ	NOUN
ap-10605	211	23	,	,	PUNCT
ap-10605	211	24	jµν	jµν	NOUN
ap-10605	211	25	,	,	PUNCT
ap-10605	211	26	kµ	kµ	PROPN
ap-10605	211	27	,	,	PUNCT
ap-10605	211	28	d	d	X
ap-10605	211	29	}	}	PUNCT
ap-10605	211	30	in	in	ADP
ap-10605	211	31	other	other	ADJ
ap-10605	211	32	words	word	NOUN
ap-10605	211	33	,	,	PUNCT
ap-10605	211	34	this	this	PRON
ap-10605	211	35	means	mean	VERB
ap-10605	211	36	that	that	SCONJ
ap-10605	211	37	the	the	DET
ap-10605	211	38	basis	basis	NOUN
ap-10605	211	39	elements	element	NOUN
ap-10605	211	40	are	be	AUX
ap-10605	211	41	ordered	order	VERB
ap-10605	211	42	exactly	exactly	ADV
ap-10605	211	43	in	in	ADP
ap-10605	211	44	the	the	DET
ap-10605	211	45	same	same	ADJ
ap-10605	211	46	way	way	NOUN
ap-10605	211	47	as	as	SCONJ
ap-10605	211	48	they	they	PRON
ap-10605	211	49	are	be	AUX
ap-10605	211	50	presented	present	VERB
ap-10605	211	51	in	in	ADP
ap-10605	211	52	the	the	DET
ap-10605	211	53	appendices	appendix	NOUN
ap-10605	211	54	.	.	PUNCT
ap-10605	212	1	the	the	DET
ap-10605	212	2	theory	theory	NOUN
ap-10605	212	3	allows	allow	VERB
ap-10605	212	4	us	we	PRON
ap-10605	212	5	to	to	PART
ap-10605	212	6	construct	construct	VERB
ap-10605	212	7	one	one	NUM
ap-10605	212	8	realization	realization	NOUN
ap-10605	212	9	for	for	ADP
ap-10605	212	10	the	the	DET
ap-10605	212	11	both	both	DET
ap-10605	212	12	de	de	PROPN
ap-10605	212	13	sitter	sitter	NOUN
ap-10605	212	14	algebras	algebra	NOUN
ap-10605	212	15	by	by	ADP
ap-10605	212	16	parametrizing	parametrize	VERB
ap-10605	212	17	the	the	DET
ap-10605	212	18	structure	structure	NOUN
ap-10605	212	19	constants	constant	NOUN
ap-10605	212	20	with	with	ADP
ap-10605	212	21	a	a	DET
ap-10605	212	22	parameter	parameter	NOUN
ap-10605	212	23	that	that	PRON
ap-10605	212	24	changes	change	VERB
ap-10605	212	25	the	the	DET
ap-10605	212	26	sign	sign	NOUN
ap-10605	212	27	,	,	PUNCT
ap-10605	212	28	but	but	CCONJ
ap-10605	212	29	this	this	PRON
ap-10605	212	30	significantly	significantly	ADV
ap-10605	212	31	complicates	complicate	VERB
ap-10605	212	32	the	the	DET
ap-10605	212	33	calculations	calculation	NOUN
ap-10605	212	34	and	and	CCONJ
ap-10605	212	35	the	the	DET
ap-10605	212	36	appearance	appearance	NOUN
ap-10605	212	37	of	of	ADP
ap-10605	212	38	the	the	DET
ap-10605	212	39	realizations	realization	NOUN
ap-10605	212	40	.	.	PUNCT
ap-10605	213	1	in	in	ADP
ap-10605	213	2	the	the	DET
ap-10605	213	3	future	future	NOUN
ap-10605	213	4	,	,	PUNCT
ap-10605	213	5	we	we	PRON
ap-10605	213	6	plan	plan	VERB
ap-10605	213	7	to	to	PART
ap-10605	213	8	construct	construct	VERB
ap-10605	213	9	projections	projection	NOUN
ap-10605	213	10	of	of	ADP
ap-10605	213	11	the	the	DET
ap-10605	213	12	obtained	obtain	VERB
ap-10605	213	13	generating	generating	NOUN
ap-10605	213	14	realizations	realization	NOUN
ap-10605	213	15	onto	onto	ADP
ap-10605	213	16	spaces	space	NOUN
ap-10605	213	17	of	of	ADP
ap-10605	213	18	lower	low	ADJ
ap-10605	213	19	dimensions	dimension	NOUN
ap-10605	213	20	,	,	PUNCT
ap-10605	213	21	find	find	VERB
ap-10605	213	22	differential	differential	ADJ
ap-10605	213	23	invariants	invariant	NOUN
ap-10605	213	24	for	for	ADP
ap-10605	213	25	them	they	PRON
ap-10605	213	26	,	,	PUNCT
ap-10605	213	27	and	and	CCONJ
ap-10605	213	28	write	write	VERB
ap-10605	213	29	invariant	invariant	ADJ
ap-10605	213	30	partial	partial	ADJ
ap-10605	213	31	differential	differential	NOUN
ap-10605	213	32	equations	equation	NOUN
ap-10605	213	33	.	.	PUNCT
ap-10605	214	1	acknowledgements	acknowledgement	NOUN
ap-10605	214	2	this	this	DET
ap-10605	214	3	work	work	NOUN
ap-10605	214	4	was	be	AUX
ap-10605	214	5	supported	support	VERB
ap-10605	214	6	by	by	ADP
ap-10605	214	7	a	a	DET
ap-10605	214	8	grant	grant	NOUN
ap-10605	214	9	from	from	ADP
ap-10605	214	10	the	the	DET
ap-10605	214	11	simons	simons	PROPN
ap-10605	214	12	foundation	foundation	PROPN
ap-10605	214	13	(	(	PUNCT
ap-10605	214	14	sfi	sfi	PROPN
ap-10605	214	15	-	-	PUNCT
ap-10605	214	16	pd	pd	NOUN
ap-10605	214	17	-	-	PUNCT
ap-10605	214	18	ukraine-00014586	ukraine-00014586	ADJ
ap-10605	214	19	,	,	PUNCT
ap-10605	214	20	m.n	m.n	PROPN
ap-10605	214	21	.	.	PROPN
ap-10605	214	22	,	,	PUNCT
ap-10605	214	23	m.s	m.s	PROPN
ap-10605	214	24	.	.	PROPN
ap-10605	214	25	)	)	PUNCT
ap-10605	214	26	.	.	PUNCT
ap-10605	215	1	references	reference	NOUN
ap-10605	215	2	[	[	X
ap-10605	215	3	1	1	NUM
ap-10605	215	4	]	]	PUNCT
ap-10605	215	5	r.	r.	PROPN
ap-10605	215	6	l.	l.	PROPN
ap-10605	215	7	anderson	anderson	PROPN
ap-10605	215	8	,	,	PUNCT
ap-10605	215	9	s.	s.	PROPN
ap-10605	215	10	m.	m.	PROPN
ap-10605	215	11	davison	davison	PROPN
ap-10605	215	12	.	.	PUNCT
ap-10605	216	1	a	a	DET
ap-10605	216	2	generalization	generalization	NOUN
ap-10605	216	3	of	of	ADP
ap-10605	216	4	lie	lie	PROPN
ap-10605	216	5	’s	’s	PART
ap-10605	216	6	“	"	PUNCT
ap-10605	216	7	counting	counting	NOUN
ap-10605	216	8	”	"	PUNCT
ap-10605	216	9	theorem	theorem	NOUN
ap-10605	216	10	for	for	ADP
ap-10605	216	11	second	second	ADJ
ap-10605	216	12	-	-	PUNCT
ap-10605	216	13	order	order	NOUN
ap-10605	216	14	ordinary	ordinary	ADJ
ap-10605	216	15	differential	differential	ADJ
ap-10605	216	16	equations	equation	NOUN
ap-10605	216	17	.	.	PUNCT
ap-10605	217	1	journal	journal	PROPN
ap-10605	217	2	of	of	ADP
ap-10605	217	3	mathematical	mathematical	ADJ
ap-10605	217	4	analysis	analysis	NOUN
ap-10605	217	5	and	and	CCONJ
ap-10605	217	6	applications	application	NOUN
ap-10605	217	7	48(1):301–315	48(1):301–315	NUM
ap-10605	217	8	,	,	PUNCT
ap-10605	217	9	1974	1974	NUM
ap-10605	217	10	.	.	PUNCT
ap-10605	218	1	https://doi.org/10.1016/0022-247x(74)90236-4	https://doi.org/10.1016/0022-247x(74)90236-4	PROPN
ap-10605	218	2	558	558	NUM
ap-10605	219	1	https://doi.org/10.1016/0022-247x(74)90236-4	https://doi.org/10.1016/0022-247x(74)90236-4	PROPN
ap-10605	219	2	vol	vol	NOUN
ap-10605	219	3	.	.	PUNCT
ap-10605	220	1	65	65	NUM
ap-10605	220	2	no	no	NOUN
ap-10605	220	3	.	.	PUNCT
ap-10605	221	1	5/2025	5/2025	NUM
ap-10605	221	2	on	on	ADP
ap-10605	221	3	realizations	realization	NOUN
ap-10605	221	4	of	of	ADP
ap-10605	221	5	lie	lie	NOUN
ap-10605	221	6	algebras	algebra	NOUN
ap-10605	221	7	[	[	X
ap-10605	221	8	2	2	NUM
ap-10605	221	9	]	]	PUNCT
ap-10605	221	10	f.	f.	PROPN
ap-10605	221	11	schwarz	schwarz	PROPN
ap-10605	221	12	.	.	PUNCT
ap-10605	222	1	solving	solve	VERB
ap-10605	222	2	second	second	ADJ
ap-10605	222	3	-	-	PUNCT
ap-10605	222	4	order	order	NOUN
ap-10605	222	5	differential	differential	ADJ
ap-10605	222	6	equations	equation	NOUN
ap-10605	222	7	with	with	ADP
ap-10605	222	8	lie	lie	NOUN
ap-10605	222	9	symmetries	symmetry	NOUN
