id	sid	tid	token	lemma	pos
ap-7596	1	1	acta	acta	PROPN
ap-7596	1	2	polytechnica	polytechnica	PROPN
ap-7596	1	3	https://doi.org/10.14311/ap.2022.62.0016	https://doi.org/10.14311/ap.2022.62.0016	PROPN
ap-7596	1	4	acta	acta	PROPN
ap-7596	1	5	polytechnica	polytechnica	PROPN
ap-7596	1	6	62(1):16–22	62(1):16–22	NUM
ap-7596	1	7	,	,	PUNCT
ap-7596	1	8	2022	2022	NUM
ap-7596	1	9	©	©	ADP
ap-7596	1	10	2022	2022	NUM
ap-7596	1	11	the	the	DET
ap-7596	1	12	author(s	author(s	NOUN
ap-7596	1	13	)	)	PUNCT
ap-7596	1	14	.	.	PUNCT
ap-7596	2	1	licensed	license	VERB
ap-7596	2	2	under	under	ADP
ap-7596	2	3	a	a	DET
ap-7596	2	4	cc	cc	NOUN
ap-7596	2	5	-	-	PUNCT
ap-7596	2	6	by	by	ADP
ap-7596	2	7	4.0	4.0	NUM
ap-7596	2	8	licence	licence	NOUN
ap-7596	2	9	published	publish	VERB
ap-7596	2	10	by	by	ADP
ap-7596	2	11	the	the	DET
ap-7596	2	12	czech	czech	PROPN
ap-7596	2	13	technical	technical	PROPN
ap-7596	2	14	university	university	PROPN
ap-7596	2	15	in	in	ADP
ap-7596	2	16	prague	prague	NOUN
ap-7596	2	17	on	on	ADP
ap-7596	2	18	some	some	DET
ap-7596	2	19	algebraic	algebraic	ADJ
ap-7596	2	20	formulations	formulation	NOUN
ap-7596	2	21	within	within	ADP
ap-7596	2	22	universal	universal	ADJ
ap-7596	2	23	enveloping	enveloping	NOUN
ap-7596	2	24	algebras	algebra	NOUN
ap-7596	2	25	related	relate	VERB
ap-7596	2	26	to	to	ADP
ap-7596	2	27	superintegrability	superintegrability	NOUN
ap-7596	2	28	rutwig	rutwig	NOUN
ap-7596	2	29	campoamor	campoamor	NOUN
ap-7596	2	30	-	-	PUNCT
ap-7596	2	31	stursberg	stursberg	PROPN
ap-7596	2	32	universidad	universidad	PROPN
ap-7596	2	33	complutense	complutense	PROPN
ap-7596	2	34	de	de	PROPN
ap-7596	2	35	madrid	madrid	PROPN
ap-7596	2	36	,	,	PUNCT
ap-7596	2	37	instituto	instituto	PROPN
ap-7596	2	38	de	de	PROPN
ap-7596	2	39	matemática	matemática	PROPN
ap-7596	2	40	interdisciplinar	interdisciplinar	PROPN
ap-7596	2	41	–	–	PUNCT
ap-7596	2	42	ucm	ucm	PROPN
ap-7596	2	43	,	,	PUNCT
ap-7596	2	44	plaza	plaza	PROPN
ap-7596	2	45	de	de	X
ap-7596	2	46	ciencias	ciencias	PROPN
ap-7596	2	47	3	3	NUM
ap-7596	2	48	,	,	PUNCT
ap-7596	2	49	e-28040	e-28040	PROPN
ap-7596	2	50	madrid	madrid	PROPN
ap-7596	2	51	,	,	PUNCT
ap-7596	2	52	spain	spain	PROPN
ap-7596	2	53	correspondence	correspondence	NOUN
ap-7596	2	54	:	:	PUNCT
ap-7596	3	1	rutwig@ucm.es	rutwig@ucm.es	PROPN
ap-7596	3	2	abstract	abstract	NOUN
ap-7596	3	3	.	.	PUNCT
ap-7596	4	1	we	we	PRON
ap-7596	4	2	report	report	VERB
ap-7596	4	3	on	on	ADP
ap-7596	4	4	some	some	DET
ap-7596	4	5	recent	recent	ADJ
ap-7596	4	6	purely	purely	ADV
ap-7596	4	7	algebraic	algebraic	ADJ
ap-7596	4	8	approaches	approach	NOUN
ap-7596	4	9	to	to	ADP
ap-7596	4	10	superintegrable	superintegrable	ADJ
ap-7596	4	11	systems	system	NOUN
ap-7596	4	12	from	from	ADP
ap-7596	4	13	the	the	DET
ap-7596	4	14	perspective	perspective	NOUN
ap-7596	4	15	of	of	ADP
ap-7596	4	16	subspaces	subspace	NOUN
ap-7596	4	17	of	of	ADP
ap-7596	4	18	commuting	commute	VERB
ap-7596	4	19	polynomials	polynomial	NOUN
ap-7596	4	20	in	in	ADP
ap-7596	4	21	the	the	DET
ap-7596	4	22	enveloping	enveloping	NOUN
ap-7596	4	23	algebras	algebra	NOUN
ap-7596	4	24	of	of	ADP
ap-7596	4	25	lie	lie	NOUN
ap-7596	4	26	algebras	algebra	NOUN
ap-7596	4	27	that	that	PRON
ap-7596	4	28	generate	generate	VERB
ap-7596	4	29	quadratic	quadratic	ADJ
ap-7596	4	30	(	(	PUNCT
ap-7596	4	31	and	and	CCONJ
ap-7596	4	32	eventually	eventually	ADV
ap-7596	4	33	higher	high	ADJ
ap-7596	4	34	-	-	PUNCT
ap-7596	4	35	order	order	NOUN
ap-7596	4	36	)	)	PUNCT
ap-7596	4	37	algebras	algebras	PROPN
ap-7596	4	38	.	.	PUNCT
ap-7596	5	1	in	in	ADP
ap-7596	5	2	this	this	DET
ap-7596	5	3	context	context	NOUN
ap-7596	5	4	,	,	PUNCT
ap-7596	5	5	two	two	NUM
ap-7596	5	6	algebraic	algebraic	ADJ
ap-7596	5	7	formulations	formulation	NOUN
ap-7596	5	8	are	be	AUX
ap-7596	5	9	possible	possible	ADJ
ap-7596	5	10	;	;	PUNCT
ap-7596	5	11	a	a	DET
ap-7596	5	12	first	first	ADJ
ap-7596	5	13	one	one	NUM
ap-7596	5	14	strongly	strongly	ADV
ap-7596	5	15	dependent	dependent	ADJ
ap-7596	5	16	on	on	ADP
ap-7596	5	17	representation	representation	NOUN
ap-7596	5	18	theory	theory	NOUN
ap-7596	5	19	,	,	PUNCT
ap-7596	5	20	as	as	ADV
ap-7596	5	21	well	well	ADV
ap-7596	5	22	as	as	ADP
ap-7596	5	23	a	a	DET
ap-7596	5	24	second	second	ADJ
ap-7596	5	25	formal	formal	ADJ
ap-7596	5	26	approach	approach	NOUN
ap-7596	5	27	that	that	PRON
ap-7596	5	28	focuses	focus	VERB
ap-7596	5	29	on	on	ADP
ap-7596	5	30	the	the	DET
ap-7596	5	31	explicit	explicit	ADJ
ap-7596	5	32	construction	construction	NOUN
ap-7596	5	33	within	within	ADP
ap-7596	5	34	commutants	commutant	NOUN
ap-7596	5	35	of	of	ADP
ap-7596	5	36	algebraic	algebraic	ADJ
ap-7596	5	37	integrals	integral	NOUN
ap-7596	5	38	for	for	ADP
ap-7596	5	39	appropriate	appropriate	ADJ
ap-7596	5	40	algebraic	algebraic	ADJ
ap-7596	5	41	hamiltonians	hamiltonian	NOUN
ap-7596	5	42	defined	define	VERB
ap-7596	5	43	in	in	ADP
ap-7596	5	44	terms	term	NOUN
ap-7596	5	45	of	of	ADP
ap-7596	5	46	suitable	suitable	ADJ
ap-7596	5	47	subalgebras	subalgebra	NOUN
ap-7596	5	48	.	.	PUNCT
ap-7596	6	1	the	the	DET
ap-7596	6	2	potential	potential	ADJ
ap-7596	6	3	use	use	NOUN
ap-7596	6	4	in	in	ADP
ap-7596	6	5	this	this	DET
ap-7596	6	6	context	context	NOUN
ap-7596	6	7	of	of	ADP
ap-7596	6	8	the	the	DET
ap-7596	6	9	notion	notion	NOUN
ap-7596	6	10	of	of	ADP
ap-7596	6	11	virtual	virtual	ADJ
ap-7596	6	12	copies	copy	NOUN
ap-7596	6	13	of	of	ADP
ap-7596	6	14	lie	lie	NOUN
ap-7596	6	15	algebras	algebra	NOUN
ap-7596	6	16	is	be	AUX
ap-7596	6	17	briefly	briefly	ADV
ap-7596	6	18	commented	comment	VERB
ap-7596	6	19	.	.	PUNCT
ap-7596	7	1	keywords	keyword	NOUN
ap-7596	7	2	:	:	PUNCT
ap-7596	7	3	enveloping	envelop	VERB
ap-7596	7	4	algebras	algebra	NOUN
ap-7596	7	5	,	,	PUNCT
ap-7596	7	6	commutants	commutant	NOUN
ap-7596	7	7	,	,	PUNCT
ap-7596	7	8	quadratic	quadratic	ADJ
ap-7596	7	9	algebras	algebra	NOUN
ap-7596	7	10	,	,	PUNCT
ap-7596	7	11	superintegrability	superintegrability	NOUN
ap-7596	7	12	.	.	PUNCT
ap-7596	8	1	1	1	X
ap-7596	8	2	.	.	X
ap-7596	8	3	introduction	introduction	NOUN
ap-7596	8	4	both	both	CCONJ
ap-7596	8	5	the	the	DET
ap-7596	8	6	study	study	NOUN
ap-7596	8	7	of	of	ADP
ap-7596	8	8	(	(	PUNCT
ap-7596	8	9	quasi-)exactly	quasi-)exactly	ADV
ap-7596	8	10	solvable	solvable	ADJ
ap-7596	8	11	systems	system	NOUN
ap-7596	8	12	,	,	PUNCT
ap-7596	8	13	as	as	ADV
ap-7596	8	14	well	well	ADV
ap-7596	8	15	as	as	ADP
ap-7596	8	16	that	that	PRON
ap-7596	8	17	of	of	ADP
ap-7596	8	18	super	super	ADJ
ap-7596	8	19	-	-	ADJ
ap-7596	8	20	integrable	integrable	ADJ
ap-7596	8	21	systems	system	NOUN
ap-7596	8	22	make	make	VERB
ap-7596	8	23	an	an	DET
ap-7596	8	24	extensive	extensive	ADJ
ap-7596	8	25	use	use	NOUN
ap-7596	8	26	of	of	ADP
ap-7596	8	27	the	the	DET
ap-7596	8	28	universal	universal	ADJ
ap-7596	8	29	enveloping	enveloping	NOUN
ap-7596	8	30	algebras	algebra	NOUN
ap-7596	8	31	of	of	ADP
ap-7596	8	32	lie	lie	NOUN
ap-7596	8	33	algebras	algebra	NOUN
ap-7596	8	34	,	,	PUNCT
ap-7596	8	35	either	either	CCONJ
ap-7596	8	36	in	in	ADP
ap-7596	8	37	the	the	DET
ap-7596	8	38	context	context	NOUN
ap-7596	8	39	of	of	ADP
ap-7596	8	40	the	the	DET
ap-7596	8	41	so	so	ADV
ap-7596	8	42	-	-	PUNCT
ap-7596	8	43	called	call	VERB
ap-7596	8	44	hidden	hide	VERB
ap-7596	8	45	algebras	algebra	NOUN
ap-7596	8	46	or	or	CCONJ
ap-7596	8	47	as	as	ADP
ap-7596	8	48	symmetry	symmetry	NOUN
ap-7596	8	49	algebras	algebra	NOUN
ap-7596	8	50	of	of	ADP
ap-7596	8	51	the	the	DET
ap-7596	8	52	system	system	NOUN
ap-7596	8	53	.	.	PUNCT
ap-7596	9	1	of	of	ADP
ap-7596	9	2	particular	particular	ADJ
ap-7596	9	3	interest	interest	NOUN
ap-7596	9	4	are	be	AUX
ap-7596	9	5	those	those	DET
ap-7596	9	6	systems	system	NOUN
ap-7596	9	7	that	that	PRON
ap-7596	9	8	,	,	PUNCT
ap-7596	9	9	beyond	beyond	ADP
ap-7596	9	10	super	super	ADJ
ap-7596	9	11	-	-	ADJ
ap-7596	9	12	integrability	integrability	ADJ
ap-7596	9	13	properties	property	NOUN
ap-7596	9	14	,	,	PUNCT
ap-7596	9	15	also	also	ADV
ap-7596	9	16	belong	belong	VERB
ap-7596	9	17	to	to	ADP
ap-7596	9	18	the	the	DET
ap-7596	9	19	class	class	NOUN
ap-7596	9	20	of	of	ADP
ap-7596	9	21	(	(	PUNCT