ap-10605	222	10	.	.	PUNCT
ap-10605	223	1	acta	acta	PROPN
ap-10605	223	2	applicandae	applicandae	PROPN
ap-10605	223	3	mathematica	mathematica	PROPN
ap-10605	223	4	60(1):39–113	60(1):39–113	PROPN
ap-10605	223	5	,	,	PUNCT
ap-10605	223	6	2000	2000	NUM
ap-10605	223	7	.	.	PUNCT
ap-10605	224	1	https://doi.org/10.1023/a:1006321609161	https://doi.org/10.1023/a:1006321609161	ADJ
ap-10605	224	2	[	[	X
ap-10605	224	3	3	3	NUM
ap-10605	224	4	]	]	X
ap-10605	224	5	h.	h.	PROPN
ap-10605	224	6	makaruk	makaruk	PROPN
ap-10605	224	7	.	.	PUNCT
ap-10605	225	1	real	real	ADJ
ap-10605	225	2	lie	lie	NOUN
ap-10605	225	3	algebras	algebra	NOUN
ap-10605	225	4	of	of	ADP
ap-10605	225	5	dimension	dimension	NOUN
ap-10605	225	6	d	d	PROPN
ap-10605	225	7	≤	≤	NUM
ap-10605	225	8	4	4	NUM
ap-10605	225	9	which	which	PRON
ap-10605	225	10	fulfil	fulfil	VERB
ap-10605	225	11	the	the	DET
ap-10605	225	12	einstein	einstein	PROPN
ap-10605	225	13	equations	equation	NOUN
ap-10605	225	14	.	.	PUNCT
ap-10605	226	1	reports	report	NOUN
ap-10605	226	2	on	on	ADP
ap-10605	226	3	mathematical	mathematical	ADJ
ap-10605	226	4	physics	physics	NOUN
ap-10605	226	5	32(3):375–383	32(3):375–383	PROPN
ap-10605	226	6	,	,	PUNCT
ap-10605	226	7	1993	1993	NUM
ap-10605	226	8	.	.	PUNCT
ap-10605	227	1	https://doi.org/10.1016/0034-4877(93)90030-i	https://doi.org/10.1016/0034-4877(93)90030-i	NOUN
ap-10605	228	1	[	[	X
ap-10605	228	2	4	4	X
ap-10605	228	3	]	]	X
ap-10605	228	4	r.	r.	PROPN
ap-10605	228	5	o.	o.	PROPN
ap-10605	228	6	popovych	popovych	PROPN
ap-10605	228	7	,	,	PUNCT
ap-10605	228	8	v.	v.	ADP
ap-10605	228	9	m.	m.	NOUN
ap-10605	228	10	boyko	boyko	PROPN
ap-10605	228	11	,	,	PUNCT
ap-10605	228	12	m.	m.	NOUN
ap-10605	228	13	o.	o.	PROPN
ap-10605	228	14	nesterenko	nesterenko	PROPN
ap-10605	228	15	,	,	PUNCT
ap-10605	228	16	m.	m.	NOUN
ap-10605	228	17	w.	w.	PROPN
ap-10605	228	18	lutfullin	lutfullin	PROPN
ap-10605	228	19	.	.	PUNCT
ap-10605	229	1	realizations	realization	NOUN
ap-10605	229	2	of	of	ADP
ap-10605	229	3	real	real	ADJ
ap-10605	229	4	low	low	ADJ
ap-10605	229	5	-	-	PUNCT
ap-10605	229	6	dimensional	dimensional	ADJ
ap-10605	229	7	lie	lie	NOUN
ap-10605	229	8	algebras	algebra	NOUN
ap-10605	229	9	.	.	PUNCT
ap-10605	230	1	journal	journal	PROPN
ap-10605	230	2	of	of	ADP
ap-10605	230	3	physics	physics	PROPN
ap-10605	230	4	a	a	PRON
ap-10605	230	5	:	:	PUNCT
ap-10605	230	6	mathematical	mathematical	ADJ
ap-10605	230	7	and	and	CCONJ
ap-10605	230	8	general	general	ADJ
ap-10605	230	9	36(26):7337	36(26):7337	NUM
ap-10605	230	10	,	,	PUNCT
ap-10605	230	11	2003	2003	NUM
ap-10605	230	12	.	.	PUNCT
ap-10605	231	1	https://doi.org/10.1088/0305-4470/36/26/309	https://doi.org/10.1088/0305-4470/36/26/309	ADJ
ap-10605	231	2	[	[	X
ap-10605	231	3	5	5	NUM
ap-10605	231	4	]	]	PUNCT
ap-10605	231	5	r.	r.	PROPN
ap-10605	231	6	j.	j.	PROPN
ap-10605	231	7	blattner	blattner	PROPN
ap-10605	231	8	.	.	PUNCT
ap-10605	232	1	induced	induced	ADJ
ap-10605	232	2	and	and	CCONJ
ap-10605	232	3	produced	produce	VERB
ap-10605	232	4	representations	representation	NOUN
ap-10605	232	5	of	of	ADP
ap-10605	232	6	lie	lie	NOUN
ap-10605	232	7	algebras	algebra	NOUN
ap-10605	232	8	.	.	PUNCT
ap-10605	233	1	transactions	transaction	NOUN
ap-10605	233	2	of	of	ADP
ap-10605	233	3	the	the	DET
ap-10605	233	4	american	american	PROPN
ap-10605	233	5	mathematical	mathematical	PROPN
ap-10605	233	6	society	society	PROPN
ap-10605	233	7	144:457–474	144:457–474	NOUN
ap-10605	233	8	,	,	PUNCT
ap-10605	233	9	1969	1969	NUM
ap-10605	233	10	.	.	PUNCT
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ap-10605	235	1	[	[	X
ap-10605	235	2	6	6	NUM
ap-10605	235	3	]	]	PUNCT
ap-10605	235	4	a.	a.	NOUN
ap-10605	235	5	a.	a.	NOUN
ap-10605	235	6	magazev	magazev	PROPN
ap-10605	235	7	,	,	PUNCT
ap-10605	235	8	v.	v.	PROPN
ap-10605	235	9	b.	b.	PROPN
ap-10605	235	10	mikheyev	mikheyev	PROPN
ap-10605	235	11	,	,	PUNCT
ap-10605	235	12	i.	i.	PROPN
ap-10605	235	13	v.	v.	PROPN
ap-10605	235	14	shirokov	shirokov	PROPN
ap-10605	235	15	.	.	PUNCT
ap-10605	236	1	computation	computation	NOUN
ap-10605	236	2	of	of	ADP
ap-10605	236	3	composition	composition	NOUN
ap-10605	236	4	functions	function	NOUN
ap-10605	236	5	and	and	CCONJ
ap-10605	236	6	invariant	invariant	ADJ
ap-10605	236	7	vector	vector	NOUN
ap-10605	236	8	fields	field	NOUN
ap-10605	236	9	in	in	ADP
ap-10605	236	10	terms	term	NOUN
ap-10605	236	11	of	of	ADP
ap-10605	236	12	structure	structure	NOUN
ap-10605	236	13	constants	constant	NOUN
ap-10605	236	14	of	of	ADP
ap-10605	236	15	associated	associated	ADJ
ap-10605	236	16	lie	lie	NOUN
ap-10605	236	17	algebras	algebras	PROPN
ap-10605	236	18	.	.	PUNCT
ap-10605	236	19	symmetry	symmetry	PROPN
ap-10605	236	20	,	,	PUNCT
ap-10605	236	21	integrability	integrability	NOUN
ap-10605	236	22	and	and	CCONJ
ap-10605	236	23	geometry	geometry	NOUN
ap-10605	236	24	:	:	PUNCT
ap-10605	236	25	methods	method	NOUN
ap-10605	236	26	and	and	CCONJ
ap-10605	236	27	applications	application	NOUN
ap-10605	236	28	11:66	11:66	NUM
ap-10605	236	29	,	,	PUNCT
ap-10605	236	30	2015	2015	NUM
ap-10605	236	31	.	.	PUNCT
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ap-10605	237	2	[	[	X
ap-10605	237	3	7	7	NUM
ap-10605	237	4	]	]	X
ap-10605	237	5	d.	d.	PROPN
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ap-10605	237	7	.	.	PUNCT
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ap-10605	238	2	of	of	ADP
ap-10605	238	3	realizations	realization	NOUN
ap-10605	238	4	of	of	ADP
ap-10605	238	5	low	low	ADJ
ap-10605	238	6	-	-	PUNCT
ap-10605	238	7	dimensional	dimensional	ADJ
ap-10605	238	8	lie	lie	NOUN
ap-10605	238	9	algebras	algebra	NOUN
ap-10605	238	10	.	.	PUNCT
ap-10605	239	1	master	master	PROPN
ap-10605	239	2	’s	’s	PART
ap-10605	239	3	thesis	thesis	NOUN
ap-10605	239	4	,	,	PUNCT
ap-10605	239	5	czech	czech	PROPN
ap-10605	239	6	technical	technical	PROPN
ap-10605	239	7	university	university	PROPN
ap-10605	239	8	in	in	ADP
ap-10605	239	9	prague	prague	PROPN
ap-10605	239	10	,	,	PUNCT
ap-10605	239	11	faculty	faculty	NOUN
ap-10605	239	12	of	of	ADP
ap-10605	239	13	nuclear	nuclear	ADJ
ap-10605	239	14	sciences	science	NOUN
ap-10605	239	15	and	and	CCONJ
ap-10605	239	16	physical	physical	ADJ
ap-10605	239	17	engineering	engineering	NOUN
ap-10605	239	18	,	,	PUNCT
ap-10605	239	19	2017	2017	NUM
ap-10605	239	20	.	.	PUNCT
ap-10605	240	1	[	[	X
ap-10605	240	2	2025	2025	NUM
ap-10605	240	3	-	-	SYM
ap-10605	240	4	06	06	NUM
ap-10605	240	5	-	-	SYM
ap-10605	240	6	05	05	NUM
ap-10605	240	7	]	]	PUNCT
ap-10605	240	8	.	.	PUNCT
ap-10605	241	1	https://physics.fjfi.cvut.cz/publications/mf/	https://physics.fjfi.cvut.cz/publications/mf/	NOUN