ap-7596	9	22	quasi-)exactly	quasi-)exactly	ADV
ap-7596	9	23	solvable	solvable	ADJ
ap-7596	9	24	systems	system	NOUN
ap-7596	9	25	[	[	X
ap-7596	9	26	1–5	1–5	X
ap-7596	9	27	]	]	X
ap-7596	9	28	.	.	PUNCT
ap-7596	10	1	in	in	ADP
ap-7596	10	2	particular	particular	ADJ
ap-7596	10	3	,	,	PUNCT
ap-7596	10	4	quadratic	quadratic	ADJ
ap-7596	10	5	subalgebras	subalgebra	NOUN
ap-7596	10	6	have	have	AUX
ap-7596	10	7	been	be	AUX
ap-7596	10	8	shown	show	VERB
ap-7596	10	9	to	to	PART
ap-7596	10	10	be	be	AUX
ap-7596	10	11	a	a	DET
ap-7596	10	12	powerful	powerful	ADJ
ap-7596	10	13	tool	tool	NOUN
ap-7596	10	14	for	for	ADP
ap-7596	10	15	classifying	classify	VERB
ap-7596	10	16	and	and	CCONJ
ap-7596	10	17	comparing	compare	VERB
ap-7596	10	18	superintegrable	superintegrable	ADJ
ap-7596	10	19	systems	system	NOUN
ap-7596	10	20	,	,	PUNCT
ap-7596	10	21	as	as	SCONJ
ap-7596	10	22	shown	show	VERB
ap-7596	10	23	in	in	ADP
ap-7596	10	24	[	[	X
ap-7596	10	25	6	6	NUM
ap-7596	10	26	]	]	PUNCT
ap-7596	10	27	,	,	PUNCT
ap-7596	10	28	where	where	SCONJ
ap-7596	10	29	the	the	DET
ap-7596	10	30	scheme	scheme	NOUN
ap-7596	10	31	of	of	ADP
ap-7596	10	32	superintegrable	superintegrable	ADJ
ap-7596	10	33	systems	system	NOUN
ap-7596	10	34	on	on	ADP
ap-7596	10	35	a	a	DET
ap-7596	10	36	two	two	NUM
ap-7596	10	37	-	-	PUNCT
ap-7596	10	38	dimensional	dimensional	ADJ
ap-7596	10	39	conformally	conformally	ADV
ap-7596	10	40	flat	flat	ADJ
ap-7596	10	41	space	space	NOUN
ap-7596	10	42	has	have	AUX
ap-7596	10	43	been	be	AUX
ap-7596	10	44	characterized	characterize	VERB
ap-7596	10	45	in	in	ADP
ap-7596	10	46	terms	term	NOUN
ap-7596	10	47	of	of	ADP
ap-7596	10	48	contractions	contraction	NOUN
ap-7596	10	49	.	.	PUNCT
ap-7596	11	1	additional	additional	ADJ
ap-7596	11	2	examples	example	NOUN
ap-7596	11	3	in	in	ADP
ap-7596	11	4	higher	high	ADJ
ap-7596	11	5	dimensions	dimension	NOUN
ap-7596	11	6	[	[	X
ap-7596	11	7	7	7	X
ap-7596	11	8	]	]	PUNCT
ap-7596	11	9	lead	lead	VERB
ap-7596	11	10	us	we	PRON
ap-7596	11	11	to	to	PART
ap-7596	11	12	suspect	suspect	VERB
ap-7596	11	13	that	that	SCONJ
ap-7596	11	14	n	n	CCONJ
ap-7596	11	15	-	-	PUNCT
ap-7596	11	16	dimensional	dimensional	ADJ
ap-7596	11	17	superintegrable	superintegrable	ADJ
ap-7596	11	18	systems	system	NOUN
ap-7596	11	19	are	be	AUX
ap-7596	11	20	somehow	somehow	ADV
ap-7596	11	21	associated	associate	VERB
ap-7596	11	22	to	to	ADP
ap-7596	11	23	(	(	PUNCT
ap-7596	11	24	higher	high	ADJ
ap-7596	11	25	rank	rank	NOUN
ap-7596	11	26	)	)	PUNCT
ap-7596	11	27	polynomials	polynomial	NOUN
ap-7596	11	28	in	in	ADP
ap-7596	11	29	a	a	DET
ap-7596	11	30	suitable	suitable	ADJ
ap-7596	11	31	enveloping	enveloping	NOUN
ap-7596	11	32	algebra	algebra	NOUN
ap-7596	11	33	[	[	X
ap-7596	11	34	8	8	NUM
ap-7596	11	35	]	]	PUNCT
ap-7596	11	36	,	,	PUNCT
ap-7596	11	37	further	far	ADV
ap-7596	11	38	stimulating	stimulate	VERB
ap-7596	11	39	the	the	DET
ap-7596	11	40	search	search	NOUN
ap-7596	11	41	of	of	ADP
ap-7596	11	42	alternative	alternative	ADJ
ap-7596	11	43	algebraic	algebraic	ADJ
ap-7596	11	44	approaches	approach	NOUN
ap-7596	11	45	based	base	VERB
ap-7596	11	46	on	on	ADP
ap-7596	11	47	the	the	DET
ap-7596	11	48	structural	structural	ADJ
ap-7596	11	49	properties	property	NOUN
ap-7596	11	50	of	of	ADP
ap-7596	11	51	enveloping	envelop	VERB
ap-7596	11	52	algebras	algebra	NOUN
ap-7596	11	53	.	.	PUNCT
ap-7596	12	1	although	although	SCONJ
ap-7596	12	2	the	the	DET
ap-7596	12	3	precise	precise	ADJ
ap-7596	12	4	fundamental	fundamental	ADJ
ap-7596	12	5	properties	property	NOUN
ap-7596	12	6	of	of	ADP
ap-7596	12	7	enveloping	envelop	VERB
ap-7596	12	8	algebras	algebra	NOUN
ap-7596	12	9	of	of	ADP
ap-7596	12	10	generic	generic	ADJ
ap-7596	12	11	semidirect	semidirect	NOUN
ap-7596	12	12	sums	sum	NOUN
ap-7596	12	13	of	of	ADP
ap-7596	12	14	simple	simple	ADJ
ap-7596	12	15	and	and	CCONJ
ap-7596	12	16	solvable	solvable	ADJ
ap-7596	12	17	lie	lie	NOUN
ap-7596	12	18	algebras	algebra	NOUN
ap-7596	12	19	are	be	AUX
ap-7596	12	20	still	still	ADV
ap-7596	12	21	far	far	ADV
ap-7596	12	22	from	from	ADP
ap-7596	12	23	being	be	AUX
ap-7596	12	24	completely	completely	ADV
ap-7596	12	25	understood	understand	VERB
ap-7596	12	26	,	,	PUNCT
ap-7596	12	27	a	a	DET
ap-7596	12	28	purely	purely	ADV
ap-7596	12	29	formal	formal	ADJ
ap-7596	12	30	ansatz	ansatz	NOUN
ap-7596	12	31	applied	apply	VERB
ap-7596	12	32	to	to	ADP
ap-7596	12	33	the	the	DET
ap-7596	12	34	case	case	NOUN
ap-7596	12	35	of	of	ADP
ap-7596	12	36	the	the	DET
ap-7596	12	37	schrödinger	schrödinger	ADJ
ap-7596	12	38	algebras	algebra	NOUN
ap-7596	12	39	ŝ(n	ŝ(n	NUM
ap-7596	12	40	)	)	PUNCT
ap-7596	12	41	has	have	AUX
ap-7596	12	42	recently	recently	ADV
ap-7596	12	43	been	be	AUX
ap-7596	12	44	shown	show	VERB
ap-7596	12	45	to	to	PART
ap-7596	12	46	provide	provide	VERB
ap-7596	12	47	some	some	DET
ap-7596	12	48	interesting	interesting	ADJ
ap-7596	12	49	features	feature	NOUN
ap-7596	12	50	[	[	X
ap-7596	12	51	9	9	NUM
ap-7596	12	52	]	]	PUNCT
ap-7596	12	53	.	.	PUNCT
ap-7596	13	1	in	in	ADP
ap-7596	13	2	this	this	DET
ap-7596	13	3	work	work	NOUN
ap-7596	13	4	we	we	PRON
ap-7596	13	5	comment	comment	VERB
ap-7596	13	6	on	on	ADP
ap-7596	13	7	some	some	DET
ap-7596	13	8	purely	purely	ADV
ap-7596	13	9	algebraic	algebraic	ADJ
ap-7596	13	10	approaches	approach	NOUN
ap-7596	13	11	formulated	formulate	VERB
ap-7596	13	12	in	in	ADP
ap-7596	13	13	the	the	DET
ap-7596	13	14	enveloping	enveloping	NOUN
ap-7596	13	15	algebras	algebra	NOUN
ap-7596	13	16	of	of	ADP
ap-7596	13	17	lie	lie	NOUN
ap-7596	13	18	algebras	algebra	NOUN
ap-7596	13	19	for	for	ADP
ap-7596	13	20	the	the	DET
ap-7596	13	21	identification	identification	NOUN
ap-7596	13	22	or	or	CCONJ
ap-7596	13	23	construction	construction	NOUN
ap-7596	13	24	of	of	ADP
ap-7596	13	25	quadratic	quadratic	ADJ
ap-7596	13	26	algebras	algebra	NOUN
ap-7596	13	27	that	that	PRON
ap-7596	13	28	may	may	AUX
ap-7596	13	29	lead	lead	VERB
ap-7596	13	30	to	to	ADP
ap-7596	13	31	super	super	ADJ
ap-7596	13	32	-	-	ADJ
ap-7596	13	33	integrable	integrable	ADJ
ap-7596	13	34	systems	system	NOUN
ap-7596	13	35	,	,	PUNCT
ap-7596	13	36	once	once	ADV
ap-7596	13	37	a	a	DET
ap-7596	13	38	suitable	suitable	ADJ
ap-7596	13	39	realization	realization	NOUN
ap-7596	13	40	of	of	ADP
ap-7596	13	41	the	the	DET
ap-7596	13	42	enveloping	enveloping	NOUN
ap-7596	13	43	algebra	algebra	NOUN
ap-7596	13	44	by	by	ADP
ap-7596	13	45	first	first	ADJ
ap-7596	13	46	-	-	PUNCT
ap-7596	13	47	order	order	NOUN
ap-7596	13	48	differential	differential	NOUN
ap-7596	13	49	operators	operator	NOUN
ap-7596	13	50	has	have	AUX
ap-7596	13	51	been	be	AUX
ap-7596	13	52	chosen	choose	VERB
ap-7596	13	53	.	.	PUNCT
ap-7596	14	1	the	the	DET
ap-7596	14	2	motivation	motivation	NOUN
ap-7596	14	3	for	for	ADP
ap-7596	14	4	this	this	DET
ap-7596	14	5	analysis	analysis	NOUN
ap-7596	14	6	lies	lie	VERB
ap-7596	14	7	primarily	primarily	ADV
ap-7596	14	8	on	on	ADP
ap-7596	14	9	the	the	DET
ap-7596	14	10	inspection	inspection	NOUN
ap-7596	14	11	of	of	ADP
ap-7596	14	12	super	super	ADJ
ap-7596	14	13	-	-	ADJ
ap-7596	14	14	integrable	integrable	ADJ
ap-7596	14	15	systems	system	NOUN
ap-7596	14	16	from	from	ADP
ap-7596	14	17	the	the	DET
ap-7596	14	18	point	point	NOUN
ap-7596	14	19	of	of	ADP
ap-7596	14	20	view	view	NOUN
ap-7596	14	21	of	of	ADP
ap-7596	14	22	the	the	DET
ap-7596	14	23	algebraic	algebraic	ADJ
ap-7596	14	24	properties	property	NOUN
ap-7596	14	25	of	of	ADP
ap-7596	14	26	first	first	ADJ
ap-7596	14	27	integrals	integral	NOUN
ap-7596	14	28	seen	see	VERB
ap-7596	14	29	as	as	ADP
ap-7596	14	30	elements	element	NOUN
ap-7596	14	31	of	of	ADP
ap-7596	14	32	an	an	DET
ap-7596	14	33	enveloping	enveloping	NOUN
ap-7596	14	34	algebra	algebra	NOUN
ap-7596	14	35	,	,	PUNCT
ap-7596	14	36	as	as	ADV
ap-7596	14	37	well	well	ADV
ap-7596	14	38	as	as	ADP
ap-7596	14	39	an	an	DET
ap-7596	14	40	attempt	attempt	NOUN
ap-7596	14	41	to	to	PART
ap-7596	14	42	determine	determine	VERB
ap-7596	14	43	to	to	ADP
ap-7596	14	44	which	which	DET
ap-7596	14	45	extent	extent	NOUN
ap-7596	14	46	these	these	DET
ap-7596	14	47	integrals	integral	NOUN
ap-7596	14	48	are	be	AUX
ap-7596	14	49	characterized	characterize	VERB
ap-7596	14	50	algebraically	algebraically	ADV
ap-7596	14	51	by	by	ADP
ap-7596	14	52	the	the	DET
ap-7596	14	53	hidden	hide	VERB
ap-7596	14	54	algebra	algebra	NOUN
ap-7596	14	55	[	[	X
ap-7596	14	56	10	10	NUM
ap-7596	14	57	]	]	PUNCT
ap-7596	14	58	.	.	PUNCT
ap-7596	15	1	this	this	PRON
ap-7596	15	2	moreover	moreover	ADV
ap-7596	15	3	suggests	suggest	VERB
ap-7596	15	4	a	a	DET
ap-7596	15	5	realization	realization	NOUN
ap-7596	15	6	-	-	PUNCT
ap-7596	15	7	free	free	ADJ
ap-7596	15	8	description	description	NOUN
ap-7596	15	9	of	of	ADP
ap-7596	15	10	systems	system	NOUN
ap-7596	15	11	in	in	ADP
ap-7596	15	12	terms	term	NOUN
ap-7596	15	13	of	of	ADP
ap-7596	15	14	commutants	commutant	NOUN
ap-7596	15	15	of	of	ADP
ap-7596	15	16	algebraic	algebraic	ADJ
ap-7596	15	17	hamiltonians	hamiltonian	NOUN
ap-7596	15	18	in	in	ADP
ap-7596	15	19	enveloping	envelop	VERB
ap-7596	15	20	algebras	algebra	NOUN
ap-7596	15	21	[	[	X
ap-7596	15	22	11	11	NUM
ap-7596	15	23	]	]	PUNCT
ap-7596	15	24	,	,	PUNCT
ap-7596	15	25	in	in	ADP
ap-7596	15	26	which	which	PRON
ap-7596	15	27	elements	element	NOUN
ap-7596	15	28	of	of	ADP
ap-7596	15	29	the	the	DET
ap-7596	15	30	coadjoint	coadjoint	NOUN
ap-7596	15	31	representation	representation	NOUN
ap-7596	15	32	of	of	ADP
ap-7596	15	33	lie	lie	NOUN
ap-7596	15	34	algebras	algebra	NOUN
ap-7596	15	35	may	may	AUX
ap-7596	15	36	be	be	AUX
ap-7596	15	37	useful	useful	ADJ
ap-7596	15	38	to	to	PART
ap-7596	15	39	simplify	simplify	VERB
ap-7596	15	40	computations	computation	NOUN
ap-7596	15	41	.	.	PUNCT
ap-7596	16	1	2	2	X
ap-7596	16	2	.	.	X
ap-7596	16	3	first	first	ADJ
ap-7596	16	4	algebraic	algebraic	PROPN
ap-7596	16	5	reformulation	reformulation	NOUN
ap-7596	16	6	in	in	ADP
ap-7596	16	7	the	the	DET
ap-7596	16	8	context	context	NOUN
ap-7596	16	9	of	of	ADP
ap-7596	16	10	(	(	PUNCT
ap-7596	16	11	quasi)-exactly	quasi)-exactly	ADV
ap-7596	16	12	solvable	solvable	ADJ
ap-7596	16	13	problems	problem	NOUN
ap-7596	16	14	,	,	PUNCT
ap-7596	16	15	the	the	DET
ap-7596	16	16	hamiltonians	hamiltonian	NOUN
ap-7596	16	17	are	be	AUX
ap-7596	16	18	described	describe	VERB
ap-7596	16	19	as	as	ADP
ap-7596	16	20	differential	differential	ADJ
ap-7596	16	21	operators	operator	NOUN
ap-7596	16	22	in	in	ADP
ap-7596	16	23	p	p	PROPN
ap-7596	16	24	variables	variable	NOUN
ap-7596	16	25	that	that	PRON
ap-7596	16	26	admit	admit	VERB
ap-7596	16	27	an	an	DET
ap-7596	16	28	expression	expression	NOUN
ap-7596	16	29	as	as	ADP
ap-7596	16	30	elements	element	NOUN
ap-7596	16	31	in	in	ADP
ap-7596	16	32	the	the	DET
ap-7596	16	33	enveloping	enveloping	NOUN
ap-7596	16	34	algebra	algebra	NOUN
ap-7596	16	35	of	of	ADP
ap-7596	16	36	a	a	DET
ap-7596	16	37	lie	lie	NOUN
ap-7596	16	38	algebra	algebra	NOUN
ap-7596	16	39	g	g	NOUN
ap-7596	16	40	,	,	PUNCT
ap-7596	16	41	commonly	commonly	ADV
ap-7596	16	42	known	know	VERB
ap-7596	16	43	as	as	ADP
ap-7596	16	44	the	the	DET
ap-7596	16	45	hidden	hidden	ADJ
ap-7596	16	46	algebra	algebra	NOUN
ap-7596	16	47	,	,	PUNCT
ap-7596	16	48	not	not	PART
ap-7596	16	49	necessarily	necessarily	ADV
ap-7596	16	50	associated	associate	VERB
ap-7596	16	51	to	to	ADP
ap-7596	16	52	any	any	DET
ap-7596	16	53	symmetry	symmetry	NOUN
ap-7596	16	54	algebra	algebra	NOUN
ap-7596	16	55	of	of	ADP
ap-7596	16	56	the	the	DET
ap-7596	16	57	system	system	NOUN
ap-7596	16	58	.	.	PUNCT
ap-7596	17	1	the	the	DET
ap-7596	17	2	main	main	ADJ
ap-7596	17	3	requirement	requirement	NOUN
ap-7596	17	4	is	be	AUX
ap-7596	17	5	the	the	DET
ap-7596	17	6	existence	existence	NOUN
ap-7596	17	7	of	of	ADP
ap-7596	17	8	a	a	DET
ap-7596	17	9	representation	representation	NOUN
ap-7596	17	10	of	of	ADP
ap-7596	17	11	g	g	PROPN
ap-7596	17	12	that	that	PRON
ap-7596	17	13	is	be	AUX
ap-7596	17	14	invariant	invariant	ADJ
ap-7596	17	15	for	for	ADP
ap-7596	17	16	the	the	DET
ap-7596	17	17	hamiltonian	hamiltonian	NOUN
ap-7596	17	18	,	,	PUNCT
ap-7596	17	19	a	a	DET
ap-7596	17	20	constraint	constraint	NOUN
ap-7596	17	21	that	that	PRON
ap-7596	17	22	allows	allow	VERB
ap-7596	17	23	us	we	PRON
ap-7596	17	24	to	to	PART
ap-7596	17	25	determine	determine	VERB
ap-7596	17	26	its	its	PRON
ap-7596	17	27	spectrum	spectrum	NOUN
ap-7596	17	28	(	(	PUNCT
ap-7596	17	29	either	either	CCONJ
ap-7596	17	30	partially	partially	ADV
ap-7596	17	31	or	or	CCONJ
ap-7596	17	32	completely	completely	ADV
ap-7596	17	33	)	)	PUNCT
ap-7596	17	34	using	use	VERB
ap-7596	17	35	algebraic	algebraic	ADJ
ap-7596	17	36	methods	method	NOUN
ap-7596	17	37	[	[	X
ap-7596	17	38	12	12	NUM
ap-7596	17	39	]	]	PUNCT
ap-7596	17	40	.	.	PUNCT
ap-7596	18	1	so	so	ADV
ap-7596	18	2	,	,	PUNCT
ap-7596	18	3	for	for	ADP
ap-7596	18	4	example	example	NOUN
ap-7596	18	5	,	,	PUNCT
ap-7596	18	6	the	the	DET
ap-7596	18	7	universal	universal	ADJ
ap-7596	18	8	enveloping	enveloping	NOUN
ap-7596	18	9	algebra	algebra	NOUN
ap-7596	18	10	of	of	ADP
ap-7596	18	11	the	the	DET
ap-7596	18	12	simple	simple	ADJ
ap-7596	18	13	lie	lie	NOUN
ap-7596	18	14	algebra	algebra	NOUN
ap-7596	18	15	sl(2,r	sl(2,r	NOUN
ap-7596	18	16	)	)	PUNCT
ap-7596	18	17	and	and	CCONJ
ap-7596	18	18	its	its	PRON
ap-7596	18	19	realization	realization	NOUN
ap-7596	18	20	as	as	ADP
ap-7596	18	21	first	first	ADJ
ap-7596	18	22	-	-	PUNCT
ap-7596	18	23	order	order	NOUN
ap-7596	18	24	differential	differential	NOUN
ap-7596	18	25	operators	operator	NOUN
ap-7596	18	26	on	on	ADP
ap-7596	18	27	the	the	DET
ap-7596	18	28	real	real	ADJ
ap-7596	18	29	line	line	NOUN
ap-7596	18	30	provide	provide	VERB
ap-7596	18	31	a	a	DET
ap-7596	18	32	characterization	characterization	NOUN
ap-7596	18	33	of	of	ADP
ap-7596	18	34	quasi	quasi	ADJ
ap-7596	18	35	-	-	ADJ
ap-7596	18	36	exactly	exactly	ADV
ap-7596	18	37	solvable	solvable	ADJ
ap-7596	18	38	one	one	NUM
ap-7596	18	39	-	-	PUNCT
ap-7596	18	40	dimensional	dimensional	ADJ
ap-7596	18	41	systems	system	NOUN
ap-7596	18	42	[	[	X
ap-7596	18	43	13	13	NUM
ap-7596	18	44	]	]	PUNCT
ap-7596	18	45	.	.	PUNCT
ap-7596	19	1	a	a	DET
ap-7596	19	2	second	second	ADJ
ap-7596	19	3	type	type	NOUN
ap-7596	19	4	of	of	ADP
ap-7596	19	5	systems	system	NOUN
ap-7596	19	6	that	that	PRON
ap-7596	19	7	uses	use	VERB
ap-7596	19	8	the	the	DET
ap-7596	19	9	structural	structural	ADJ
ap-7596	19	10	properties	property	NOUN
ap-7596	19	11	of	of	ADP
ap-7596	19	12	enveloping	envelop	VERB
ap-7596	19	13	algebras	algebras	PROPN
ap-7596	19	14	is	be	AUX
ap-7596	19	15	given	give	VERB
ap-7596	19	16	by	by	ADP
ap-7596	19	17	super	super	ADJ
ap-7596	19	18	-	-	ADJ
ap-7596	19	19	integrable	integrable	ADJ
ap-7596	19	20	systems	system	NOUN
ap-7596	19	21	,	,	PUNCT
ap-7596	19	22	where	where	SCONJ
ap-7596	19	23	both	both	CCONJ
ap-7596	19	24	the	the	DET
ap-7596	19	25	hamiltonian	hamiltonian	NOUN
ap-7596	19	26	and	and	CCONJ
ap-7596	19	27	the	the	DET
ap-7596	19	28	constants	constant	NOUN
ap-7596	19	29	of	of	ADP
ap-7596	19	30	the	the	DET
ap-7596	19	31	motion	motion	NOUN
ap-7596	19	32	are	be	AUX
ap-7596	19	33	interpreted	interpret	VERB
ap-7596	19	34	in	in	ADP
ap-7596	19	35	the	the	DET
ap-7596	19	36	enveloping	enveloping	NOUN
ap-7596	19	37	algebra	algebra	NOUN
ap-7596	19	38	of	of	ADP
ap-7596	19	39	some	some	DET
ap-7596	19	40	lie	lie	NOUN
ap-7596	19	41	algebra	algebra	NOUN
ap-7596	19	42	g.	g.	NOUN
ap-7596	19	43	merely	merely	ADV
ap-7596	19	44	integrable	integrable	ADJ
ap-7596	19	45	n	n	CCONJ
ap-7596	19	46	-	-	PUNCT
ap-7596	19	47	dimensional	dimensional	ADJ
ap-7596	19	48	systems	system	NOUN
ap-7596	19	49	can	can	AUX
ap-7596	19	50	be	be	AUX
ap-7596	19	51	interpreted	interpret	VERB
ap-7596	19	52	as	as	ADP
ap-7596	19	53	the	the	DET
ap-7596	19	54	image	image	NOUN
ap-7596	19	55	,	,	PUNCT
ap-7596	19	56	via	via	ADP
ap-7596	19	57	a	a	DET
ap-7596	19	58	realization	realization	NOUN
ap-7596	19	59	φ	φ	NUM
ap-7596	19	60	by	by	ADP
ap-7596	19	61	first	first	ADJ
ap-7596	19	62	-	-	PUNCT
ap-7596	19	63	order	order	NOUN
ap-7596	19	64	differential	differential	NOUN
ap-7596	19	65	operators	operator	NOUN
ap-7596	19	66	,	,	PUNCT
ap-7596	19	67	of	of	ADP
ap-7596	19	68	an	an	DET
ap-7596	19	69	abelian	abelian	ADJ
ap-7596	19	70	subalgebra	subalgebra	NOUN