ap-10605	241	2	2017	2017	NUM
ap-10605	241	3	/	/	SYM
ap-10605	241	4	dp_mf_17_gromada.pdf	dp_mf_17_gromada.pdf	PROPN
ap-10605	241	5	[	[	X
ap-10605	241	6	8	8	NUM
ap-10605	241	7	]	]	PUNCT
ap-10605	241	8	m.	m.	NOUN
ap-10605	241	9	havlíček	havlíček	PROPN
ap-10605	241	10	,	,	PUNCT
ap-10605	241	11	w.	w.	PROPN
ap-10605	241	12	lassner	lassner	NOUN
ap-10605	241	13	.	.	PUNCT
ap-10605	242	1	canonical	canonical	ADJ
ap-10605	242	2	realizations	realization	NOUN
ap-10605	242	3	of	of	ADP
ap-10605	242	4	the	the	DET
ap-10605	242	5	lie	lie	NOUN
ap-10605	242	6	algebras	algebra	NOUN
ap-10605	242	7	gl(n	gl(n	X
ap-10605	242	8	,	,	PUNCT
ap-10605	242	9	r	r	NOUN
ap-10605	242	10	)	)	PUNCT
ap-10605	242	11	and	and	CCONJ
ap-10605	242	12	sl(n	sl(n	NOUN
ap-10605	242	13	,	,	PUNCT
ap-10605	242	14	r	r	NOUN
ap-10605	242	15	)	)	PUNCT
ap-10605	242	16	.	.	PUNCT
ap-10605	243	1	i.	i.	PROPN
ap-10605	243	2	formulae	formulae	PROPN
ap-10605	243	3	and	and	CCONJ
ap-10605	243	4	classification	classification	NOUN
ap-10605	243	5	.	.	PUNCT
ap-10605	244	1	reports	report	NOUN
ap-10605	244	2	on	on	ADP
ap-10605	244	3	mathematical	mathematical	ADJ
ap-10605	244	4	physics	physics	NOUN
ap-10605	244	5	8(3):391–399	8(3):391–399	NOUN
ap-10605	244	6	,	,	PUNCT
ap-10605	244	7	1975	1975	NUM
ap-10605	244	8	.	.	PUNCT
ap-10605	245	1	https://doi.org/10.1016/0034-4877(75)90081-6	https://doi.org/10.1016/0034-4877(75)90081-6	PROPN
ap-10605	245	2	559	559	NUM
ap-10605	246	1	https://doi.org/10.1023/a:1006321609161	https://doi.org/10.1023/a:1006321609161	ADJ
ap-10605	246	2	https://doi.org/10.1016/0034-4877(93)90030-i	https://doi.org/10.1016/0034-4877(93)90030-i	PROPN
ap-10605	246	3	https://doi.org/10.1088/0305-4470/36/26/309	https://doi.org/10.1088/0305-4470/36/26/309	ADJ
ap-10605	246	4	https://doi.org/10.2307/1995292	https://doi.org/10.2307/1995292	X
ap-10605	246	5	https://doi.org/10.3842/sigma.2015.066	https://doi.org/10.3842/sigma.2015.066	VERB
ap-10605	246	6	https://physics.fjfi.cvut.cz/publications/mf/2017/dp_mf_17_gromada.pdf	https://physics.fjfi.cvut.cz/publications/mf/2017/dp_mf_17_gromada.pdf	NOUN
ap-10605	246	7	https://physics.fjfi.cvut.cz/publications/mf/2017/dp_mf_17_gromada.pdf	https://physics.fjfi.cvut.cz/publications/mf/2017/dp_mf_17_gromada.pdf	NOUN
ap-10605	246	8	https://doi.org/10.1016/0034-4877(75)90081-6	https://doi.org/10.1016/0034-4877(75)90081-6	PROPN
ap-10605	246	9	m.	m.	NOUN
ap-10605	246	10	nesterenko	nesterenko	PROPN
ap-10605	246	11	,	,	PUNCT
ap-10605	246	12	s.	s.	PROPN
ap-10605	246	13	pošta	pošta	PROPN
ap-10605	246	14	,	,	PUNCT
ap-10605	246	15	m.	m.	NOUN
ap-10605	246	16	staryi	staryi	PROPN
ap-10605	246	17	acta	acta	PROPN
ap-10605	246	18	polytechnica	polytechnica	PROPN
ap-10605	246	19	appendix	appendix	VERB
ap-10605	246	20	a.	a.	NOUN
ap-10605	246	21	in	in	ADP
ap-10605	246	22	this	this	DET
ap-10605	246	23	appendix	appendix	NOUN
ap-10605	246	24	we	we	PRON
ap-10605	246	25	present	present	VERB
ap-10605	246	26	generic	generic	ADJ
ap-10605	246	27	realizations	realization	NOUN
ap-10605	246	28	of	of	ADP
ap-10605	246	29	lie	lie	NOUN
ap-10605	246	30	algebras	algebra	NOUN
ap-10605	246	31	of	of	ADP
ap-10605	246	32	three	three	NUM
ap-10605	246	33	important	important	ADJ
ap-10605	246	34	conformal	conformal	ADJ
ap-10605	246	35	groups	group	NOUN
ap-10605	246	36	:	:	PUNCT
ap-10605	246	37	the	the	DET
ap-10605	246	38	standard	standard	ADJ
ap-10605	246	39	conformal	conformal	NOUN
ap-10605	246	40	group	group	NOUN
ap-10605	246	41	c(3	c(3	PROPN
ap-10605	246	42	,	,	PUNCT
ap-10605	246	43	1	1	NUM
ap-10605	246	44	)	)	PUNCT
ap-10605	246	45	and	and	CCONJ
ap-10605	246	46	two	two	NUM
ap-10605	246	47	conformal	conformal	ADJ
ap-10605	246	48	groups	group	NOUN
ap-10605	246	49	of	of	ADP
ap-10605	246	50	pseudo	pseudo	NOUN
ap-10605	246	51	-	-	ADJ
ap-10605	246	52	euclidean	euclidean	ADJ
ap-10605	246	53	spaces	space	NOUN
ap-10605	246	54	c(3	c(3	ADV
ap-10605	246	55	,	,	PUNCT
ap-10605	246	56	0	0	NUM
ap-10605	246	57	)	)	PUNCT
ap-10605	246	58	and	and	CCONJ
ap-10605	246	59	c(2	c(2	PROPN
ap-10605	246	60	,	,	PUNCT
ap-10605	246	61	1	1	NUM
ap-10605	246	62	)	)	PUNCT
ap-10605	246	63	.	.	PUNCT
ap-10605	247	1	a.1	a.1	X
ap-10605	247	2	.	.	PUNCT
ap-10605	248	1	generic	generic	ADJ
ap-10605	248	2	realization	realization	NOUN
ap-10605	248	3	of	of	ADP
ap-10605	248	4	the	the	DET
ap-10605	248	5	conformal	conformal	NOUN
ap-10605	248	6	algebra	algebra	NOUN
ap-10605	248	7	c(3	c(3	VERB
ap-10605	248	8	,	,	PUNCT
ap-10605	248	9	1	1	NUM
ap-10605	248	10	)	)	PUNCT
ap-10605	248	11	to	to	PART
ap-10605	248	12	simplify	simplify	VERB
ap-10605	248	13	the	the	DET
ap-10605	248	14	form	form	NOUN
ap-10605	248	15	of	of	ADP
ap-10605	248	16	the	the	DET
ap-10605	248	17	formulas	formula	NOUN
ap-10605	248	18	,	,	PUNCT
ap-10605	248	19	we	we	PRON
ap-10605	248	20	introduce	introduce	VERB
ap-10605	248	21	the	the	DET
ap-10605	248	22	notations	notation	NOUN
ap-10605	248	23	:	:	PUNCT
ap-10605	248	24	sin	sin	NOUN
ap-10605	248	25	xi	xi	NOUN
ap-10605	249	1	=	=	SYM
ap-10605	249	2	si	si	X
ap-10605	249	3	,	,	PUNCT
ap-10605	249	4	cos	cos	PROPN
ap-10605	249	5	xi	xi	PROPN
ap-10605	249	6	=	=	SYM
ap-10605	249	7	ci	ci	PROPN
ap-10605	249	8	,	,	PUNCT
ap-10605	249	9	tan	tan	NOUN
ap-10605	249	10	xi	xi	NOUN
ap-10605	249	11	=	=	SYM
ap-10605	249	12	ti	ti	PROPN
ap-10605	249	13	,	,	PUNCT
ap-10605	249	14	sinh	sinh	NOUN
ap-10605	249	15	xi	xi	PUNCT
ap-10605	249	16	=	=	PROPN
ap-10605	249	17	shi	shi	PROPN
ap-10605	249	18	,	,	PUNCT
ap-10605	249	19	cosh	cosh	NOUN
ap-10605	249	20	xi	xi	X
ap-10605	249	21	=	=	PUNCT
ap-10605	249	22	chi	chi	PROPN
ap-10605	249	23	,	,	PUNCT
ap-10605	249	24	tanh	tanh	PROPN
ap-10605	249	25	xi	xi	X
ap-10605	250	1	=	=	PUNCT
ap-10605	250	2	thi	thi	PROPN
ap-10605	250	3	,	,	PUNCT
ap-10605	250	4	i	i	NOUN
ap-10605	250	5	=	=	NOUN
ap-10605	250	6	1	1	NUM
ap-10605	250	7	,	,	PUNCT
ap-10605	250	8	.	.	PUNCT
ap-10605	250	9	.	.	PUNCT
ap-10605	251	1	.	.	PUNCT
ap-10605	252	1	,	,	PUNCT
ap-10605	253	1	10	10	NUM
ap-10605	253	2	.	.	PUNCT
ap-10605	254	1	rgeneric(c(3	rgeneric(c(3	NOUN
ap-10605	254	2	,	,	PUNCT
ap-10605	254	3	1	1	NUM
ap-10605	254	4	)	)	PUNCT
ap-10605	254	5	)	)	PUNCT
ap-10605	254	6	:	:	PUNCT
ap-10605	255	1	p1	p1	NOUN
ap-10605	255	2	=	=	SYM
ap-10605	255	3	∂1	∂1	ADJ
ap-10605	255	4	,	,	PUNCT
ap-10605	255	5	p2	p2	PROPN
ap-10605	255	6	=	=	SYM
ap-10605	255	7	∂2	∂2	PROPN
ap-10605	255	8	,	,	PUNCT
ap-10605	255	9	p3	p3	PROPN
ap-10605	255	10	=	=	SYM
ap-10605	255	11	∂3	∂3	PROPN
ap-10605	255	12	,	,	PUNCT
ap-10605	255	13	p4	p4	ADJ
ap-10605	255	14	=	=	PUNCT