ap-7596	19	71	a	a	PRON
ap-7596	19	72	of	of	ADP
ap-7596	19	73	u(g	u(g	PROPN
ap-7596	19	74	)	)	PUNCT
ap-7596	19	75	,	,	PUNCT
ap-7596	19	76	while	while	SCONJ
ap-7596	19	77	super	super	ADJ
ap-7596	19	78	-	-	ADJ
ap-7596	19	79	integrable	integrable	ADJ
ap-7596	19	80	systems	system	NOUN
ap-7596	19	81	would	would	AUX
ap-7596	19	82	correspond	correspond	VERB
ap-7596	19	83	to	to	ADP
ap-7596	19	84	nonabelian	nonabelian	ADJ
ap-7596	19	85	extensions	extension	NOUN
ap-7596	19	86	of	of	ADP
ap-7596	19	87	a.	a.	NOUN
ap-7596	19	88	the	the	DET
ap-7596	19	89	problem	problem	NOUN
ap-7596	19	90	under	under	ADP
ap-7596	19	91	what	what	DET
ap-7596	19	92	conditions	condition	NOUN
ap-7596	19	93	a	a	DET
ap-7596	19	94	system	system	NOUN
ap-7596	19	95	both	both	PRON
ap-7596	19	96	exhibits	exhibit	VERB
ap-7596	19	97	super	super	ADJ
ap-7596	19	98	-	-	ADJ
ap-7596	19	99	integrability	integrability	ADJ
ap-7596	19	100	and	and	CCONJ
ap-7596	19	101	(	(	PUNCT
ap-7596	19	102	quasi-)exact	quasi-)exact	ADJ
ap-7596	19	103	solvability	solvability	NOUN
ap-7596	19	104	has	have	AUX
ap-7596	19	105	been	be	AUX
ap-7596	19	106	analyzed	analyze	VERB
ap-7596	19	107	in	in	ADP
ap-7596	19	108	detail	detail	NOUN
ap-7596	19	109	,	,	PUNCT
ap-7596	19	110	and	and	CCONJ
ap-7596	19	111	large	large	ADJ
ap-7596	19	112	classes	class	NOUN
ap-7596	19	113	of	of	ADP
ap-7596	19	114	super	super	ADJ
ap-7596	19	115	-	-	ADJ
ap-7596	19	116	integrable	integrable	ADJ
ap-7596	19	117	systems	system	NOUN
ap-7596	19	118	that	that	PRON
ap-7596	19	119	are	be	AUX
ap-7596	19	120	exactly	exactly	ADV
ap-7596	19	121	solvable	solvable	ADJ
ap-7596	19	122	have	have	AUX
ap-7596	19	123	been	be	AUX
ap-7596	19	124	found	find	VERB
ap-7596	19	125	(	(	PUNCT
ap-7596	19	126	see	see	VERB
ap-7596	19	127	[	[	X
ap-7596	19	128	3	3	NUM
ap-7596	19	129	,	,	PUNCT
ap-7596	19	130	14	14	NUM
ap-7596	19	131	,	,	PUNCT
ap-7596	19	132	15	15	NUM
ap-7596	19	133	]	]	PUNCT
ap-7596	19	134	and	and	CCONJ
ap-7596	19	135	references	reference	NOUN
ap-7596	19	136	therein	therein	ADV
ap-7596	19	137	)	)	PUNCT
ap-7596	19	138	.	.	PUNCT
ap-7596	20	1	16	16	NUM
ap-7596	21	1	https://doi.org/10.14311/ap.2022.62.0016	https://doi.org/10.14311/ap.2022.62.0016	PROPN
ap-7596	21	2	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
ap-7596	21	3	https://www.cvut.cz/en	https://www.cvut.cz/en	PROPN
ap-7596	21	4	vol	vol	NOUN
ap-7596	21	5	.	.	PROPN
ap-7596	22	1	62	62	NUM
ap-7596	22	2	no	no	INTJ
ap-7596	22	3	.	.	PUNCT
ap-7596	23	1	1/2022	1/2022	NUM
ap-7596	23	2	on	on	ADP
ap-7596	23	3	some	some	DET
ap-7596	23	4	algebraic	algebraic	ADJ
ap-7596	23	5	formulations	formulation	NOUN
ap-7596	23	6	.	.	PUNCT
ap-7596	23	7	.	.	PUNCT
ap-7596	23	8	.	.	PUNCT
ap-7596	24	1	a	a	DET
ap-7596	24	2	first	first	ADJ
ap-7596	24	3	algebraic	algebraic	ADJ
ap-7596	24	4	formulation	formulation	NOUN
ap-7596	24	5	,	,	PUNCT
ap-7596	24	6	as	as	SCONJ
ap-7596	24	7	developed	develop	VERB
ap-7596	24	8	in	in	ADP
ap-7596	24	9	[	[	X
ap-7596	24	10	10	10	NUM
ap-7596	24	11	]	]	PUNCT
ap-7596	24	12	,	,	PUNCT
ap-7596	24	13	is	be	AUX
ap-7596	24	14	motivated	motivate	VERB
ap-7596	24	15	by	by	ADP
ap-7596	24	16	the	the	DET
ap-7596	24	17	use	use	NOUN
ap-7596	24	18	of	of	ADP
ap-7596	24	19	quadratic	quadratic	ADJ
ap-7596	24	20	algebras	algebra	NOUN
ap-7596	24	21	in	in	ADP
ap-7596	24	22	the	the	DET
ap-7596	24	23	context	context	NOUN
ap-7596	24	24	of	of	ADP
ap-7596	24	25	super	super	ADJ
ap-7596	24	26	-	-	ADJ
ap-7596	24	27	integrable	integrable	ADJ
ap-7596	24	28	(	(	PUNCT
ap-7596	24	29	and	and	CCONJ
ap-7596	24	30	exactly	exactly	ADV
ap-7596	24	31	solvable	solvable	ADJ
ap-7596	24	32	)	)	PUNCT
ap-7596	24	33	systems	system	NOUN
ap-7596	24	34	with	with	ADP
ap-7596	24	35	a	a	DET
ap-7596	24	36	given	give	VERB
ap-7596	24	37	hidden	hide	VERB
ap-7596	24	38	algebra	algebra	NOUN
ap-7596	24	39	g	g	PROPN
ap-7596	25	1	[	[	X
ap-7596	25	2	3	3	NUM
ap-7596	25	3	]	]	PUNCT
ap-7596	25	4	.	.	PUNCT
ap-7596	26	1	to	to	ADP
ap-7596	26	2	this	this	DET
ap-7596	26	3	extent	extent	NOUN
ap-7596	26	4	,	,	PUNCT
ap-7596	26	5	we	we	PRON
ap-7596	26	6	consider	consider	VERB
ap-7596	26	7	a	a	DET
ap-7596	26	8	hamiltonian	hamiltonian	ADJ
ap-7596	26	9	h	h	NOUN
ap-7596	26	10	expressed	express	VERB
ap-7596	26	11	in	in	ADP
ap-7596	26	12	terms	term	NOUN
ap-7596	26	13	of	of	ADP
ap-7596	26	14	a	a	DET
ap-7596	26	15	subalgebra	subalgebra	NOUN
ap-7596	26	16	m	m	VERB
ap-7596	26	17	⊂	⊂	NOUN
ap-7596	26	18	g	g	NOUN
ap-7596	26	19	via	via	ADP
ap-7596	26	20	a	a	DET
ap-7596	26	21	realization	realization	NOUN
ap-7596	26	22	φ	φ	NUM
ap-7596	26	23	by	by	ADP
ap-7596	26	24	differential	differential	ADJ
ap-7596	26	25	operators	operator	NOUN
ap-7596	26	26	of	of	ADP
ap-7596	26	27	the	the	DET
ap-7596	26	28	lie	lie	NOUN
ap-7596	26	29	algebra	algebra	VERB
ap-7596	26	30	g	g	NOUN
ap-7596	26	31	:	:	PUNCT
ap-7596	27	1	h	h	NOUN
ap-7596	27	2	=	=	PUNCT
ap-7596	27	3	dim	dim	PROPN
ap-7596	27	4	m∑	m∑	INTJ
ap-7596	28	1	i	i	PRON
ap-7596	28	2	,	,	PUNCT
ap-7596	28	3	j=1	j=1	NOUN
ap-7596	28	4	αijφ(xi)φ(xj	αijφ(xi)φ(xj	ADV
ap-7596	28	5	)	)	PUNCT
ap-7596	29	1	+	+	CCONJ
ap-7596	29	2	dim	dim	ADJ
ap-7596	29	3	m∑	m∑	NOUN
ap-7596	29	4	k=1	k=1	PRON
ap-7596	29	5	βkφ(xk	βkφ(xk	PUNCT
ap-7596	29	6	)	)	PUNCT
ap-7596	30	1	+	+	NUM
ap-7596	30	2	γ0	γ0	NOUN
ap-7596	30	3	,	,	PUNCT
ap-7596	30	4	(	(	PUNCT
ap-7596	30	5	1	1	X
ap-7596	30	6	)	)	PUNCT
ap-7596	30	7	where	where	SCONJ
ap-7596	30	8	αij	αij	NOUN
ap-7596	30	9	,	,	PUNCT
ap-7596	30	10	βk	βk	NOUN
ap-7596	30	11	,	,	PUNCT
ap-7596	30	12	γ0	γ0	NOUN
ap-7596	30	13	are	be	AUX
ap-7596	30	14	constants	constant	NOUN
ap-7596	30	15	and	and	CCONJ
ap-7596	30	16	{	{	PUNCT
ap-7596	30	17	x1	x1	PROPN
ap-7596	30	18	,	,	PUNCT
ap-7596	30	19	.	.	PUNCT
ap-7596	30	20	.	.	PUNCT
ap-7596	30	21	.	.	PUNCT
ap-7596	31	1	,	,	PUNCT
ap-7596	31	2	xdim	xdim	PROPN
ap-7596	31	3	m	m	PROPN
ap-7596	31	4	}	}	PUNCT
ap-7596	31	5	is	be	AUX
ap-7596	31	6	a	a	DET
ap-7596	31	7	basis	basis	NOUN
ap-7596	31	8	of	of	ADP
ap-7596	31	9	m.	m.	NOUN
ap-7596	31	10	in	in	ADP
ap-7596	31	11	this	this	DET
ap-7596	31	12	context	context	NOUN
ap-7596	31	13	,	,	PUNCT
ap-7596	31	14	the	the	DET
ap-7596	31	15	hamiltonian	hamiltonian	ADJ
ap-7596	31	16	h	h	NOUN
ap-7596	31	17	is	be	AUX
ap-7596	31	18	obtained	obtain	VERB
ap-7596	31	19	as	as	ADP
ap-7596	31	20	the	the	DET
ap-7596	31	21	image	image	NOUN
ap-7596	31	22	of	of	ADP
ap-7596	31	23	a	a	DET
ap-7596	31	24	quadratic	quadratic	ADJ
ap-7596	31	25	element	element	NOUN
ap-7596	31	26	ha	ha	INTJ
ap-7596	31	27	in	in	ADP
ap-7596	31	28	the	the	DET
ap-7596	31	29	universal	universal	ADJ
ap-7596	31	30	enveloping	enveloping	NOUN
ap-7596	31	31	algebra	algebra	NOUN
ap-7596	31	32	u(m	u(m	PROPN
ap-7596	31	33	)	)	PUNCT
ap-7596	31	34	⊂	⊂	PUNCT
ap-7596	31	35	u(g	u(g	PROPN
ap-7596	31	36	)	)	PUNCT
ap-7596	31	37	.	.	PUNCT
ap-7596	32	1	similarly	similarly	ADV
ap-7596	32	2	,	,	PUNCT
ap-7596	32	3	the	the	DET
ap-7596	32	4	(	(	PUNCT
ap-7596	32	5	independent	independent	ADJ
ap-7596	32	6	)	)	PUNCT
ap-7596	32	7	constants	constant	NOUN
ap-7596	32	8	of	of	ADP
ap-7596	32	9	the	the	DET
ap-7596	32	10	motion	motion	NOUN
ap-7596	32	11	φ1	φ1	PROPN
ap-7596	32	12	,	,	PUNCT
ap-7596	32	13	.	.	PUNCT
ap-7596	32	14	.	.	PUNCT
ap-7596	33	1	.	.	PUNCT
ap-7596	34	1	,	,	PUNCT
ap-7596	34	2	φs	φs	PROPN
ap-7596	34	3	can	can	AUX
ap-7596	34	4	also	also	ADV
ap-7596	34	5	be	be	AUX
ap-7596	34	6	rewritten	rewrite	VERB
ap-7596	34	7	as	as	ADP
ap-7596	34	8	the	the	DET
ap-7596	34	9	image	image	NOUN
ap-7596	34	10	of	of	ADP
ap-7596	34	11	elements	element	NOUN
ap-7596	34	12	in	in	ADP
ap-7596	34	13	the	the	DET
ap-7596	34	14	enveloping	enveloping	NOUN
ap-7596	34	15	algebra	algebra	NOUN
ap-7596	34	16	u(g	u(g	PROPN
ap-7596	34	17	)	)	PUNCT
ap-7596	34	18	.	.	PUNCT
ap-7596	35	1	as	as	ADP
ap-7596	35	2	differential	differential	ADJ
ap-7596	35	3	operators	operator	NOUN
ap-7596	35	4	they	they	PRON
ap-7596	35	5	satisfy	satisfy	VERB
ap-7596	35	6	the	the	DET
ap-7596	35	7	commutators	commutator	NOUN
ap-7596	36	1	[	[	X
ap-7596	36	2	h	h	NOUN
ap-7596	36	3	,	,	PUNCT
ap-7596	36	4	φj	φj	X
ap-7596	36	5	]	]	PUNCT
ap-7596	36	6	=	=	SYM