ap-10605	255	15	∂4	∂4	NOUN
ap-10605	255	16	,	,	PUNCT
ap-10605	255	17	j12	j12	NOUN
ap-10605	255	18	=	=	PUNCT
ap-10605	256	1	x2∂1	x2∂1	PROPN
ap-10605	256	2	−	−	PROPN
ap-10605	256	3	x1∂x2	x1∂x2	NOUN
ap-10605	256	4	+	+	CCONJ
ap-10605	256	5	∂5	∂5	PROPN
ap-10605	256	6	,	,	PUNCT
ap-10605	256	7	j13	j13	NOUN
ap-10605	256	8	=	=	SYM
ap-10605	256	9	x3∂1	x3∂1	PROPN
ap-10605	257	1	−	−	PROPN
ap-10605	257	2	x1∂3	x1∂3	INTJ
ap-10605	258	1	−	−	PROPN
ap-10605	259	1	th6s5∂5	th6s5∂5	PROPN
ap-10605	259	2	+	+	PUNCT
ap-10605	260	1	c5∂6	c5∂6	PROPN
ap-10605	260	2	+	+	CCONJ
ap-10605	260	3	2	2	NUM
ap-10605	260	4	s5	s5	NOUN
ap-10605	260	5	ch6	ch6	NOUN
ap-10605	260	6	∂8	∂8	PROPN
ap-10605	260	7	,	,	PUNCT
ap-10605	260	8	j14	j14	PROPN
ap-10605	260	9	=	=	PUNCT
ap-10605	260	10	−	−	PROPN
ap-10605	261	1	x4∂1	x4∂1	PROPN
ap-10605	262	1	−	−	PROPN
ap-10605	263	1	x1∂4	x1∂4	PROPN
ap-10605	264	1	+	+	CCONJ
ap-10605	264	2	2t7s5	2t7s5	NUM
ap-10605	264	3	ch6	ch6	NOUN
ap-10605	264	4	∂5	∂5	VERB
ap-10605	264	5	+	+	SYM
ap-10605	264	6	t7s6c5∂6	t7s6c5∂6	NOUN
ap-10605	265	1	+	+	CCONJ
ap-10605	265	2	c5c6∂7	c5c6∂7	PROPN
ap-10605	265	3	+	+	CCONJ
ap-10605	265	4	s9s6c5c8	s9s6c5c8	NOUN
ap-10605	265	5	+	+	CCONJ
ap-10605	265	6	th6s7c9s5	th6s7c9s5	NOUN
ap-10605	265	7	+	+	CCONJ
ap-10605	265	8	s9s8s5	s9s8s5	PROPN
ap-10605	265	9	c7c9	c7c9	PUNCT
ap-10605	265	10	∂8	∂8	NUM
ap-10605	265	11	−	−	PROPN
ap-10605	265	12	c5s6s8	c5s6s8	ADJ
ap-10605	265	13	−	−	X
ap-10605	265	14	s5c8	s5c8	INTJ
ap-10605	265	15	c7	c7	PROPN
ap-10605	265	16	∂9	∂9	PROPN
ap-10605	266	1	+	+	CCONJ
ap-10605	267	1	s5s8	s5s8	PUNCT
ap-10605	267	2	+	+	NUM
ap-10605	267	3	c5s6c8	c5s6c8	NOUN
ap-10605	267	4	c7c9	c7c9	PROPN
ap-10605	267	5	∂10	∂10	PROPN
ap-10605	267	6	,	,	PUNCT
ap-10605	267	7	j23	j23	PROPN
ap-10605	267	8	=	=	PUNCT
ap-10605	268	1	x3∂2	x3∂2	PROPN
ap-10605	268	2	−	−	PROPN
ap-10605	269	1	x2∂3	x2∂3	PROPN
ap-10605	270	1	+	+	CCONJ
ap-10605	270	2	−th6c5∂5	−th6c5∂5	PROPN
ap-10605	270	3	−	−	PROPN
ap-10605	271	1	s5∂6	s5∂6	PROPN
ap-10605	271	2	+	+	CCONJ
ap-10605	271	3	c5	c5	PROPN
ap-10605	271	4	ch6	ch6	PROPN
ap-10605	271	5	∂8	∂8	PROPN
ap-10605	271	6	,	,	PUNCT
ap-10605	271	7	j24	j24	PROPN
ap-10605	271	8	=	=	PUNCT
ap-10605	271	9	−	−	PROPN
ap-10605	272	1	x4∂2	x4∂2	PROPN
ap-10605	273	1	−	−	PROPN
ap-10605	273	2	x2∂4	x2∂4	PROPN
ap-10605	274	1	+	+	CCONJ
ap-10605	274	2	t7c5	t7c5	PROPN
ap-10605	274	3	c7ch6	c7ch6	PROPN
ap-10605	274	4	∂5	∂5	NOUN
ap-10605	274	5	−	−	ADP
ap-10605	274	6	t7s5s6∂6	t7s5s6∂6	NOUN
ap-10605	274	7	−	−	NOUN
ap-10605	274	8	s5c6∂7	s5c6∂7	NOUN
ap-10605	274	9	+	+	NUM
ap-10605	274	10	th6s7c9c5	th6s7c9c5	NOUN
ap-10605	274	11	−	−	NOUN
ap-10605	274	12	s9s6c8s5	s9s6c8s5	NOUN
ap-10605	274	13	+	+	CCONJ
ap-10605	274	14	s9c5s8	s9c5s8	ADJ
ap-10605	274	15	c7c9	c7c9	X
ap-10605	274	16	∂8	∂8	X
ap-10605	274	17	+	+	CCONJ
ap-10605	274	18	c5c8	c5c8	ADJ
ap-10605	274	19	+	+	CCONJ
ap-10605	274	20	s5s6s8	s5s6s8	PROPN
ap-10605	274	21	c7	c7	PROPN
ap-10605	274	22	∂9	∂9	PROPN
ap-10605	274	23	−	−	PROPN
ap-10605	274	24	s5s6c8	s5s6c8	PROPN
ap-10605	274	25	−	−	PROPN
ap-10605	274	26	c5s8	c5s8	NOUN
ap-10605	274	27	c7c9	c7c9	PROPN
ap-10605	274	28	∂10	∂10	PROPN
ap-10605	274	29	,	,	PUNCT
ap-10605	274	30	j34	j34	NOUN
ap-10605	274	31	=	=	PUNCT
ap-10605	274	32	−	−	PROPN
ap-10605	275	1	x4∂3	x4∂3	INTJ
ap-10605	275	2	−	−	PROPN
ap-10605	276	1	x3∂4	x3∂4	PUNCT
ap-10605	277	1	+	+	PUNCT
ap-10605	278	1	c6t7∂6	c6t7∂6	NOUN
ap-10605	278	2	−	−	NOUN
ap-10605	278	3	s6∂7	s6∂7	SYM
ap-10605	279	1	+	+	NUM
ap-10605	279	2	t9c8c6	t9c8c6	PROPN
ap-10605	279	3	c7	c7	PROPN
ap-10605	279	4	∂8	∂8	NUM
ap-10605	279	5	−	−	PROPN
ap-10605	279	6	s8c6	s8c6	PROPN
ap-10605	279	7	c7	c7	PROPN
ap-10605	279	8	∂9	∂9	NOUN
ap-10605	279	9	+	+	CCONJ
ap-10605	279	10	c6c8	c6c8	PROPN
ap-10605	279	11	c7c9	c7c9	PROPN
ap-10605	279	12	∂10	∂10	PROPN
ap-10605	279	13	,	,	PUNCT
ap-10605	279	14	k1	k1	NOUN
ap-10605	279	15	=	=	SYM
ap-10605	279	16	(	(	PUNCT
ap-10605	279	17	x2	x2	NOUN
ap-10605	279	18	1	1	NUM
ap-10605	279	19	−	−	NOUN
ap-10605	279	20	x2	x2	NOUN
ap-10605	279	21	2	2	NUM
ap-10605	279	22	−	−	NOUN
ap-10605	280	1	x2	x2	NOUN
ap-10605	280	2	3	3	NUM
ap-10605	281	1	+	+	NUM
ap-10605	281	2	x2	x2	PROPN
ap-10605	281	3	4	4	X
ap-10605	281	4	)	)	PUNCT
ap-10605	281	5	∂1	∂1	NOUN
ap-10605	281	6	+	+	CCONJ
ap-10605	281	7	2x1x2∂2	2x1x2∂2	X
ap-10605	281	8	+	+	CCONJ
ap-10605	281	9	2x1x3∂3	2x1x3∂3	ADJ
ap-10605	281	10	+	+	CCONJ
ap-10605	281	11	2x1x4∂4	2x1x4∂4	ADJ
ap-10605	281	12	−	−	NOUN
ap-10605	281	13	2	2	NUM
ap-10605	281	14	(	(	PUNCT
ap-10605	281	15	x2	x2	PROPN
ap-10605	281	16	+	+	CCONJ
ap-10605	281	17	x4t7s5	x4t7s5	PRON
ap-10605	281	18	ch6	ch6	NOUN
ap-10605	281	19	−	−	PROPN
ap-10605	281	20	x3th6s5	x3th6s5	PROPN
ap-10605	281	21	)	)	PUNCT
ap-10605	281	22	∂5	∂5	VERB
ap-10605	281	23	−	−	PROPN
ap-10605	281	24	2(x4t7s6	2(x4t7s6	PUNCT
ap-10605	282	1	+	+	CCONJ
ap-10605	282	2	x3)c5∂6	x3)c5∂6	PROPN
ap-10605	282	3	−	−	PROPN
ap-10605	282	4	2x4c5c6∂7	2x4c5c6∂7	NUM
ap-10605	282	5	−	−	NUM
ap-10605	282	6	2	2	NUM
ap-10605	282	7	(	(	PUNCT
ap-10605	282	8	x4t9s6c5c8	x4t9s6c5c8	PROPN
ap-10605	282	9	c7	c7	PROPN
ap-10605	282	10	+	+	PROPN
ap-10605	282	11	x4t7th6s5	x4t7th6s5	X
ap-10605	283	1	+	+	CCONJ
ap-10605	283	2	x3s5	x3s5	PROPN
ap-10605	283	3	ch6	ch6	PROPN
ap-10605	284	1	+	+	CCONJ
ap-10605	284	2	x4t9s5s8	x4t9s5s8	PROPN
ap-10605	284	3	c7	c7	PROPN
ap-10605	284	4	)	)	PUNCT
ap-10605	284	5	∂8	∂8	X
ap-10605	284	6	+	+	CCONJ
ap-10605	284	7	2(c5s6s8	2(c5s6s8	NUM
ap-10605	284	8	−	−	PROPN
ap-10605	284	9	s5c8)x4	s5c8)x4	PUNCT
ap-10605	284	10	c7	c7	PROPN
ap-10605	284	11	∂9	∂9	AUX
ap-10605	284	12	−	−	PROPN
ap-10605	285	1	2(s5s8	2(s5s8	NUM
ap-10605	285	2	+	+	SYM
ap-10605	285	3	c5s6c8)x4	c5s6c8)x4	PROPN
ap-10605	285	4	c7c9	c7c9	PROPN
ap-10605	285	5	∂10	∂10	NOUN
ap-10605	285	6	−	−	PROPN
ap-10605	285	7	(	(	PUNCT
ap-10605	285	8	2x1x11	2x1x11	NUM
ap-10605	285	9	−	−	NOUN
ap-10605	285	10	ch7c5c6)∂11	ch7c5c6)∂11	NOUN
ap-10605	285	11	+	+	CCONJ
ap-10605	285	12	(	(	PUNCT
ap-10605	285	13	sh7sh9c5c6	sh7sh9c5c6	NOUN
ap-10605	285	14	+	+	NUM
ap-10605	285	15	ch9(s5c8	ch9(s5c8	PROPN
ap-10605	285	16	−	−	PROPN
ap-10605	285	17	s6s8c5	s6s8c5	NOUN
ap-10605	285	18	)	)	PUNCT
ap-10605	285	19	−	−	PROPN
ap-10605	285	20	2x1x12)∂12	2x1x12)∂12	NUM
ap-10605	285	21	+	+	CCONJ
ap-10605	285	22	(	(	PUNCT
ap-10605	285	23	sh9sh10(s5c8	sh9sh10(s5c8	VERB
ap-10605	285	24	−	−	PROPN
ap-10605	285	25	c5s6s8	c5s6s8	NOUN
ap-10605	285	26	)	)	PUNCT
ap-10605	285	27	+	+	NUM
ap-10605	285	28	ch10(s6c8c5	ch10(s6c8c5	NOUN
ap-10605	285	29	+	+	CCONJ
ap-10605	285	30	s5s8	s5s8	PUNCT
ap-10605	285	31	)	)	PUNCT
ap-10605	285	32	+	+	NOUN