ap-7596	36	7	0	0	NUM
ap-7596	36	8	,	,	PUNCT
ap-7596	36	9	1	1	NUM
ap-7596	36	10	≤	≤	NUM
ap-7596	36	11	j	j	PROPN
ap-7596	36	12	≤	≤	PROPN
ap-7596	36	13	s.	s.	PROPN
ap-7596	36	14	(	(	PUNCT
ap-7596	36	15	2	2	X
ap-7596	36	16	)	)	PUNCT
ap-7596	36	17	the	the	DET
ap-7596	36	18	commutators	commutator	NOUN
ap-7596	36	19	[	[	X
ap-7596	36	20	φi	φi	ADP
ap-7596	36	21	,	,	PUNCT
ap-7596	36	22	φj	φj	X
ap-7596	36	23	]	]	PUNCT
ap-7596	36	24	provide	provide	VERB
ap-7596	36	25	additional	additional	ADJ
ap-7596	36	26	(	(	PUNCT
ap-7596	36	27	dependent	dependent	ADJ
ap-7596	36	28	)	)	PUNCT
ap-7596	36	29	higher	high	ADJ
ap-7596	36	30	-	-	PUNCT
ap-7596	36	31	order	order	NOUN
ap-7596	36	32	constants	constant	NOUN
ap-7596	36	33	of	of	ADP
ap-7596	36	34	the	the	DET
ap-7596	36	35	motion	motion	NOUN
ap-7596	36	36	.	.	PUNCT
ap-7596	37	1	a	a	DET
ap-7596	37	2	specially	specially	ADV
ap-7596	37	3	interesting	interesting	ADJ
ap-7596	37	4	case	case	NOUN
ap-7596	37	5	is	be	AUX
ap-7596	37	6	given	give	VERB
ap-7596	37	7	whenever	whenever	SCONJ
ap-7596	37	8	the	the	DET
ap-7596	37	9	first	first	ADJ
ap-7596	37	10	integrals	integral	NOUN
ap-7596	37	11	generate	generate	VERB
ap-7596	37	12	a	a	DET
ap-7596	37	13	quadratic	quadratic	ADJ
ap-7596	37	14	algebra	algebra	NOUN
ap-7596	37	15	.	.	PUNCT
ap-7596	38	1	abstracting	abstract	VERB
ap-7596	38	2	from	from	ADP
ap-7596	38	3	the	the	DET
ap-7596	38	4	specific	specific	ADJ
ap-7596	38	5	realization	realization	NOUN
ap-7596	38	6	φ	φ	NOUN
ap-7596	38	7	,	,	PUNCT
ap-7596	38	8	and	and	CCONJ
ap-7596	38	9	focusing	focus	VERB
ap-7596	38	10	merely	merely	ADV
ap-7596	38	11	on	on	ADP
ap-7596	38	12	the	the	DET
ap-7596	38	13	underlying	underlie	VERB
ap-7596	38	14	algebraic	algebraic	ADJ
ap-7596	38	15	formulation	formulation	NOUN
ap-7596	38	16	,	,	PUNCT
ap-7596	38	17	the	the	DET
ap-7596	38	18	formal	formal	ADJ
ap-7596	38	19	polynomial	polynomial	ADJ
ap-7596	38	20	ha	ha	INTJ
ap-7596	38	21	=	=	PUNCT
ap-7596	38	22	dim	dim	NOUN
ap-7596	39	1	m∑	m∑	INTJ
ap-7596	39	2	i	i	PRON
ap-7596	39	3	,	,	PUNCT
ap-7596	39	4	j=1	j=1	PROPN
ap-7596	39	5	αijxixj	αijxixj	PROPN
ap-7596	40	1	+	+	CCONJ
ap-7596	40	2	dim	dim	ADJ
ap-7596	40	3	m∑	m∑	VERB
ap-7596	40	4	k=1	k=1	PROPN
ap-7596	40	5	βkxk	βkxk	PROPN
ap-7596	41	1	+	+	NUM
ap-7596	41	2	γ0	γ0	NOUN
ap-7596	41	3	in	in	ADP
ap-7596	41	4	the	the	DET
ap-7596	41	5	enveloping	enveloping	NOUN
ap-7596	41	6	algebra	algebra	NOUN
ap-7596	41	7	u(m	u(m	ADP
ap-7596	41	8	)	)	PUNCT
ap-7596	41	9	of	of	ADP
ap-7596	41	10	m	m	PROPN
ap-7596	41	11	allows	allow	VERB
ap-7596	41	12	us	we	PRON
ap-7596	41	13	to	to	PART
ap-7596	41	14	recover	recover	VERB
ap-7596	41	15	hamiltonian	hamiltonian	ADJ
ap-7596	41	16	h	h	NOUN
ap-7596	41	17	of	of	ADP
ap-7596	41	18	the	the	DET
ap-7596	41	19	system	system	NOUN
ap-7596	41	20	once	once	SCONJ
ap-7596	41	21	the	the	DET
ap-7596	41	22	generators	generator	NOUN
ap-7596	41	23	are	be	AUX
ap-7596	41	24	realized	realize	VERB
ap-7596	41	25	by	by	ADP
ap-7596	41	26	the	the	DET
ap-7596	41	27	differential	differential	ADJ
ap-7596	41	28	operators	operator	NOUN
ap-7596	41	29	.	.	PUNCT
ap-7596	42	1	in	in	ADP
ap-7596	42	2	analogous	analogous	ADJ
ap-7596	42	3	form	form	NOUN
ap-7596	42	4	,	,	PUNCT
ap-7596	42	5	we	we	PRON
ap-7596	42	6	can	can	AUX
ap-7596	42	7	find	find	VERB
ap-7596	42	8	elements	element	NOUN
ap-7596	42	9	j1	j1	PROPN
ap-7596	42	10	,	,	PUNCT
ap-7596	42	11	.	.	PUNCT
ap-7596	42	12	.	.	PUNCT
ap-7596	43	1	.	.	PUNCT
ap-7596	44	1	,	,	PUNCT
ap-7596	44	2	js	js	ADP
ap-7596	44	3	in	in	ADP
ap-7596	44	4	u(g	u(g	PROPN
ap-7596	44	5	)	)	PUNCT
ap-7596	44	6	that	that	PRON
ap-7596	44	7	correspond	correspond	VERB
ap-7596	44	8	,	,	PUNCT
ap-7596	44	9	via	via	ADP
ap-7596	44	10	the	the	DET
ap-7596	44	11	realization	realization	NOUN
ap-7596	44	12	φ	φ	NOUN
ap-7596	44	13	,	,	PUNCT
ap-7596	44	14	to	to	ADP
ap-7596	44	15	the	the	DET
ap-7596	44	16	first	first	ADJ
ap-7596	44	17	integrals	integral	NOUN
ap-7596	44	18	φ1	φ1	PROPN
ap-7596	44	19	,	,	PUNCT
ap-7596	44	20	.	.	PUNCT
ap-7596	44	21	.	.	PUNCT
ap-7596	45	1	.	.	PUNCT
ap-7596	46	1	,	,	PUNCT
ap-7596	46	2	φs	φs	ADP
ap-7596	46	3	of	of	ADP
ap-7596	46	4	the	the	DET
ap-7596	46	5	system	system	NOUN
ap-7596	46	6	.	.	PUNCT
ap-7596	47	1	while	while	SCONJ
ap-7596	47	2	for	for	ADP
ap-7596	47	3	the	the	DET
ap-7596	47	4	initial	initial	ADJ
ap-7596	47	5	system	system	NOUN
ap-7596	47	6	the	the	DET
ap-7596	47	7	relations	relation	NOUN
ap-7596	48	1	[	[	X
ap-7596	48	2	h	h	X
ap-7596	48	3	,	,	PUNCT
ap-7596	48	4	φk	φk	ADP
ap-7596	48	5	]	]	PUNCT
ap-7596	48	6	=	=	SYM
ap-7596	48	7	0	0	NUM
ap-7596	48	8	,	,	PUNCT
ap-7596	48	9	1	1	NUM
ap-7596	48	10	≤	≤	NUM
ap-7596	48	11	k	k	X
ap-7596	48	12	≤	≤	PROPN
ap-7596	48	13	s	s	PART
ap-7596	48	14	,	,	PUNCT
ap-7596	48	15	are	be	AUX
ap-7596	48	16	ensured	ensure	VERB
ap-7596	48	17	,	,	PUNCT
ap-7596	48	18	there	there	PRON
ap-7596	48	19	is	be	VERB
ap-7596	48	20	no	no	DET
ap-7596	48	21	necessity	necessity	NOUN
ap-7596	48	22	that	that	SCONJ
ap-7596	48	23	the	the	DET
ap-7596	48	24	polynomials	polynomial	NOUN
ap-7596	48	25	jk	jk	PROPN
ap-7596	48	26	commute	commute	VERB
ap-7596	48	27	with	with	ADP
ap-7596	48	28	ha	ha	INTJ
ap-7596	48	29	in	in	ADP
ap-7596	48	30	u(g	u(g	PROPN
ap-7596	48	31	)	)	PUNCT
ap-7596	48	32	,	,	PUNCT
ap-7596	48	33	although	although	SCONJ
ap-7596	48	34	the	the	DET
ap-7596	48	35	relation	relation	NOUN
ap-7596	48	36	[	[	X
ap-7596	48	37	ha	ha	INTJ
ap-7596	48	38	,	,	PUNCT
ap-7596	48	39	jk	jk	PROPN
ap-7596	48	40	]	]	X
ap-7596	48	41	=	=	SYM
ap-7596	48	42	0	0	PUNCT
ap-7596	48	43	(	(	PUNCT
ap-7596	48	44	mod	mod	PROPN
ap-7596	48	45	φ	φ	PROPN
ap-7596	48	46	)	)	PUNCT
ap-7596	48	47	(	(	PUNCT
ap-7596	48	48	3	3	X
ap-7596	48	49	)	)	PUNCT
ap-7596	48	50	is	be	AUX
ap-7596	48	51	satisfied	satisfied	ADJ
ap-7596	48	52	.	.	PUNCT
ap-7596	49	1	similarly	similarly	ADV
ap-7596	49	2	,	,	PUNCT
ap-7596	49	3	for	for	ADP
ap-7596	49	4	the	the	DET
ap-7596	49	5	polynomial	polynomial	ADJ
ap-7596	49	6	relations	relation	NOUN
ap-7596	49	7	[	[	X
ap-7596	49	8	φi	φi	ADP
ap-7596	49	9	,	,	PUNCT
ap-7596	49	10	φj	φj	X
ap-7596	49	11	]	]	PUNCT
ap-7596	49	12	=	=	PUNCT
ap-7596	49	13	αkℓ	αkℓ	VERB
ap-7596	49	14	ij	ij	NOUN
ap-7596	49	15	φkφℓ	φkφℓ	ADV
ap-7596	49	16	+	+	CCONJ
ap-7596	49	17	βk	βk	ADP
ap-7596	49	18	ijφk	ijφk	NOUN
ap-7596	49	19	of	of	ADP
ap-7596	49	20	the	the	DET
ap-7596	49	21	first	first	ADJ
ap-7596	49	22	integrals	integral	NOUN
ap-7596	49	23	,	,	PUNCT
ap-7596	49	24	the	the	DET
ap-7596	49	25	commutators	commutator	NOUN
ap-7596	49	26	in	in	ADP
ap-7596	49	27	u(g	u(g	ADJ
ap-7596	49	28	)	)	PUNCT
ap-7596	49	29	lead	lead	NOUN
ap-7596	49	30	to	to	ADP
ap-7596	49	31	the	the	DET
ap-7596	49	32	relation	relation	NOUN
ap-7596	50	1	[	[	X
ap-7596	50	2	ji	ji	X
ap-7596	50	3	,	,	PUNCT
ap-7596	50	4	jj	jj	PROPN
ap-7596	50	5	]	]	X
ap-7596	50	6	=	=	PUNCT
ap-7596	50	7	αkℓ	αkℓ	VERB
ap-7596	50	8	ij	ij	NOUN
ap-7596	50	9	jkjℓ	jkjℓ	ADJ
ap-7596	50	10	+	+	CCONJ
ap-7596	50	11	βk	βk	ADP
ap-7596	50	12	ijjk	ijjk	NOUN
ap-7596	50	13	(	(	PUNCT
ap-7596	50	14	mod	mod	PROPN
ap-7596	50	15	φ	φ	PROPN
ap-7596	50	16	)	)	PUNCT
ap-7596	50	17	(	(	PUNCT
ap-7596	50	18	4	4	X
ap-7596	50	19	)	)	PUNCT
ap-7596	50	20	if	if	SCONJ
ap-7596	50	21	equations	equation	NOUN
ap-7596	50	22	(	(	PUNCT
ap-7596	50	23	3	3	NUM
ap-7596	50	24	)	)	PUNCT
ap-7596	50	25	and	and	CCONJ
ap-7596	50	26	(	(	PUNCT
ap-7596	50	27	4	4	X
ap-7596	50	28	)	)	PUNCT
ap-7596	50	29	are	be	AUX
ap-7596	50	30	satisfied	satisfied	ADJ
ap-7596	50	31	for	for	ADP
ap-7596	50	32	any	any	DET
ap-7596	50	33	realization	realization	NOUN
ap-7596	50	34	φ	φ	NOUN
ap-7596	50	35	,	,	PUNCT
ap-7596	50	36	then	then	ADV
ap-7596	50	37	the	the	DET
ap-7596	50	38	problem	problem	NOUN
ap-7596	50	39	is	be	AUX
ap-7596	50	40	entirely	entirely	ADV
ap-7596	50	41	characterized	characterize	VERB
ap-7596	50	42	algebraically	algebraically	ADV
ap-7596	50	43	by	by	ADP
ap-7596	50	44	the	the	DET
ap-7596	50	45	reduction	reduction	NOUN
ap-7596	50	46	chain	chain	NOUN
ap-7596	50	47	m	m	PROPN
ap-7596	51	1	⊂	⊂	PROPN
ap-7596	51	2	g.	g.	NOUN
ap-7596	52	1	it	it	PRON
ap-7596	52	2	should	should	AUX
ap-7596	52	3	be	be	AUX