ap-10605	285	33	sh7ch9sh10c5c6	sh7ch9sh10c5c6	NOUN
ap-10605	285	34	−	−	ADP
ap-10605	285	35	2x1x13)∂13	2x1x13)∂13	NUM
ap-10605	285	36	+	+	CCONJ
ap-10605	285	37	(	(	PUNCT
ap-10605	285	38	sh9ch10(s5c8	sh9ch10(s5c8	NUM
ap-10605	285	39	+	+	CCONJ
ap-10605	285	40	c5s6s8	c5s6s8	ADJ
ap-10605	285	41	)	)	PUNCT
ap-10605	285	42	+	+	NUM
ap-10605	285	43	sh10(s6c8c5	sh10(s6c8c5	NOUN
ap-10605	285	44	+	+	CCONJ
ap-10605	285	45	s5s8	s5s8	PUNCT
ap-10605	285	46	)	)	PUNCT
ap-10605	285	47	+	+	NUM
ap-10605	285	48	sh7ch9ch10c5c6	sh7ch9ch10c5c6	NOUN
ap-10605	285	49	−	−	ADP
ap-10605	285	50	2x1x14)∂14	2x1x14)∂14	PROPN
ap-10605	286	1	+	+	CCONJ
ap-10605	286	2	2x1∂15	2x1∂15	NUM
ap-10605	286	3	,	,	PUNCT
ap-10605	286	4	k2	k2	NOUN
ap-10605	286	5	=	=	PUNCT
ap-10605	286	6	2x1x2∂1	2x1x2∂1	PROPN
ap-10605	287	1	+	+	CCONJ
ap-10605	287	2	(	(	PUNCT
ap-10605	287	3	−x1	−x1	NOUN
ap-10605	287	4	2	2	NUM
ap-10605	287	5	+	+	CCONJ
ap-10605	287	6	x2	x2	PROPN
ap-10605	287	7	2	2	NUM
ap-10605	287	8	−	−	NOUN
ap-10605	287	9	x3	x3	NOUN
ap-10605	287	10	2	2	NUM
ap-10605	287	11	+	+	CCONJ
ap-10605	287	12	x4	x4	PROPN
ap-10605	287	13	2)∂x2	2)∂x2	NOUN
ap-10605	287	14	+	+	CCONJ
ap-10605	287	15	2x2x3∂3	2x2x3∂3	ADJ
ap-10605	287	16	+	+	CCONJ
ap-10605	287	17	2x2x4∂4	2x2x4∂4	ADJ
ap-10605	287	18	+	+	CCONJ
ap-10605	287	19	2	2	NUM
ap-10605	287	20	(	(	PUNCT
ap-10605	287	21	x4c5t7	x4c5t7	PROPN
ap-10605	287	22	ch6	ch6	PROPN
ap-10605	287	23	−	−	PROPN
ap-10605	288	1	x1	x1	INTJ
ap-10605	288	2	−	−	PROPN
ap-10605	288	3	x3c5th6	x3c5th6	PUNCT
ap-10605	288	4	)	)	PUNCT
ap-10605	289	1	∂5	∂5	VERB
ap-10605	290	1	+	+	X
ap-10605	290	2	2(x3	2(x3	NUM
ap-10605	291	1	+	+	CCONJ
ap-10605	291	2	x4t7s6)s5∂6	x4t7s6)s5∂6	X
ap-10605	291	3	+	+	CCONJ
ap-10605	291	4	2x4s5c6∂7	2x4s5c6∂7	SYM
ap-10605	291	5	+	+	NUM
ap-10605	291	6	2	2	NUM
ap-10605	291	7	(	(	PUNCT
ap-10605	291	8	x4t9	x4t9	X
ap-10605	291	9	c7	c7	PROPN
ap-10605	291	10	(	(	PUNCT
ap-10605	291	11	s6c8s5	s6c8s5	PROPN
ap-10605	291	12	−	−	PROPN
ap-10605	291	13	c5s8	c5s8	NOUN
ap-10605	291	14	)	)	PUNCT
ap-10605	291	15	−	−	PROPN
ap-10605	292	1	x4th7c5	x4th7c5	PROPN
ap-10605	292	2	−	−	PROPN
ap-10605	292	3	x3c5	x3c5	PUNCT
ap-10605	292	4	ch6	ch6	NOUN
ap-10605	292	5	)	)	PUNCT
ap-10605	292	6	∂8	∂8	X
ap-10605	293	1	−	−	PROPN
ap-10605	293	2	2(c5c8	2(c5c8	PROPN
ap-10605	294	1	+	+	CCONJ
ap-10605	294	2	s5s6s8)x4	s5s6s8)x4	PROPN
ap-10605	294	3	c7	c7	PROPN
ap-10605	294	4	∂9	∂9	NOUN
ap-10605	294	5	+	+	CCONJ
ap-10605	294	6	2(s5s6c8	2(s5s6c8	NUM
ap-10605	294	7	−	−	PROPN
ap-10605	294	8	c5s8)x4	c5s8)x4	ADJ
ap-10605	294	9	c7c9	c7c9	PROPN
ap-10605	294	10	∂10	∂10	NOUN
ap-10605	294	11	−	−	PROPN
ap-10605	294	12	(	(	PUNCT
ap-10605	294	13	2x2x11	2x2x11	NUM
ap-10605	294	14	+	+	CCONJ
ap-10605	294	15	ch7s5c6)∂11	ch7s5c6)∂11	NOUN
ap-10605	294	16	+	+	CCONJ
ap-10605	294	17	(	(	PUNCT
ap-10605	294	18	ch9(c5c8	ch9(c5c8	X
ap-10605	294	19	+	+	SYM
ap-10605	294	20	s5s6s8	s5s6s8	NOUN
ap-10605	294	21	)	)	PUNCT
ap-10605	294	22	−	−	ADP
ap-10605	295	1	sh7sh9s5c6	sh7sh9s5c6	PRON
ap-10605	295	2	−	−	PROPN
ap-10605	295	3	2x2x12	2x2x12	NUM
ap-10605	295	4	)	)	PUNCT
ap-10605	296	1	∂12	∂12	NOUN
ap-10605	296	2	+	+	CCONJ
ap-10605	296	3	(	(	PUNCT
ap-10605	296	4	sh9ch10c5c8	sh9ch10c5c8	VERB
ap-10605	296	5	+	+	CCONJ
ap-10605	296	6	ch10c5s8	ch10c5s8	VERB
ap-10605	296	7	−	−	PROPN
ap-10605	296	8	sh7sh10ch9s5c6	sh7sh10ch9s5c6	ADV
ap-10605	296	9	−	−	PROPN
ap-10605	296	10	ch10s5s6c8	ch10s5s6c8	NOUN
ap-10605	297	1	+	+	CCONJ
ap-10605	297	2	sh9sh10s5s6s8	sh9sh10s5s6s8	PROPN
ap-10605	297	3	−	−	PROPN
ap-10605	297	4	2x2x13	2x2x13	NUM
ap-10605	297	5	)	)	PUNCT
ap-10605	298	1	∂13	∂13	NOUN
ap-10605	298	2	+	+	CCONJ
ap-10605	298	3	(	(	PUNCT
ap-10605	298	4	sh9ch10(c5c8	sh9ch10(c5c8	NOUN
ap-10605	298	5	+	+	CCONJ
ap-10605	298	6	s5s6c8	s5s6c8	NOUN
ap-10605	298	7	)	)	PUNCT
ap-10605	299	1	+	+	CCONJ
ap-10605	299	2	sh10(s8c5	sh10(s8c5	PROPN
ap-10605	299	3	−	−	PROPN
ap-10605	299	4	s5s6c8	s5s6c8	NOUN
ap-10605	299	5	)	)	PUNCT
ap-10605	299	6	−	−	ADP
ap-10605	299	7	sh7ch9ch10s5c6	sh7ch9ch10s5c6	NOUN
ap-10605	299	8	−	−	PROPN
ap-10605	299	9	2x2x14	2x2x14	NUM
ap-10605	299	10	)	)	PUNCT
ap-10605	300	1	∂14	∂14	ADV
ap-10605	300	2	+	+	ADP
ap-10605	300	3	2x2∂15	2x2∂15	NOUN
ap-10605	300	4	,	,	PUNCT
ap-10605	300	5	k3	k3	PROPN
ap-10605	300	6	=	=	NOUN
ap-10605	300	7	2x1x3∂1	2x1x3∂1	PROPN
ap-10605	301	1	+	+	CCONJ
ap-10605	302	1	2x2x3∂x2	2x2x3∂x2	NUM
ap-10605	302	2	+	+	CCONJ
ap-10605	302	3	(	(	PUNCT
ap-10605	302	4	−x2	−x2	PROPN
ap-10605	302	5	1	1	NUM
ap-10605	302	6	−	−	NOUN
ap-10605	302	7	x2	x2	NOUN
ap-10605	302	8	2	2	NUM
ap-10605	303	1	+	+	CCONJ
ap-10605	303	2	x2	x2	PROPN
ap-10605	303	3	3	3	NUM
ap-10605	304	1	+	+	NUM
ap-10605	304	2	x2	x2	PROPN
ap-10605	304	3	4	4	X
ap-10605	304	4	)	)	PUNCT
ap-10605	304	5	∂3	∂3	NOUN
ap-10605	305	1	+	+	CCONJ
ap-10605	305	2	2x3x4∂4	2x3x4∂4	PROPN
ap-10605	305	3	−	−	NOUN
ap-10605	305	4	2th6(x1s5	2th6(x1s5	NOUN
ap-10605	306	1	+	+	CCONJ
ap-10605	306	2	x2c5)∂5	x2c5)∂5	PROPN
ap-10605	306	3	−	−	PROPN
ap-10605	306	4	2(x4t7c6	2(x4t7c6	NUM
ap-10605	307	1	−	−	NOUN
ap-10605	307	2	x1c5	x1c5	X
ap-10605	307	3	+	+	CCONJ
ap-10605	307	4	x2s5)∂6	x2s5)∂6	PROPN
ap-10605	307	5	+	+	CCONJ
ap-10605	307	6	2x4s6∂7	2x4s6∂7	NOUN
ap-10605	307	7	+	+	CCONJ
ap-10605	307	8	(	(	PUNCT
ap-10605	307	9	x1s5	x1s5	PUNCT
ap-10605	308	1	+	+	CCONJ
ap-10605	308	2	x2c5	x2c5	ADJ
ap-10605	308	3	ch6	ch6	NOUN
ap-10605	309	1	−	−	NOUN
ap-10605	309	2	2x4t9c6c8	2x4t9c6c8	NUM
ap-10605	309	3	c7	c7	NOUN
ap-10605	309	4	)	)	PUNCT
ap-10605	310	1	∂8	∂8	X
ap-10605	310	2	+	+	CCONJ
ap-10605	311	1	2s8c6x4	2s8c6x4	NUM
ap-10605	311	2	c7	c7	PROPN
ap-10605	311	3	∂9	∂9	PROPN
ap-10605	311	4	−	−	PROPN
ap-10605	311	5	2c6c8x4	2c6c8x4	NUM
ap-10605	311	6	c7c9	c7c9	PROPN
ap-10605	311	7	∂10	∂10	NOUN
ap-10605	311	8	−	−	PROPN
ap-10605	312	1	(	(	PUNCT
ap-10605	312	2	ch7s6	ch7s6	PROPN
ap-10605	312	3	+	+	NUM
ap-10605	312	4	2x3x11)∂11	2x3x11)∂11	NUM
ap-10605	312	5	−	−	NOUN
ap-10605	312	6	(	(	PUNCT
ap-10605	313	1	ch9c6s8	ch9c6s8	PROPN
ap-10605	313	2	+	+	NUM
ap-10605	313	3	2x3x12	2x3x12	NUM
ap-10605	314	1	+	+	CCONJ
ap-10605	314	2	sh7sh9s6)∂12	sh7sh9s6)∂12	PROPN
ap-10605	314	3	+	+	CCONJ
ap-10605	314	4	(	(	PUNCT
ap-10605	314	5	ch10c6c8	ch10c6c8	PROPN
ap-10605	314	6	−	−	PROPN
ap-10605	314	7	sh9sh10c6s8	sh9sh10c6s8	ADJ
ap-10605	314	8	−	−	PROPN
ap-10605	314	9	sh7ch9sh10s6	sh7ch9sh10s6	NOUN
ap-10605	314	10	−	−	PROPN
ap-10605	314	11	2x3x13	2x3x13	NUM
ap-10605	314	12	)	)	PUNCT
ap-10605	315	1	∂13	∂13	NOUN
ap-10605	315	2	+	+	CCONJ
ap-10605	315	3	(	(	PUNCT
ap-10605	315	4	ch10c6c8	ch10c6c8	PROPN
ap-10605	315	5	−	−	PROPN