ap-7596	52	4	observed	observe	VERB
ap-7596	52	5	that	that	SCONJ
ap-7596	52	6	this	this	DET
ap-7596	52	7	situation	situation	NOUN
ap-7596	52	8	is	be	AUX
ap-7596	52	9	rather	rather	ADV
ap-7596	52	10	exceptional	exceptional	ADJ
ap-7596	52	11	,	,	PUNCT
ap-7596	52	12	as	as	SCONJ
ap-7596	52	13	the	the	DET
ap-7596	52	14	analysis	analysis	NOUN
ap-7596	52	15	of	of	ADP
ap-7596	52	16	the	the	DET
ap-7596	52	17	exactly	exactly	ADV
ap-7596	52	18	solvable	solvable	ADJ
ap-7596	52	19	systems	system	NOUN
ap-7596	52	20	described	describe	VERB
ap-7596	52	21	in	in	ADP
ap-7596	52	22	[	[	X
ap-7596	52	23	3	3	NUM
ap-7596	52	24	]	]	PUNCT
ap-7596	52	25	from	from	ADP
ap-7596	52	26	the	the	DET
ap-7596	52	27	point	point	NOUN
ap-7596	52	28	of	of	ADP
ap-7596	52	29	view	view	NOUN
ap-7596	52	30	of	of	ADP
ap-7596	52	31	the	the	DET
ap-7596	52	32	first	first	ADJ
ap-7596	52	33	algebraic	algebraic	ADJ
ap-7596	52	34	formulation	formulation	NOUN
ap-7596	52	35	indicates	indicate	VERB
ap-7596	52	36	that	that	SCONJ
ap-7596	52	37	,	,	PUNCT
ap-7596	52	38	in	in	ADP
ap-7596	52	39	general	general	ADJ
ap-7596	52	40	,	,	PUNCT
ap-7596	52	41	the	the	DET
ap-7596	52	42	first	first	ADJ
ap-7596	52	43	integrals	integral	NOUN
ap-7596	52	44	of	of	ADP
ap-7596	52	45	the	the	DET
ap-7596	52	46	system	system	NOUN
ap-7596	52	47	do	do	AUX
ap-7596	52	48	not	not	PART
ap-7596	52	49	correspond	correspond	VERB
ap-7596	52	50	,	,	PUNCT
ap-7596	52	51	at	at	ADP
ap-7596	52	52	the	the	DET
ap-7596	52	53	level	level	NOUN
ap-7596	52	54	of	of	ADP
ap-7596	52	55	the	the	DET
ap-7596	52	56	enveloping	enveloping	NOUN
ap-7596	52	57	algebra	algebra	NOUN
ap-7596	52	58	of	of	ADP
ap-7596	52	59	the	the	DET
ap-7596	52	60	hidden	hide	VERB
ap-7596	52	61	algebra	algebra	NOUN
ap-7596	52	62	,	,	PUNCT
ap-7596	52	63	to	to	PART
ap-7596	52	64	polynomials	polynomial	VERB
ap-7596	52	65	that	that	PRON
ap-7596	52	66	commute	commute	VERB
ap-7596	52	67	with	with	ADP
ap-7596	52	68	the	the	DET
ap-7596	52	69	algebraic	algebraic	ADJ
ap-7596	52	70	hamiltonian	hamiltonian	NOUN
ap-7596	52	71	,	,	PUNCT
ap-7596	52	72	showing	show	VERB
ap-7596	52	73	that	that	SCONJ
ap-7596	52	74	the	the	DET
ap-7596	52	75	commutativity	commutativity	NOUN
ap-7596	52	76	properties	property	NOUN
ap-7596	52	77	are	be	AUX
ap-7596	52	78	a	a	DET
ap-7596	52	79	consequence	consequence	NOUN
ap-7596	52	80	of	of	ADP
ap-7596	52	81	the	the	DET
ap-7596	52	82	realization	realization	NOUN
ap-7596	52	83	by	by	ADP
ap-7596	52	84	differential	differential	ADJ
ap-7596	52	85	operators	operator	NOUN
ap-7596	52	86	.	.	PUNCT
ap-7596	53	1	using	use	VERB
ap-7596	53	2	the	the	DET
ap-7596	53	3	correspondence	correspondence	NOUN
ap-7596	53	4	existing	exist	VERB
ap-7596	53	5	between	between	ADP
ap-7596	53	6	the	the	DET
ap-7596	53	7	representations	representation	NOUN
ap-7596	53	8	of	of	ADP
ap-7596	53	9	g	g	NOUN
ap-7596	53	10	and	and	CCONJ
ap-7596	53	11	those	those	PRON
ap-7596	53	12	of	of	ADP
ap-7596	53	13	its	its	PRON
ap-7596	53	14	enveloping	enveloping	NOUN
ap-7596	53	15	algebra	algebra	NOUN
ap-7596	53	16	u(g	u(g	PROPN
ap-7596	53	17	)	)	PUNCT
ap-7596	53	18	(	(	PUNCT
ap-7596	53	19	see	see	VERB
ap-7596	53	20	e.g.	e.g.	ADV
ap-7596	53	21	[	[	X
ap-7596	53	22	11	11	NUM
ap-7596	53	23	]	]	PUNCT
ap-7596	53	24	)	)	PUNCT
ap-7596	53	25	and	and	CCONJ
ap-7596	53	26	identifying	identify	VERB
ap-7596	53	27	a	a	DET
ap-7596	53	28	lie	lie	NOUN
ap-7596	53	29	algebra	algebra	NOUN
ap-7596	53	30	g	g	NOUN
ap-7596	53	31	with	with	ADP
ap-7596	53	32	the	the	DET
ap-7596	53	33	first	first	ADJ
ap-7596	53	34	-	-	PUNCT
ap-7596	53	35	order	order	NOUN
ap-7596	53	36	(	(	PUNCT
ap-7596	53	37	left	leave	VERB
ap-7596	53	38	-	-	PUNCT
ap-7596	53	39	invariant	invariant	ADJ
ap-7596	53	40	)	)	PUNCT
ap-7596	53	41	differential	differential	NOUN
ap-7596	53	42	operators	operator	NOUN
ap-7596	53	43	on	on	ADP
ap-7596	53	44	a	a	DET
ap-7596	53	45	lie	lie	NOUN
ap-7596	53	46	group	group	NOUN
ap-7596	53	47	g	g	NOUN
ap-7596	53	48	admitting	admit	VERB
ap-7596	53	49	g	g	PROPN
ap-7596	53	50	as	as	ADP
ap-7596	53	51	its	its	PRON
ap-7596	53	52	lie	lie	NOUN
ap-7596	53	53	algebra	algebra	NOUN
ap-7596	53	54	,	,	PUNCT
ap-7596	53	55	it	it	PRON
ap-7596	53	56	follows	follow	VERB
ap-7596	53	57	that	that	SCONJ
ap-7596	53	58	the	the	DET
ap-7596	53	59	universal	universal	ADJ
ap-7596	53	60	enveloping	enveloping	NOUN
ap-7596	53	61	algebra	algebra	NOUN
ap-7596	53	62	can	can	AUX
ap-7596	53	63	be	be	AUX
ap-7596	53	64	seen	see	VERB
ap-7596	53	65	as	as	ADP
ap-7596	53	66	the	the	DET
ap-7596	53	67	set	set	NOUN
ap-7596	53	68	of	of	ADP
ap-7596	53	69	(	(	PUNCT
ap-7596	53	70	left	left	ADJ
ap-7596	53	71	-	-	PUNCT
ap-7596	53	72	invariant	invariant	ADJ
ap-7596	53	73	)	)	PUNCT
ap-7596	53	74	differential	differential	NOUN
ap-7596	53	75	operators	operator	NOUN
ap-7596	53	76	on	on	ADP
ap-7596	53	77	g	g	NOUN
ap-7596	53	78	of	of	ADP
ap-7596	53	79	arbitrary	arbitrary	ADJ
ap-7596	53	80	order	order	NOUN
ap-7596	53	81	.	.	PUNCT
ap-7596	54	1	therefore	therefore	ADV
ap-7596	54	2	,	,	PUNCT
ap-7596	54	3	if	if	SCONJ
ap-7596	54	4	φ	φ	PROPN
ap-7596	54	5	:	:	PUNCT
ap-7596	54	6	g	g	PROPN
ap-7596	54	7	→	→	SYM
ap-7596	54	8	x(rn	x(rn	PROPN
ap-7596	54	9	)	)	PUNCT
ap-7596	54	10	is	be	AUX
ap-7596	54	11	some	some	DET
ap-7596	54	12	realization	realization	NOUN
ap-7596	54	13	of	of	ADP
ap-7596	54	14	the	the	DET
ap-7596	54	15	lie	lie	NOUN
ap-7596	54	16	algebra	algebra	NOUN
ap-7596	54	17	by	by	ADP
ap-7596	54	18	first	first	ADJ
ap-7596	54	19	-	-	PUNCT
ap-7596	54	20	order	order	NOUN
ap-7596	54	21	differential	differential	NOUN
ap-7596	54	22	operators	operator	NOUN
ap-7596	54	23	,	,	PUNCT
ap-7596	54	24	it	it	PRON
ap-7596	54	25	can	can	AUX
ap-7596	54	26	be	be	AUX
ap-7596	54	27	uniquely	uniquely	ADV
ap-7596	54	28	extended	extend	VERB
ap-7596	54	29	to	to	ADP
ap-7596	54	30	a	a	DET
ap-7596	54	31	realization	realization	NOUN
ap-7596	54	32	φ̂	φ̂	PUNCT
ap-7596	54	33	:	:	PUNCT
ap-7596	54	34	u(g	u(g	PROPN
ap-7596	54	35	)	)	PUNCT
ap-7596	54	36	→	→	SYM
ap-7596	54	37	x(rn	x(rn	PROPN
ap-7596	54	38	)	)	PUNCT
ap-7596	54	39	.	.	PUNCT
ap-7596	55	1	in	in	ADP
ap-7596	55	2	this	this	DET
ap-7596	55	3	context	context	NOUN
ap-7596	55	4	,	,	PUNCT
ap-7596	55	5	this	this	DET
ap-7596	55	6	first	first	ADJ
ap-7596	55	7	algebraic	algebraic	ADJ
ap-7596	55	8	reformulation	reformulation	NOUN
ap-7596	55	9	of	of	ADP
ap-7596	55	10	the	the	DET
ap-7596	55	11	system	system	NOUN
ap-7596	55	12	is	be	AUX
ap-7596	55	13	still	still	ADV
ap-7596	55	14	strongly	strongly	ADV
ap-7596	55	15	related	relate	VERB
ap-7596	55	16	to	to	ADP
ap-7596	55	17	the	the	DET
ap-7596	55	18	representation	representation	NOUN
ap-7596	55	19	theory	theory	NOUN
ap-7596	55	20	of	of	ADP
ap-7596	55	21	lie	lie	NOUN
ap-7596	55	22	algebras	algebra	NOUN
ap-7596	55	23	.	.	PUNCT
ap-7596	56	1	more	more	ADV
ap-7596	56	2	precisely	precisely	ADV
ap-7596	56	3	,	,	PUNCT
ap-7596	56	4	supposed	suppose	VERB
ap-7596	56	5	that	that	SCONJ
ap-7596	56	6	ha	ha	INTJ
ap-7596	56	7	∈	∈	PROPN
ap-7596	56	8	u(m	u(m	PROPN
ap-7596	56	9	)	)	PUNCT
ap-7596	56	10	is	be	AUX
ap-7596	56	11	an	an	DET
ap-7596	56	12	algebraic	algebraic	ADJ
ap-7596	56	13	hamiltonian	hamiltonian	NOUN
ap-7596	56	14	defined	define	VERB
ap-7596	56	15	in	in	ADP
ap-7596	56	16	the	the	DET
ap-7596	56	17	enveloping	enveloping	NOUN
ap-7596	56	18	of	of	ADP
ap-7596	56	19	some	some	DET
ap-7596	56	20	subalgebra	subalgebra	NOUN
ap-7596	56	21	m	m	VERB
ap-7596	56	22	⊂	⊂	NOUN
ap-7596	56	23	g	g	NOUN
ap-7596	56	24	and	and	CCONJ
ap-7596	56	25	that	that	SCONJ
ap-7596	56	26	the	the	DET
ap-7596	56	27	(	(	PUNCT
ap-7596	56	28	independent	independent	ADJ
ap-7596	56	29	)	)	PUNCT
ap-7596	56	30	polynomials	polynomial	NOUN
ap-7596	56	31	j1	j1	PROPN
ap-7596	56	32	,	,	PUNCT
ap-7596	56	33	.	.	PUNCT
ap-7596	56	34	.	.	PUNCT
ap-7596	56	35	.	.	PUNCT
ap-7596	57	1	,	,	PUNCT
ap-7596	57	2	js	js	INTJ
ap-7596	57	3	generate	generate	VERB
ap-7596	57	4	a	a	DET
ap-7596	57	5	quadratic	quadratic	ADJ
ap-7596	57	6	algebra	algebra	NOUN
ap-7596	57	7	,	,	PUNCT
ap-7596	57	8	that	that	ADV
ap-7596	57	9	is	is	ADV
ap-7596	57	10	,	,	PUNCT
ap-7596	57	11	satisfy	satisfy	VERB
ap-7596	57	12	the	the	DET
ap-7596	57	13	conditions	condition	NOUN
ap-7596	58	1	[	[	X
ap-7596	58	2	ji	ji	X
ap-7596	58	3	,	,	PUNCT
ap-7596	58	4	jj	jj	PROPN
ap-7596	58	5	]	]	X
ap-7596	58	6	=	=	PUNCT
ap-7596	58	7	αkℓ	αkℓ	VERB
ap-7596	58	8	ij	ij	NOUN
ap-7596	58	9	jkjℓ	jkjℓ	ADJ
ap-7596	58	10	+	+	CCONJ
ap-7596	58	11	βk	βk	ADP
ap-7596	58	12	ijjk	ijjk	NOUN
ap-7596	58	13	,	,	PUNCT
ap-7596	58	14	(	(	PUNCT
ap-7596	58	15	5	5	X
ap-7596	58	16	)	)	PUNCT
ap-7596	58	17	we	we	PRON
ap-7596	58	18	consider	consider	VERB
ap-7596	58	19	the	the	DET
ap-7596	58	20	(	(	PUNCT
ap-7596	58	21	two	two	NUM
ap-7596	58	22	-	-	PUNCT
ap-7596	58	23	sided	sided	ADJ
ap-7596	58	24	)	)	PUNCT
ap-7596	58	25	ideal	ideal	NOUN
ap-7596	58	26	i	i	PRON
ap-7596	58	27	in	in	ADP
ap-7596	58	28	u(g	u(g	PROPN
ap-7596	58	29	)	)	PUNCT
ap-7596	58	30	generated	generate	VERB
ap-7596	58	31	by	by	ADP
ap-7596	58	32	the	the	DET
ap-7596	58	33	polynomials	polynomial	NOUN
ap-7596	58	34	qi	qi	NOUN
ap-7596	58	35	:	:	PUNCT
ap-7596	58	36	=	=	SYM
ap-7596	59	1	[	[	X
ap-7596	59	2	ha	ha	INTJ
ap-7596	59	3	,	,	PUNCT
ap-7596	59	4	ji	ji	X
ap-7596	59	5	]	]	X
ap-7596	59	6	,	,	PUNCT
ap-7596	59	7	1	1	NUM
ap-7596	59	8	≤	≤	NUM
ap-7596	59	9	i	i	PRON
ap-7596	59	10	≤	≤	VERB
ap-7596	59	11	s.	s.	PROPN
ap-7596	59	12	the	the	DET
ap-7596	59	13	problem	problem	NOUN
ap-7596	59	14	is	be	AUX
ap-7596	59	15	now	now	ADV
ap-7596	59	16	to	to	PART
ap-7596	59	17	analyze	analyze	VERB
ap-7596	59	18	whether	whether	SCONJ
ap-7596	59	19	there	there	PRON
ap-7596	59	20	exists	exist	VERB
ap-7596	59	21	an	an	DET
ap-7596	59	22	equivalence	equivalence	NOUN
ap-7596	59	23	class	class	NOUN
ap-7596	59	24	of	of	ADP
ap-7596	59	25	(	(	PUNCT
ap-7596	59	26	faithful	faithful	ADJ
ap-7596	59	27	)	)	PUNCT
ap-7596	59	28	representations	representation	NOUN
ap-7596	59	29	φ	φ	NOUN
ap-7596	59	30	:	:	PUNCT
ap-7596	59	31	g	g	PROPN
ap-7596	59	32	→	→	SYM
ap-7596	59	33	x(rn	x(rn	PROPN
ap-7596	59	34	)	)	PUNCT
ap-7596	59	35	such	such	ADJ
ap-7596	59	36	that	that	PRON
ap-7596	59	37	for	for	ADP
ap-7596	59	38	the	the	DET
ap-7596	59	39	corresponding	corresponding	ADJ
ap-7596	59	40	extension	extension	NOUN
ap-7596	59	41	φ̂	φ̂	PUNCT
ap-7596	59	42	:	:	PUNCT
ap-7596	59	43	u(g	u(g	PROPN
ap-7596	59	44	)	)	PUNCT
ap-7596	59	45	→	→	SYM
ap-7596	59	46	x(rn	x(rn	PROPN
ap-7596	59	47	)	)	PUNCT
ap-7596	59	48	,	,	PUNCT
ap-7596	59	49	the	the	DET
ap-7596	59	50	image	image	NOUN
ap-7596	59	51	of	of	ADP
ap-7596	59	52	the	the	DET
ap-7596	59	53	ideal	ideal	NOUN
ap-7596	59	54	i	i	PRON
ap-7596	59	55	is	be	AUX
ap-7596	59	56	contained	contain	VERB
ap-7596	59	57	in	in	ADP
ap-7596	59	58	the	the	DET
ap-7596	59	59	kernel	kernel	PROPN
ap-7596	59	60	ker	ker	PROPN
ap-7596	59	61	φ̂	φ̂	PROPN
ap-7596	59	62	,	,	PUNCT
ap-7596	59	63	ensuring	ensure	VERB
ap-7596	59	64	that	that	SCONJ
ap-7596	59	65	the	the	DET
ap-7596	59	66	realized	realize	VERB
ap-7596	59	67	polynomials	polynomial	NOUN
ap-7596	59	68	φ̂(qi	φ̂(qi	PRON
ap-7596	59	69	)	)	PUNCT
ap-7596	59	70	correspond	correspond	VERB
ap-7596	59	71	to	to	ADP
ap-7596	59	72	first	first	ADJ
ap-7596	59	73	integrals	integral	NOUN
ap-7596	59	74	of	of	ADP
ap-7596	59	75	the	the	DET
ap-7596	59	76	hamiltonian	hamiltonian	NOUN
ap-7596	59	77	in	in	ADP
ap-7596	59	78	the	the	DET
ap-7596	59	79	given	give	VERB
ap-7596	59	80	realization	realization	NOUN
ap-7596	59	81	.	.	PUNCT
ap-7596	60	1	in	in	ADP
ap-7596	60	2	some	some	DET
ap-7596	60	3	sense	sense	NOUN
ap-7596	60	4	,	,	PUNCT
ap-7596	60	5	this	this	PRON
ap-7596	60	6	is	be	AUX
ap-7596	60	7	a	a	DET
ap-7596	60	8	special	special	ADJ
ap-7596	60	9	case	case	NOUN
ap-7596	60	10	of	of	ADP
ap-7596	60	11	an	an	DET
ap-7596	60	12	important	important	ADJ
ap-7596	60	13	and	and	CCONJ
ap-7596	60	14	still	still	ADV
ap-7596	60	15	unsolved	unsolved	ADJ
ap-7596	60	16	problem	problem	NOUN
ap-7596	60	17	,	,	PUNCT
ap-7596	60	18	namely	namely	ADV
ap-7596	60	19	the	the	DET
ap-7596	60	20	embedding	embedding	NOUN
ap-7596	60	21	of	of	ADP
ap-7596	60	22	a	a	DET
ap-7596	60	23	lie	lie	NOUN
ap-7596	60	24	algebra	algebra	VERB
ap-7596	60	25	g	g	NOUN
ap-7596	60	26	into	into	ADP
ap-7596	60	27	the	the	DET
ap-7596	60	28	enveloping	enveloping	NOUN
ap-7596	60	29	algebra	algebra	NOUN
ap-7596	60	30	u(k	u(k	PROPN
ap-7596	60	31	)	)	PUNCT
ap-7596	60	32	of	of	ADP
ap-7596	60	33	another	another	DET
ap-7596	60	34	lie	lie	NOUN
ap-7596	60	35	algebra	algebra	PROPN
ap-7596	60	36	k	k	NOUN
ap-7596	60	37	,	,	PUNCT
ap-7596	60	38	for	for	ADP
ap-7596	60	39	which	which	PRON
ap-7596	60	40	currently	currently	ADV
ap-7596	60	41	only	only	ADV
ap-7596	60	42	the	the	DET
ap-7596	60	43	case	case	NOUN
ap-7596	60	44	of	of	ADP
ap-7596	60	45	embeddings	embedding	NOUN
ap-7596	60	46	ι	ι	X
ap-7596	60	47	:	:	PUNCT
ap-7596	60	48	g	g	PROPN
ap-7596	60	49	→	→	SYM
ap-7596	60	50	u(g	u(g	PROPN
ap-7596	60	51	)	)	PUNCT
ap-7596	60	52	for	for	ADP
ap-7596	60	53	g	g	PROPN
ap-7596	60	54	semisimple	semisimple	NOUN
ap-7596	60	55	has	have	AUX
ap-7596	60	56	been	be	AUX
ap-7596	60	57	completely	completely	ADV
ap-7596	60	58	solved	solve	VERB
ap-7596	60	59	[	[	X
ap-7596	60	60	16	16	NUM
ap-7596	60	61	]	]	PUNCT
ap-7596	60	62	,	,	PUNCT
ap-7596	60	63	using	use	VERB
ap-7596	60	64	techniques	technique	NOUN
ap-7596	60	65	of	of	ADP
ap-7596	60	66	deformation	deformation	NOUN
ap-7596	60	67	theory	theory	NOUN
ap-7596	60	68	[	[	X
ap-7596	60	69	17	17	NUM
ap-7596	60	70	]	]	PUNCT
ap-7596	60	71	.	.	PUNCT
ap-7596	61	1	we	we	PRON
ap-7596	61	2	illustrate	illustrate	VERB
ap-7596	61	3	the	the	DET
ap-7596	61	4	preceding	precede	VERB
ap-7596	61	5	procedure	procedure	NOUN
ap-7596	61	6	considering	consider	VERB
ap-7596	61	7	the	the	DET
ap-7596	61	8	six	six	NUM
ap-7596	61	9	-	-	PUNCT
ap-7596	61	10	dimensional	dimensional	ADJ
ap-7596	61	11	non	non	ADJ
ap-7596	61	12	-	-	ADJ
ap-7596	61	13	solvable	solvable	ADJ
ap-7596	61	14	lie	lie	NOUN
ap-7596	61	15	algebra	algebra	NOUN
ap-7596	61	16	r	r	NOUN
ap-7596	61	17	⊂	⊂	X
ap-7596	61	18	sl(3,r	sl(3,r	PROPN
ap-7596	61	19	)	)	PUNCT
ap-7596	61	20	with	with	ADP
ap-7596	61	21	basis	basis	NOUN
ap-7596	61	22	{	{	PUNCT
ap-7596	61	23	x1	x1	PROPN
ap-7596	61	24	,	,	PUNCT
ap-7596	61	25	.	.	PUNCT
ap-7596	61	26	.	.	PUNCT
ap-7596	62	1	.	.	PUNCT
ap-7596	63	1	,	,	PUNCT
ap-7596	63	2	x6	x6	PROPN
ap-7596	63	3	}	}	PUNCT
ap-7596	63	4	and	and	CCONJ
ap-7596	63	5	nonvanishing	nonvanishe	VERB
ap-7596	63	6	commutators	commutator	NOUN
ap-7596	64	1	[	[	X
ap-7596	64	2	x1	x1	ADJ
ap-7596	64	3	,	,	PUNCT
ap-7596	64	4	x2	x2	PROPN
ap-7596	64	5	]	]	X
ap-7596	64	6	=	=	SYM
ap-7596	64	7	x1	x1	PROPN
ap-7596	64	8	,	,	PUNCT
ap-7596	64	9	[	[	X
ap-7596	64	10	x1	x1	PROPN
ap-7596	64	11	,	,	PUNCT
ap-7596	64	12	x5	x5	NOUN
ap-7596	64	13	]	]	X
ap-7596	64	14	=	=	SYM
ap-7596	64	15	x4	x4	PROPN
ap-7596	64	16	,	,	PUNCT
ap-7596	64	17	[	[	X
ap-7596	64	18	x2	x2	X
ap-7596	64	19	,	,	PUNCT
ap-7596	64	20	x5	x5	NOUN
ap-7596	64	21	]	]	X
ap-7596	64	22	=	=	SYM
ap-7596	64	23	x5	x5	PROPN
ap-7596	64	24	,	,	PUNCT
ap-7596	64	25	[	[	X
ap-7596	64	26	x2	x2	X
ap-7596	64	27	,	,	PUNCT
ap-7596	64	28	x6	x6	PROPN
ap-7596	64	29	]	]	X
ap-7596	64	30	=	=	SYM
ap-7596	64	31	−x6	−x6	PROPN
ap-7596	64	32	,	,	PUNCT
ap-7596	64	33	[	[	X
ap-7596	64	34	x3	x3	ADJ
ap-7596	64	35	,	,	PUNCT
ap-7596	64	36	x4	x4	PROPN
ap-7596	64	37	]	]	X
ap-7596	64	38	=	=	SYM
ap-7596	64	39	−x4	−x4	PROPN
ap-7596	64	40	,	,	PUNCT
ap-7596	64	41	[	[	X
ap-7596	64	42	x3	x3	ADJ
ap-7596	64	43	,	,	PUNCT
ap-7596	64	44	x5	x5	NOUN
ap-7596	64	45	]	]	X
ap-7596	64	46	=	=	SYM
ap-7596	64	47	−x5	−x5	PROPN
ap-7596	64	48	,	,	PUNCT
ap-7596	65	1	[	[	X
ap-7596	65	2	x3	x3	ADJ
ap-7596	65	3	,	,	PUNCT
ap-7596	65	4	x6	x6	PROPN
ap-7596	65	5	]	]	X
ap-7596	65	6	=	=	SYM
ap-7596	65	7	x6	x6	PROPN
ap-7596	66	1	[	[	X
ap-7596	66	2	x4	x4	PROPN
ap-7596	66	3	,	,	PUNCT
ap-7596	66	4	x6	x6	PROPN
ap-7596	66	5	]	]	PUNCT
ap-7596	66	6	=	=	PUNCT
ap-7596	66	7	x1	x1	ADJ
ap-7596	66	8	,	,	PUNCT
ap-7596	66	9	[	[	X
ap-7596	66	10	x5	x5	NOUN
ap-7596	66	11	,	,	PUNCT
ap-7596	66	12	x6	x6	PROPN
ap-7596	66	13	]	]	PUNCT
ap-7596	66	14	=	=	SYM
ap-7596	67	1	x2	x2	PROPN
ap-7596	67	2	−	−	NOUN
ap-7596	67	3	x3	x3	ADJ
ap-7596	67	4	.	.	PUNCT