ap-10605	315	6	sh9ch10c6s8	sh9ch10c6s8	NOUN
ap-10605	315	7	−	−	NOUN
ap-10605	315	8	sh7ch9ch10s6	sh7ch9ch10s6	PUNCT
ap-10605	315	9	−	−	PROPN
ap-10605	315	10	2x3x14	2x3x14	NUM
ap-10605	315	11	)	)	PUNCT
ap-10605	316	1	∂14	∂14	ADV
ap-10605	316	2	+	+	PUNCT
ap-10605	316	3	2x3∂15	2x3∂15	ADJ
ap-10605	316	4	,	,	PUNCT
ap-10605	316	5	560	560	NUM
ap-10605	316	6	vol	vol	NOUN
ap-10605	316	7	.	.	PUNCT
ap-10605	317	1	65	65	NUM
ap-10605	317	2	no	no	NOUN
ap-10605	317	3	.	.	PUNCT
ap-10605	318	1	5/2025	5/2025	NUM
ap-10605	318	2	on	on	ADP
ap-10605	318	3	realizations	realization	NOUN
ap-10605	318	4	of	of	ADP
ap-10605	318	5	lie	lie	NOUN
ap-10605	318	6	algebras	algebras	PROPN
ap-10605	318	7	k4	k4	PROPN
ap-10605	318	8	=	=	PUNCT
ap-10605	318	9	−	−	PROPN
ap-10605	318	10	2x1x4∂1	2x1x4∂1	PROPN
ap-10605	318	11	−	−	PROPN
ap-10605	319	1	2x2x4∂x2	2x2x4∂x2	NUM
ap-10605	319	2	−	−	NOUN
ap-10605	319	3	2x4x3∂3	2x4x3∂3	NOUN
ap-10605	319	4	−	−	PROPN
ap-10605	320	1	(	(	PUNCT
ap-10605	320	2	x2	x2	NOUN
ap-10605	320	3	1	1	NUM
ap-10605	321	1	+	+	NUM
ap-10605	321	2	x2	x2	PROPN
ap-10605	321	3	2	2	NUM
ap-10605	322	1	+	+	NUM
ap-10605	322	2	x2	x2	PROPN
ap-10605	322	3	3	3	NUM
ap-10605	323	1	+	+	NUM
ap-10605	323	2	x2	x2	PROPN
ap-10605	323	3	4	4	X
ap-10605	323	4	)	)	PUNCT
ap-10605	323	5	∂4	∂4	NOUN
ap-10605	323	6	+	+	CCONJ
ap-10605	323	7	2t7(x1s5	2t7(x1s5	NUM
ap-10605	324	1	+	+	CCONJ
ap-10605	324	2	x2c5	x2c5	X
ap-10605	324	3	)	)	PUNCT
ap-10605	324	4	ch6	ch6	NOUN
ap-10605	324	5	∂5	∂5	NOUN
ap-10605	324	6	+	+	CCONJ
ap-10605	325	1	2t7(x1s6c5	2t7(x1s6c5	NUM
ap-10605	325	2	−	−	NOUN
ap-10605	325	3	x2s6s5	x2s6s5	PROPN
ap-10605	325	4	+	+	CCONJ
ap-10605	325	5	x3c6)∂6	x3c6)∂6	PROPN
ap-10605	325	6	−	−	PROPN
ap-10605	325	7	2(x2c6s5	2(x2c6s5	NUM
ap-10605	325	8	−	−	NOUN
ap-10605	325	9	x1c6c5	x1c6c5	PROPN
ap-10605	325	10	+	+	NUM
ap-10605	325	11	x3s6)∂7	x3s6)∂7	PROPN
ap-10605	326	1	+	+	CCONJ
ap-10605	326	2	2	2	NUM
ap-10605	326	3	(	(	PUNCT
ap-10605	326	4	t9	t9	PROPN
ap-10605	326	5	c7	c7	PROPN
ap-10605	326	6	(	(	PUNCT
ap-10605	326	7	x2s5s6c8	x2s5s6c8	PROPN
ap-10605	326	8	−	−	PROPN
ap-10605	326	9	x1s6c5c8	x1s6c5c8	PROPN
ap-10605	326	10	−	−	PROPN
ap-10605	327	1	x3c6c8	x3c6c8	PROPN
ap-10605	327	2	−	−	PROPN
ap-10605	327	3	x1s5s8	x1s5s8	PROPN
ap-10605	327	4	−	−	PROPN
ap-10605	327	5	x2s8c5	x2s8c5	PROPN
ap-10605	327	6	)	)	PUNCT
ap-10605	327	7	−	−	PROPN
ap-10605	328	1	th6t7(x1s5	th6t7(x1s5	NOUN
ap-10605	328	2	+	+	CCONJ
ap-10605	328	3	x2c5	x2c5	PROPN
ap-10605	328	4	)	)	PUNCT
ap-10605	328	5	)	)	PUNCT
ap-10605	329	1	∂8	∂8	X
ap-10605	329	2	−	−	PROPN
ap-10605	329	3	2	2	NUM
ap-10605	329	4	c7	c7	PROPN
ap-10605	329	5	(	(	PUNCT
ap-10605	329	6	x2	x2	INTJ
ap-10605	329	7	−	−	PROPN
ap-10605	329	8	s5s6s8	s5s6s8	PROPN
ap-10605	329	9	+	+	CCONJ
ap-10605	329	10	x1c5s6s8	x1c5s6s8	PROPN
ap-10605	329	11	+	+	CCONJ
ap-10605	329	12	x3c6s8	x3c6s8	PROPN
ap-10605	329	13	−	−	PROPN
ap-10605	329	14	x1s5c8	x1s5c8	NOUN
ap-10605	329	15	−	−	PROPN
ap-10605	330	1	x2c5c8)∂9	x2c5c8)∂9	PROPN
ap-10605	330	2	+	+	CCONJ
ap-10605	330	3	2	2	NUM
ap-10605	330	4	c7c9	c7c9	X
ap-10605	330	5	(	(	PUNCT
ap-10605	330	6	x1c5s6c8	x1c5s6c8	NOUN
ap-10605	330	7	−	−	PROPN
ap-10605	330	8	x2s5s6c8	x2s5s6c8	PROPN
ap-10605	330	9	+	+	CCONJ
ap-10605	330	10	x3c6c8	x3c6c8	PROPN
ap-10605	330	11	+	+	CCONJ
ap-10605	330	12	x1s5s8	x1s5s8	PUNCT
ap-10605	331	1	+	+	PUNCT
ap-10605	331	2	x2c5s8)∂10	x2c5s8)∂10	PUNCT
ap-10605	332	1	+	+	CCONJ
ap-10605	332	2	(	(	PUNCT
ap-10605	332	3	2x4x11	2x4x11	NUM
ap-10605	332	4	+	+	CCONJ
ap-10605	332	5	sh7)∂11	sh7)∂11	NOUN
ap-10605	332	6	+	+	CCONJ
ap-10605	332	7	(	(	PUNCT
ap-10605	332	8	2x4x12	2x4x12	NUM
ap-10605	332	9	+	+	CCONJ
ap-10605	332	10	ch7sh9)∂12	ch7sh9)∂12	VERB
ap-10605	332	11	+	+	CCONJ
ap-10605	332	12	(	(	PUNCT
ap-10605	332	13	2x4x13	2x4x13	NUM
ap-10605	332	14	+	+	CCONJ
ap-10605	332	15	ch7ch9sh10)∂13	ch7ch9sh10)∂13	PROPN
ap-10605	332	16	+	+	CCONJ
ap-10605	332	17	(	(	PUNCT
ap-10605	332	18	2x4x14	2x4x14	NUM
ap-10605	332	19	+	+	CCONJ
ap-10605	332	20	ch7ch9ch10)∂14	ch7ch9ch10)∂14	PROPN
ap-10605	332	21	−	−	PROPN
ap-10605	332	22	2x4∂15	2x4∂15	NUM
ap-10605	332	23	,	,	PUNCT
ap-10605	332	24	d	d	PROPN
ap-10605	332	25	=	=	X
ap-10605	333	1	x1∂1	x1∂1	PROPN
ap-10605	333	2	+	+	PROPN
ap-10605	334	1	x2∂2	x2∂2	PROPN
ap-10605	335	1	+	+	CCONJ
ap-10605	336	1	x3∂3	x3∂3	PROPN
ap-10605	336	2	+	+	CCONJ
ap-10605	336	3	x4∂4	x4∂4	PROPN
ap-10605	336	4	−	−	PROPN
ap-10605	336	5	x11∂11	x11∂11	PUNCT
ap-10605	337	1	−	−	PROPN
ap-10605	338	1	x12∂12	x12∂12	PROPN
ap-10605	339	1	−	−	PROPN
ap-10605	339	2	x13∂13	x13∂13	PROPN
ap-10605	340	1	−	−	PROPN
ap-10605	340	2	x14∂14	x14∂14	PROPN
ap-10605	341	1	+	+	PUNCT
ap-10605	341	2	∂15	∂15	PROPN
ap-10605	341	3	.	.	PUNCT
ap-10605	341	4	a.2	a.2	PUNCT
ap-10605	341	5	.	.	PUNCT
ap-10605	342	1	generic	generic	ADJ
ap-10605	342	2	realizations	realization	NOUN
ap-10605	342	3	of	of	ADP
ap-10605	342	4	de	de	PROPN
ap-10605	342	5	sitter	sitter	NOUN
ap-10605	342	6	algebras	algebras	PROPN
ap-10605	342	7	rgeneric(c(3	rgeneric(c(3	PROPN
ap-10605	342	8	,	,	PUNCT
ap-10605	342	9	0	0	NUM
ap-10605	342	10	)	)	PUNCT
ap-10605	342	11	)	)	PUNCT
ap-10605	342	12	:	:	PUNCT
ap-10605	343	1	p1	p1	NOUN
ap-10605	343	2	=	=	SYM
ap-10605	343	3	∂1	∂1	ADJ
ap-10605	343	4	,	,	PUNCT
ap-10605	343	5	p2	p2	PROPN
ap-10605	343	6	=	=	SYM
ap-10605	343	7	∂2	∂2	PROPN
ap-10605	343	8	,	,	PUNCT
ap-10605	343	9	p3	p3	PROPN
ap-10605	343	10	=	=	SYM
ap-10605	343	11	∂3	∂3	PROPN
ap-10605	343	12	,	,	PUNCT
ap-10605	343	13	j12	j12	X
ap-10605	343	14	=	=	PUNCT
ap-10605	344	1	x2∂1	x2∂1	PROPN
ap-10605	344	2	−	−	PROPN
ap-10605	345	1	x1∂2	x1∂2	NOUN
ap-10605	345	2	+	+	NUM
ap-10605	345	3	∂4	∂4	PROPN
ap-10605	345	4	,	,	PUNCT
ap-10605	345	5	j13	j13	NOUN
ap-10605	345	6	=	=	SYM
ap-10605	345	7	x3∂1	x3∂1	PROPN
ap-10605	346	1	−	−	PROPN
ap-10605	346	2	x1∂3	x1∂3	INTJ
ap-10605	347	1	−	−	PROPN
ap-10605	347	2	th5s4∂4	th5s4∂4	PROPN
ap-10605	347	3	+	+	NUM
ap-10605	347	4	c4∂5	c4∂5	PROPN
ap-10605	347	5	+	+	NUM
ap-10605	347	6	s4	s4	PROPN
ap-10605	347	7	ch5	ch5	NOUN
ap-10605	347	8	∂6	∂6	NOUN
ap-10605	347	9	,	,	PUNCT
ap-10605	347	10	j23	j23	PROPN
ap-10605	347	11	=	=	PUNCT
ap-10605	348	1	x3∂2	x3∂2	PROPN
ap-10605	348	2	−	−	NOUN
ap-10605	349	1	x2∂3	x2∂3	PROPN
ap-10605	349	2	−	−	PROPN
ap-10605	350	1	th5c4∂4	th5c4∂4	ADV
ap-10605	350	2	−	−	PUNCT
ap-10605	351	1	s4∂5	s4∂5	PROPN
ap-10605	351	2	+	+	NUM
ap-10605	351	3	c4	c4	NOUN
ap-10605	351	4	ch5	ch5	NOUN
ap-10605	351	5	∂6	∂6	NOUN
ap-10605	351	6	,	,	PUNCT
ap-10605	351	7	k1	k1	NOUN
ap-10605	351	8	=	=	SYM
ap-10605	351	9	(	(	PUNCT
ap-10605	351	10	x2	x2	NOUN
ap-10605	351	11	1	1	NUM
ap-10605	351	12	−	−	NOUN
ap-10605	351	13	x2	x2	NOUN
ap-10605	352	1	2	2	NUM
ap-10605	352	2	−	−	NOUN
ap-10605	352	3	x2	x2	NOUN
ap-10605	352	4	3	3	X
ap-10605	352	5	)	)	PUNCT
ap-10605	352	6	∂1	∂1	NOUN
ap-10605	352	7	+	+	CCONJ
ap-10605	352	8	2x1x2∂2	2x1x2∂2	X
ap-10605	352	9	+	+	CCONJ
ap-10605	352	10	2x1x3∂3	2x1x3∂3	ADJ
ap-10605	352	11	+	+	CCONJ
ap-10605	352	12	2(x3s4th5	2(x3s4th5	NUM
ap-10605	352	13	−	−	NOUN
ap-10605	352	14	x2)∂4	x2)∂4	PROPN
ap-10605	353	1	−	−	PROPN
ap-10605	353	2	2x3c4∂5	2x3c4∂5	NOUN
ap-10605	353	3	−	−	PROPN
ap-10605	353	4	2x3s4	2x3s4	NUM
ap-10605	353	5	ch5	ch5	VERB
ap-10605	353	6	∂6	∂6	NOUN
ap-10605	353	7	+	+	CCONJ
ap-10605	353	8	(	(	PUNCT
ap-10605	353	9	c4c5	c4c5	X
ap-10605	353	10	−	−	PROPN
ap-10605	353	11	2x1x7)∂7	2x1x7)∂7	NUM
ap-10605	353	12	+	+	CCONJ
ap-10605	353	13	(	(	PUNCT
ap-10605	353	14	s4ch6	s4ch6	NOUN
ap-10605	353	15	−	−	PROPN
ap-10605	353	16	c4sh5sh6	c4sh5sh6	ADJ
ap-10605	353	17	−	−	PROPN
ap-10605	353	18	2x1x8)∂8	2x1x8)∂8	NUM
ap-10605	353	19	+	+	CCONJ
ap-10605	353	20	(	(	PUNCT
ap-10605	353	21	c4s5c6	c4s5c6	NOUN
ap-10605	353	22	+	+	CCONJ
ap-10605	353	23	s4s6	s4s6	ADJ
ap-10605	353	24	−	−	PROPN
ap-10605	353	25	2x1x9)∂9	2x1x9)∂9	NUM
ap-10605	353	26	+	+	CCONJ
ap-10605	353	27	2x1∂10	2x1∂10	NUM
ap-10605	353	28	,	,	PUNCT
ap-10605	353	29	k2	k2	NOUN
ap-10605	353	30	=	=	NOUN
ap-10605	353	31	2x1x2∂1	2x1x2∂1	NOUN
ap-10605	354	1	+	+	CCONJ
ap-10605	354	2	(	(	PUNCT
ap-10605	354	3	x2	x2	INTJ
ap-10605	354	4	2	2	NUM
ap-10605	354	5	−	−	NOUN
ap-10605	354	6	x2	x2	NOUN
ap-10605	354	7	1	1	NUM
ap-10605	354	8	−	−	NOUN
ap-10605	355	1	x2	x2	NOUN
ap-10605	355	2	3	3	X
ap-10605	355	3	)	)	PUNCT
ap-10605	355	4	∂2	∂2	NOUN
ap-10605	356	1	+	+	CCONJ
ap-10605	356	2	2x2x3∂3	2x2x3∂3	ADJ
ap-10605	357	1	+	+	CCONJ
ap-10605	357	2	2(x1	2(x1	NUM
ap-10605	357	3	+	+	CCONJ
ap-10605	357	4	x3c4th5)∂4	x3c4th5)∂4	ADJ
ap-10605	357	5	+	+	CCONJ
ap-10605	357	6	2x3s4∂5	2x3s4∂5	PROPN
ap-10605	357	7	−	−	PROPN
ap-10605	357	8	2x3c4	2x3c4	NUM
ap-10605	357	9	ch5	ch5	VERB
ap-10605	357	10	∂6	∂6	NOUN
ap-10605	357	11	−	−	PROPN
ap-10605	358	1	(	(	PUNCT
ap-10605	358	2	s4c5	s4c5	NOUN
ap-10605	358	3	+	+	NOUN
ap-10605	358	4	2x2x7)∂7	2x2x7)∂7	NUM
ap-10605	358	5	+	+	CCONJ
ap-10605	358	6	(	(	PUNCT
ap-10605	358	7	s4s5s6	s4s5s6	VERB
ap-10605	358	8	+	+	CCONJ
ap-10605	358	9	c4c6	c4c6	NOUN
ap-10605	358	10	−	−	NOUN
ap-10605	358	11	2x8x2)∂8	2x8x2)∂8	NUM
ap-10605	358	12	+	+	CCONJ
ap-10605	358	13	(	(	PUNCT
ap-10605	358	14	c4s6	c4s6	PRON
ap-10605	358	15	−	−	PROPN
ap-10605	358	16	s4s5c6	s4s5c6	NOUN
ap-10605	358	17	−	−	PROPN
ap-10605	358	18	2x2x9)∂9	2x2x9)∂9	NUM
ap-10605	358	19	+	+	CCONJ
ap-10605	358	20	2x2∂10	2x2∂10	NOUN
ap-10605	358	21	,	,	PUNCT
ap-10605	358	22	k3	k3	ADJ
ap-10605	358	23	=	=	PROPN
ap-10605	358	24	2x1x3∂1	2x1x3∂1	PROPN
ap-10605	359	1	+	+	CCONJ
ap-10605	359	2	2x2x3∂2	2x2x3∂2	NOUN
ap-10605	359	3	+	+	CCONJ
ap-10605	360	1	(	(	PUNCT
ap-10605	360	2	x2	x2	INTJ
ap-10605	360	3	3	3	NUM
ap-10605	360	4	−	−	NOUN
ap-10605	360	5	x2	x2	NOUN
ap-10605	360	6	1	1	NUM
ap-10605	360	7	−	−	NOUN
ap-10605	360	8	x2	x2	NOUN
ap-10605	360	9	2	2	X
ap-10605	360	10	)	)	PUNCT
ap-10605	360	11	∂3	∂3	NOUN
ap-10605	360	12	−	−	PROPN
ap-10605	360	13	2(x1s4	2(x1s4	PROPN
ap-10605	360	14	+	+	CCONJ
ap-10605	360	15	x2c4)th5∂4	x2c4)th5∂4	NOUN
ap-10605	360	16	+	+	CCONJ
ap-10605	360	17	2(x1c4	2(x1c4	NUM
ap-10605	360	18	−	−	NOUN
ap-10605	360	19	x2s4)∂5	x2s4)∂5	PROPN
ap-10605	360	20	+	+	CCONJ
ap-10605	360	21	2x1s4	2x1s4	NUM
ap-10605	360	22	+	+	CCONJ
ap-10605	360	23	x2c4	x2c4	PUNCT
ap-10605	360	24	ch5	ch5	NOUN
ap-10605	360	25	∂6	∂6	NOUN
ap-10605	360	26	−	−	PROPN
ap-10605	360	27	(	(	PUNCT
ap-10605	360	28	s5	s5	X
ap-10605	360	29	+	+	CCONJ
ap-10605	360	30	2x3x7)∂7	2x3x7)∂7	NUM
ap-10605	360	31	−	−	NOUN
ap-10605	360	32	(	(	PUNCT
ap-10605	360	33	c5s6	c5s6	X
ap-10605	360	34	+	+	X
ap-10605	360	35	2x8x3)∂8	2x8x3)∂8	NUM
ap-10605	360	36	+	+	CCONJ
ap-10605	360	37	(	(	PUNCT
ap-10605	360	38	c5c6	c5c6	NOUN
ap-10605	360	39	−	−	NOUN
ap-10605	360	40	2x9x3)∂9	2x9x3)∂9	NUM
ap-10605	360	41	+	+	CCONJ
ap-10605	360	42	2x3∂10	2x3∂10	NUM
ap-10605	360	43	,	,	PUNCT
ap-10605	360	44	d	d	NOUN
ap-10605	360	45	=	=	PUNCT
ap-10605	361	1	x1∂1	x1∂1	PROPN
ap-10605	361	2	+	+	PROPN
ap-10605	362	1	x2∂2	x2∂2	PROPN
ap-10605	363	1	+	+	CCONJ
ap-10605	363	2	x3∂3	x3∂3	PROPN
ap-10605	363	3	−	−	PROPN
ap-10605	364	1	x7∂7	x7∂7	PROPN
ap-10605	364	2	−	−	PROPN
ap-10605	365	1	x8∂8	x8∂8	PROPN
ap-10605	365	2	−	−	PROPN
ap-10605	366	1	x9∂9	x9∂9	PROPN
ap-10605	366	2	+	+	PROPN
ap-10605	366	3	∂10	∂10	PROPN
ap-10605	366	4	.	.	PUNCT
ap-10605	367	1	rgeneric(c(2	rgeneric(c(2	PROPN
ap-10605	367	2	,	,	PUNCT
ap-10605	367	3	1	1	NUM
ap-10605	367	4	)	)	PUNCT
ap-10605	367	5	)	)	PUNCT
ap-10605	368	1	:	:	PUNCT
ap-10605	368	2	p1	p1	NOUN
ap-10605	368	3	=	=	SYM
ap-10605	368	4	∂1	∂1	ADJ
ap-10605	368	5	,	,	PUNCT
ap-10605	368	6	p2	p2	PROPN
ap-10605	368	7	=	=	SYM
ap-10605	368	8	∂2	∂2	PROPN
ap-10605	368	9	,	,	PUNCT
ap-10605	368	10	p3	p3	PROPN
ap-10605	368	11	=	=	SYM
ap-10605	368	12	∂3	∂3	PROPN
ap-10605	368	13	,	,	PUNCT
ap-10605	368	14	j12	j12	X
ap-10605	368	15	=	=	PUNCT
ap-10605	369	1	x2∂1	x2∂1	PROPN
ap-10605	369	2	−	−	PROPN
ap-10605	370	1	x1∂2	x1∂2	NOUN
ap-10605	370	2	+	+	NUM
ap-10605	370	3	∂4	∂4	PROPN
ap-10605	370	4	,	,	PUNCT
ap-10605	370	5	j13	j13	NOUN
ap-10605	370	6	=	=	SYM
ap-10605	371	1	−	−	PROPN
ap-10605	372	1	x3∂1	x3∂1	PROPN
ap-10605	373	1	−	−	PROPN
ap-10605	373	2	x1∂3	x1∂3	INTJ
ap-10605	374	1	+	+	CCONJ
ap-10605	374	2	s4t5∂4	s4t5∂4	PROPN
ap-10605	374	3	+	+	CCONJ
ap-10605	374	4	c4∂5	c4∂5	PROPN
ap-10605	374	5	+	+	CCONJ
ap-10605	374	6	s4	s4	PROPN
ap-10605	374	7	c5	c5	PROPN
ap-10605	374	8	∂6	∂6	PROPN
ap-10605	374	9	,	,	PUNCT
ap-10605	374	10	j23	j23	PROPN
ap-10605	374	11	=	=	SYM
ap-10605	374	12	−	−	PROPN
ap-10605	375	1	x3∂2	x3∂2	NUM
ap-10605	375	2	−	−	PROPN
ap-10605	376	1	x2∂3	x2∂3	PROPN
ap-10605	377	1	+	+	CCONJ
ap-10605	377	2	c4t5∂4	c4t5∂4	PROPN
ap-10605	378	1	−	−	NOUN
ap-10605	379	1	s4∂5	s4∂5	PROPN
ap-10605	379	2	+	+	NUM
ap-10605	379	3	c4	c4	NOUN
ap-10605	379	4	c5	c5	PROPN
ap-10605	379	5	∂6	∂6	PROPN
ap-10605	379	6	,	,	PUNCT
ap-10605	379	7	k1	k1	NOUN
ap-10605	379	8	=	=	SYM
ap-10605	379	9	(	(	PUNCT
ap-10605	379	10	x2	x2	NOUN
ap-10605	379	11	1	1	NUM
ap-10605	379	12	−	−	NOUN
ap-10605	379	13	x2	x2	NOUN
ap-10605	379	14	2	2	NUM
ap-10605	379	15	+	+	CCONJ
ap-10605	379	16	x2	x2	PROPN
ap-10605	379	17	3	3	X
ap-10605	379	18	)	)	PUNCT
ap-10605	379	19	∂1	∂1	NOUN
ap-10605	379	20	+	+	CCONJ
ap-10605	379	21	2x1x2∂2	2x1x2∂2	X
ap-10605	379	22	+	+	CCONJ
ap-10605	379	23	2x1x3∂3	2x1x3∂3	ADJ
ap-10605	379	24	−	−	PROPN
ap-10605	379	25	2(x2	2(x2	NOUN
ap-10605	380	1	+	+	CCONJ
ap-10605	380	2	x3s4t5)∂4	x3s4t5)∂4	PROPN
ap-10605	380	3	−	−	PROPN
ap-10605	380	4	2x3c4∂5	2x3c4∂5	NOUN
ap-10605	380	5	−	−	PROPN
ap-10605	380	6	2x3s4	2x3s4	NUM
ap-10605	380	7	c5	c5	PROPN
ap-10605	380	8	∂6	∂6	VERB
ap-10605	380	9	+	+	CCONJ
ap-10605	380	10	(	(	PUNCT
ap-10605	380	11	c4ch5	c4ch5	VERB
ap-10605	380	12	−	−	PROPN
ap-10605	380	13	2x1x7)∂7	2x1x7)∂7	NUM
ap-10605	380	14	+	+	CCONJ
ap-10605	380	15	(	(	PUNCT
ap-10605	380	16	s4ch6	s4ch6	NOUN
ap-10605	380	17	+	+	CCONJ
ap-10605	380	18	c4sh5sh6	c4sh5sh6	NUM
ap-10605	380	19	−	−	NOUN
ap-10605	380	20	2x1x8)∂8	2x1x8)∂8	NUM
ap-10605	380	21	+	+	CCONJ
ap-10605	380	22	(	(	PUNCT
ap-10605	380	23	s4sh6	s4sh6	NOUN
ap-10605	380	24	+	+	CCONJ
ap-10605	380	25	c4sh5ch6	c4sh5ch6	PRON
ap-10605	380	26	−	−	NOUN
ap-10605	380	27	2x1x9)∂9	2x1x9)∂9	NUM
ap-10605	381	1	+	+	CCONJ
ap-10605	381	2	2x1∂10	2x1∂10	NUM
ap-10605	381	3	,	,	PUNCT
ap-10605	381	4	k2	k2	NOUN
ap-10605	381	5	=	=	NOUN
ap-10605	381	6	2x1x2∂1	2x1x2∂1	NOUN
ap-10605	382	1	+	+	CCONJ
ap-10605	382	2	(	(	PUNCT
ap-10605	382	3	x2	x2	NOUN
ap-10605	382	4	2	2	NUM
ap-10605	382	5	+	+	NUM
ap-10605	382	6	x2	x2	PROPN
ap-10605	382	7	3	3	NUM
ap-10605	382	8	−	−	NOUN
ap-10605	383	1	x2	x2	NOUN
ap-10605	383	2	1	1	X
ap-10605	383	3	)	)	PUNCT
ap-10605	383	4	∂2	∂2	NOUN
ap-10605	384	1	+	+	CCONJ
ap-10605	384	2	2x2x3∂3	2x2x3∂3	ADJ
ap-10605	384	3	−	−	PROPN
ap-10605	384	4	2(x3c4t5	2(x3c4t5	NUM
ap-10605	384	5	−	−	NOUN
ap-10605	384	6	x1)∂4	x1)∂4	PUNCT
ap-10605	385	1	+	+	NUM
ap-10605	385	2	2x3s4∂5	2x3s4∂5	PROPN
ap-10605	385	3	−	−	PROPN
ap-10605	385	4	2x3c4	2x3c4	NUM
ap-10605	385	5	c5	c5	PROPN
ap-10605	385	6	∂6	∂6	VERB
ap-10605	385	7	−	−	PROPN
ap-10605	385	8	(	(	PUNCT
ap-10605	385	9	2x2x7	2x2x7	NUM
ap-10605	385	10	+	+	NUM
ap-10605	385	11	s4ch5)∂7	s4ch5)∂7	PROPN
ap-10605	385	12	+	+	CCONJ
ap-10605	385	13	(	(	PUNCT
ap-10605	385	14	c4ch6	c4ch6	ADJ
ap-10605	385	15	−	−	PROPN
ap-10605	385	16	s4sh5sh6	s4sh5sh6	PROPN
ap-10605	385	17	−	−	PROPN
ap-10605	385	18	2x2x8)∂8	2x2x8)∂8	NUM
ap-10605	385	19	+	+	CCONJ
ap-10605	385	20	(	(	PUNCT
ap-10605	385	21	c4sh6	c4sh6	ADJ
ap-10605	385	22	−	−	NOUN
ap-10605	385	23	s4sh5ch6	s4sh5ch6	NUM
ap-10605	385	24	−	−	PROPN
ap-10605	385	25	2x2x9)∂9	2x2x9)∂9	NUM
ap-10605	385	26	+	+	CCONJ
ap-10605	385	27	2x2∂10	2x2∂10	NOUN
ap-10605	385	28	,	,	PUNCT
ap-10605	385	29	k3	k3	VERB
ap-10605	385	30	=	=	SYM
ap-10605	385	31	−	−	PROPN
ap-10605	385	32	2x1x3∂1	2x1x3∂1	NOUN
ap-10605	385	33	−	−	PROPN
ap-10605	385	34	2x2x3∂2	2x2x3∂2	NOUN
ap-10605	385	35	−	−	PROPN
ap-10605	386	1	(	(	PUNCT
ap-10605	386	2	x2	x2	NOUN
ap-10605	386	3	1	1	NUM
ap-10605	387	1	+	+	NUM
ap-10605	387	2	x2	x2	PROPN
ap-10605	387	3	2	2	NUM
ap-10605	388	1	+	+	NUM
ap-10605	388	2	x2	x2	PROPN
ap-10605	388	3	3	3	X
ap-10605	388	4	)	)	PUNCT
ap-10605	388	5	∂3	∂3	NOUN
ap-10605	389	1	+	+	CCONJ
ap-10605	389	2	2(t5(x1s4	2(t5(x1s4	NUM
ap-10605	389	3	+	+	CCONJ
ap-10605	389	4	x2c4)∂4	x2c4)∂4	PROPN
ap-10605	390	1	+	+	CCONJ
ap-10605	390	2	2(x1c4	2(x1c4	NUM
ap-10605	390	3	−	−	NOUN
ap-10605	390	4	x2s4)∂5	x2s4)∂5	PROPN
ap-10605	390	5	+	+	CCONJ
ap-10605	390	6	2x1s4	2x1s4	NUM
ap-10605	391	1	+	+	CCONJ
ap-10605	392	1	x2c4	x2c4	PUNCT
ap-10605	392	2	c5	c5	PROPN
ap-10605	392	3	∂6	∂6	VERB
ap-10605	392	4	+	+	CCONJ
ap-10605	392	5	(	(	PUNCT
ap-10605	392	6	2x3x7	2x3x7	NUM
ap-10605	392	7	+	+	CCONJ
ap-10605	392	8	sh5)∂7	sh5)∂7	NOUN
ap-10605	392	9	+	+	CCONJ
ap-10605	392	10	(	(	PUNCT
ap-10605	392	11	ch5sh6	ch5sh6	VERB
ap-10605	392	12	+	+	CCONJ
ap-10605	392	13	2x3x8)∂8	2x3x8)∂8	NUM
ap-10605	392	14	+	+	CCONJ
ap-10605	392	15	(	(	PUNCT
ap-10605	392	16	ch5ch6	ch5ch6	NOUN
ap-10605	392	17	+	+	CCONJ
ap-10605	392	18	2x3x9)∂9	2x3x9)∂9	NUM
ap-10605	392	19	−	−	NOUN
ap-10605	392	20	2x3∂10	2x3∂10	NUM
ap-10605	392	21	,	,	PUNCT
ap-10605	392	22	d	d	PROPN
ap-10605	392	23	=	=	PUNCT
ap-10605	393	1	x1∂1	x1∂1	PROPN
ap-10605	393	2	+	+	PROPN
ap-10605	394	1	x2∂2	x2∂2	PROPN
ap-10605	395	1	+	+	CCONJ
ap-10605	395	2	x3∂3	x3∂3	PROPN
ap-10605	395	3	−	−	PROPN
ap-10605	396	1	x7∂7	x7∂7	PROPN
ap-10605	396	2	−	−	PROPN
ap-10605	397	1	x8∂8	x8∂8	PROPN
ap-10605	397	2	−	−	PROPN
ap-10605	398	1	x9∂9	x9∂9	PROPN
ap-10605	398	2	+	+	PROPN
ap-10605	399	1	∂10	∂10	PROPN
ap-10605	399	2	.	.	PUNCT
ap-10605	400	1	561	561	NUM
ap-10605	400	2	acta	acta	PROPN
ap-10605	400	3	polytechnica	polytechnica	PROPN
ap-10605	400	4	65(5):554–561	65(5):554–561	PROPN
ap-10605	400	5	,	,	PUNCT
ap-10605	400	6	2025	2025	NUM
ap-10605	400	7	1	1	NUM
ap-10605	400	8	introduction	introduction	NOUN
ap-10605	400	9	2	2	NUM
ap-10605	400	10	definitions	definition	NOUN
ap-10605	400	11	and	and	CCONJ
ap-10605	400	12	statement	statement	NOUN
ap-10605	400	13	of	of	ADP
ap-10605	400	14	the	the	DET
ap-10605	400	15	problem	problem	NOUN
ap-10605	400	16	3	3	NUM
ap-10605	400	17	construction	construction	NOUN
ap-10605	400	18	methods	method	NOUN
ap-10605	400	19	3.1	3.1	NUM
ap-10605	400	20	the	the	DET
ap-10605	400	21	direct	direct	ADJ
ap-10605	400	22	method	method	NOUN
ap-10605	400	23	3.2	3.2	NUM
ap-10605	400	24	blattner	blattner	NOUN
ap-10605	400	25	's	's	PART
ap-10605	400	26	method	method	ADJ
ap-10605	400	27	3.3	3.3	NUM
ap-10605	400	28	shirokov	shirokov	NOUN
ap-10605	400	29	's	's	PART
ap-10605	400	30	method	method	NOUN
ap-10605	400	31	3.4	3.4	NUM
ap-10605	400	32	representations	representation	NOUN
ap-10605	400	33	and	and	CCONJ
ap-10605	400	34	realizations	realization	NOUN
ap-10605	400	35	with	with	ADP
ap-10605	400	36	linear	linear	ADJ
ap-10605	400	37	coefficients	coefficient	NOUN
ap-10605	400	38	4	4	NUM
ap-10605	400	39	realizations	realization	NOUN
ap-10605	400	40	and	and	CCONJ
ap-10605	400	41	representations	representation	NOUN
ap-10605	400	42	of	of	ADP
ap-10605	400	43	sl(2,c	sl(2,c	NOUN
ap-10605	400	44	)	)	PUNCT
ap-10605	400	45	5	5	NUM
ap-10605	400	46	realizations	realization	NOUN
ap-10605	400	47	of	of	ADP
ap-10605	400	48	conformal	conformal	ADJ
ap-10605	400	49	algebras	algebra	NOUN
ap-10605	400	50	acknowledgements	acknowledgement	NOUN
ap-10605	400	51	references	reference	VERB
ap-10605	400	52	a	a	DET
ap-10605	400	53	a.1	a.1	PUNCT
ap-10605	400	54	generic	generic	ADJ
ap-10605	400	55	realization	realization	NOUN
ap-10605	400	56	of	of	ADP
ap-10605	400	57	the	the	DET
ap-10605	400	58	conformal	conformal	ADJ
ap-10605	400	59	algebra	algebra	PROPN
ap-10605	400	60	c(3,1	c(3,1	NOUN
ap-10605	400	61	)	)	PUNCT
ap-10605	400	62	a.2	a.2	PUNCT
ap-10605	400	63	generic	generic	ADJ
ap-10605	400	64	realizations	realization	NOUN
ap-10605	400	65	of	of	ADP
ap-10605	400	66	de	de	X
ap-10605	400	67	sitter	sitter	NOUN
ap-10605	400	68	algebras	algebras	PROPN