ap-7596	68	1	superintegrable	superintegrable	ADJ
ap-7596	68	2	systems	system	NOUN
ap-7596	68	3	based	base	VERB
ap-7596	68	4	on	on	ADP
ap-7596	68	5	this	this	DET
ap-7596	68	6	hidden	hide	VERB
ap-7596	68	7	algebra	algebra	NOUN
ap-7596	68	8	r	r	NOUN
ap-7596	68	9	and	and	CCONJ
ap-7596	68	10	the	the	DET
ap-7596	68	11	vector	vector	NOUN
ap-7596	68	12	field	field	NOUN
ap-7596	68	13	realization	realization	NOUN
ap-7596	68	14	x1	x1	PROPN
ap-7596	68	15	=	=	SYM
ap-7596	68	16	∂t	∂t	PROPN
ap-7596	68	17	,	,	PUNCT
ap-7596	68	18	x2	x2	NOUN
ap-7596	68	19	=	=	NOUN
ap-7596	68	20	t∂t	t∂t	NUM
ap-7596	68	21	−	−	NUM
ap-7596	68	22	n	n	NUM
ap-7596	68	23	3	3	NUM
ap-7596	68	24	,	,	PUNCT
ap-7596	68	25	x3	x3	PROPN
ap-7596	68	26	=	=	SYM
ap-7596	68	27	su∂u	su∂u	PROPN
ap-7596	68	28	−	−	PROPN
ap-7596	68	29	n	n	NUM
ap-7596	68	30	3	3	NUM
ap-7596	68	31	,	,	PUNCT
ap-7596	68	32	x4	x4	PROPN
ap-7596	68	33	=	=	SYM
ap-7596	68	34	∂u	∂u	PROPN
ap-7596	68	35	,	,	PUNCT
ap-7596	68	36	x5	x5	PROPN
ap-7596	68	37	=	=	SYM
ap-7596	68	38	t∂u	t∂u	VERB
ap-7596	68	39	,	,	PUNCT
ap-7596	68	40	x6	x6	NOUN
ap-7596	68	41	=	=	SYM
ap-7596	68	42	u∂t	u∂t	PROPN
ap-7596	68	43	,	,	PUNCT
ap-7596	68	44	(	(	PUNCT
ap-7596	68	45	6	6	NUM
ap-7596	68	46	)	)	SYM
ap-7596	68	47	17	17	NUM
ap-7596	68	48	rutwig	rutwig	NOUN
ap-7596	68	49	campoamor	campoamor	NOUN
ap-7596	68	50	-	-	PUNCT
ap-7596	68	51	stursberg	stursberg	PROPN
ap-7596	68	52	acta	acta	PROPN
ap-7596	68	53	polytechnica	polytechnica	PROPN
ap-7596	68	54	have	have	AUX
ap-7596	68	55	been	be	AUX
ap-7596	68	56	extensively	extensively	ADV
ap-7596	68	57	studied	study	VERB
ap-7596	68	58	in	in	ADP
ap-7596	68	59	[	[	X
ap-7596	68	60	4	4	NUM
ap-7596	68	61	]	]	PUNCT
ap-7596	68	62	,	,	PUNCT
ap-7596	68	63	where	where	SCONJ
ap-7596	68	64	in	in	ADP
ap-7596	68	65	addition	addition	NOUN
ap-7596	68	66	their	their	PRON
ap-7596	68	67	exact	exact	ADJ
ap-7596	68	68	solvability	solvability	NOUN
ap-7596	68	69	was	be	AUX
ap-7596	68	70	analyzed	analyze	VERB
ap-7596	68	71	.	.	PUNCT
ap-7596	69	1	we	we	PRON
ap-7596	69	2	consider	consider	VERB
ap-7596	69	3	a	a	DET
ap-7596	69	4	special	special	ADJ
ap-7596	69	5	case	case	NOUN
ap-7596	69	6	of	of	ADP
ap-7596	69	7	the	the	DET
ap-7596	69	8	generic	generic	ADJ
ap-7596	69	9	hamiltonians	hamiltonian	NOUN
ap-7596	69	10	studied	study	VERB
ap-7596	69	11	there	there	ADV
ap-7596	69	12	.	.	PUNCT
ap-7596	70	1	taking	take	VERB
ap-7596	70	2	the	the	DET
ap-7596	70	3	values	value	NOUN
ap-7596	70	4	s	s	PART
ap-7596	70	5	=	=	X
ap-7596	70	6	k	k	X
ap-7596	70	7	=	=	SYM
ap-7596	70	8	ω	ω	PROPN
ap-7596	70	9	=	=	SYM
ap-7596	70	10	1	1	NUM
ap-7596	70	11	,	,	PUNCT
ap-7596	70	12	a	a	DET
ap-7596	70	13	=	=	SYM
ap-7596	70	14	b	b	NOUN
ap-7596	70	15	=	=	SYM
ap-7596	70	16	−	−	PROPN
ap-7596	70	17	1	1	NUM
ap-7596	70	18	2	2	NUM
ap-7596	70	19	and	and	CCONJ
ap-7596	70	20	n	n	NOUN
ap-7596	70	21	=	=	SYM
ap-7596	70	22	0	0	NUM
ap-7596	70	23	,	,	PUNCT
ap-7596	70	24	we	we	PRON
ap-7596	70	25	obtain	obtain	VERB
ap-7596	70	26	the	the	DET
ap-7596	70	27	hamiltonian	hamiltonian	ADJ
ap-7596	70	28	h1	h1	NOUN
ap-7596	70	29	and	and	CCONJ
ap-7596	70	30	two	two	NUM
ap-7596	70	31	quadratic	quadratic	ADJ
ap-7596	70	32	integrals	integral	NOUN
ap-7596	70	33	h1	h1	NOUN
ap-7596	70	34	=	=	X
ap-7596	70	35	−4t∂2	−4t∂2	NOUN
ap-7596	70	36	t	t	NOUN
ap-7596	70	37	−	−	PROPN
ap-7596	70	38	8u∂2	8u∂2	NOUN
ap-7596	71	1	tu	tu	PROPN
ap-7596	71	2	−	−	PROPN
ap-7596	71	3	4u∂2	4u∂2	NOUN
ap-7596	71	4	u	u	NOUN
ap-7596	71	5	+	+	CCONJ
ap-7596	71	6	4t∂t	4t∂t	PROPN
ap-7596	72	1	+	+	CCONJ
ap-7596	72	2	4u∂u	4u∂u	NOUN
ap-7596	72	3	,	,	PUNCT
ap-7596	72	4	φ1	φ1	NOUN
ap-7596	72	5	=	=	PUNCT
ap-7596	72	6	4u(u	4u(u	PROPN
ap-7596	72	7	−	−	ADP
ap-7596	72	8	t)∂2	t)∂2	PROPN
ap-7596	72	9	u	u	NOUN
ap-7596	72	10	,	,	PUNCT
ap-7596	72	11	φ2	φ2	PROPN
ap-7596	72	12	=	=	PUNCT
ap-7596	73	1	4(t	4(t	NUM
ap-7596	73	2	−	−	PROPN
ap-7596	73	3	u	u	NOUN
ap-7596	73	4	)	)	PUNCT
ap-7596	73	5	(	(	PUNCT
ap-7596	73	6	∂2	∂2	PROPN
ap-7596	73	7	t	t	PROPN
ap-7596	73	8	−	−	PROPN
ap-7596	73	9	∂t	∂t	PROPN
ap-7596	73	10	)	)	PUNCT
ap-7596	73	11	.	.	PUNCT
ap-7596	74	1	(	(	PUNCT
ap-7596	74	2	7	7	X
ap-7596	74	3	)	)	PUNCT
ap-7596	74	4	now	now	ADV
ap-7596	74	5	h1	h1	PROPN
ap-7596	74	6	,	,	PUNCT
ap-7596	74	7	φ1	φ1	PROPN
ap-7596	74	8	,	,	PUNCT
ap-7596	74	9	φ2	φ2	PROPN
ap-7596	74	10	are	be	AUX
ap-7596	74	11	the	the	DET
ap-7596	74	12	image	image	NOUN
ap-7596	74	13	by	by	ADP
ap-7596	74	14	the	the	DET
ap-7596	74	15	realization	realization	NOUN
ap-7596	74	16	of	of	ADP
ap-7596	74	17	the	the	DET
ap-7596	74	18	following	follow	VERB
ap-7596	74	19	polynomials	polynomial	NOUN
ap-7596	74	20	in	in	ADP
ap-7596	74	21	the	the	DET
ap-7596	74	22	enveloping	enveloping	NOUN
ap-7596	74	23	algebra	algebra	NOUN
ap-7596	74	24	of	of	ADP
ap-7596	74	25	r	r	NOUN
ap-7596	74	26	:	:	PUNCT
ap-7596	74	27	h1	h1	NOUN
ap-7596	74	28	=	=	SYM
ap-7596	74	29	4x2(1	4x2(1	NUM
ap-7596	74	30	−	−	NOUN
ap-7596	74	31	x1	x1	NUM
ap-7596	74	32	)	)	PUNCT
ap-7596	75	1	+	+	CCONJ
ap-7596	75	2	8(1	8(1	NUM
ap-7596	75	3	−	−	PROPN
ap-7596	75	4	x3)x1	x3)x1	NOUN
ap-7596	75	5	+	+	NUM
ap-7596	75	6	4(1	4(1	NUM
ap-7596	75	7	−	−	ADP
ap-7596	75	8	x4)x3	x4)x3	PROPN
ap-7596	75	9	,	,	PUNCT
ap-7596	75	10	p1	p1	PROPN
ap-7596	75	11	=	=	SYM
ap-7596	75	12	−4x3x5	−4x3x5	PROPN
ap-7596	75	13	+	+	CCONJ
ap-7596	75	14	4x2	4x2	NUM
ap-7596	75	15	3	3	NUM
ap-7596	75	16	−	−	PROPN
ap-7596	75	17	4x3	4x3	NUM
ap-7596	75	18	,	,	PUNCT
ap-7596	75	19	q1	q1	NOUN
ap-7596	75	20	=	=	PUNCT
ap-7596	76	1	4(x2x1	4(x2x1	NUM
ap-7596	76	2	−	−	NOUN
ap-7596	76	3	x6x1	x6x1	PUNCT
ap-7596	77	1	+	+	NUM
ap-7596	77	2	x6	x6	PROPN
ap-7596	77	3	−	−	PROPN
ap-7596	77	4	x2	x2	PROPN
ap-7596	77	5	)	)	PUNCT
ap-7596	77	6	.	.	PUNCT
ap-7596	78	1	at	at	ADP
ap-7596	78	2	the	the	DET
ap-7596	78	3	purely	purely	ADV
ap-7596	78	4	algebraic	algebraic	ADJ
ap-7596	78	5	level	level	NOUN
ap-7596	78	6	we	we	PRON
ap-7596	78	7	have	have	VERB
ap-7596	78	8	[	[	X
ap-7596	78	9	h1	h1	NOUN
ap-7596	78	10	,	,	PUNCT
ap-7596	78	11	p1	p1	PROPN
ap-7596	78	12	]	]	PUNCT
ap-7596	78	13	̸=	̸=	PROPN
ap-7596	78	14	0	0	NUM
ap-7596	78	15	,	,	PUNCT
ap-7596	78	16	[	[	X
ap-7596	78	17	h1	h1	X
ap-7596	78	18	,	,	PUNCT
ap-7596	78	19	q1	q1	PROPN
ap-7596	78	20	]	]	X
ap-7596	78	21	̸=	̸=	PROPN
ap-7596	78	22	0	0	NUM
ap-7596	78	23	,	,	PUNCT
ap-7596	78	24	showing	show	VERB
ap-7596	78	25	that	that	SCONJ
ap-7596	78	26	the	the	DET
ap-7596	78	27	polynomials	polynomial	NOUN
ap-7596	78	28	p1	p1	PROPN
ap-7596	78	29	and	and	CCONJ
ap-7596	78	30	q1	q1	PROPN
ap-7596	78	31	do	do	AUX
ap-7596	78	32	not	not	PART
ap-7596	78	33	belong	belong	VERB
ap-7596	78	34	to	to	ADP
ap-7596	78	35	the	the	DET
ap-7596	78	36	commutant	commutant	NOUN
ap-7596	78	37	of	of	ADP
ap-7596	78	38	h1	h1	NOUN
ap-7596	78	39	in	in	ADP
ap-7596	78	40	u(r	u(r	NOUN
ap-7596	78	41	)	)	PUNCT
ap-7596	78	42	.	.	PUNCT
ap-7596	79	1	therefore	therefore	ADV
ap-7596	79	2	,	,	PUNCT
ap-7596	79	3	the	the	DET
ap-7596	79	4	origin	origin	NOUN
ap-7596	79	5	of	of	ADP
ap-7596	79	6	the	the	DET
ap-7596	79	7	quadratic	quadratic	ADJ
ap-7596	79	8	integrals	integral	NOUN
ap-7596	79	9	of	of	ADP
ap-7596	79	10	system	system	NOUN
ap-7596	79	11	(	(	PUNCT
ap-7596	79	12	7	7	X
ap-7596	79	13	)	)	PUNCT
ap-7596	79	14	is	be	AUX
ap-7596	79	15	not	not	PART
ap-7596	79	16	algebraic	algebraic	ADJ
ap-7596	79	17	,	,	PUNCT
ap-7596	79	18	but	but	CCONJ
ap-7596	79	19	a	a	DET
ap-7596	79	20	consequence	consequence	NOUN
ap-7596	79	21	of	of	ADP
ap-7596	79	22	the	the	DET
ap-7596	79	23	specific	specific	ADJ
ap-7596	79	24	realization	realization	NOUN
ap-7596	79	25	(	(	PUNCT
ap-7596	79	26	6	6	NUM
ap-7596	79	27	)	)	PUNCT
ap-7596	79	28	.	.	PUNCT
ap-7596	80	1	if	if	SCONJ
ap-7596	80	2	we	we	PRON
ap-7596	80	3	maintain	maintain	VERB
ap-7596	80	4	the	the	DET
ap-7596	80	5	algebraic	algebraic	ADJ
ap-7596	80	6	hamiltonian	hamiltonian	NOUN
ap-7596	80	7	as	as	SCONJ
ap-7596	80	8	given	give	VERB
ap-7596	80	9	above	above	ADV
ap-7596	80	10	and	and	CCONJ
ap-7596	80	11	search	search	VERB
ap-7596	80	12	for	for	ADP
ap-7596	80	13	quadratic	quadratic	ADJ
ap-7596	80	14	polynomials	polynomial	NOUN
ap-7596	80	15	in	in	ADP
ap-7596	80	16	u(r	u(r	NOUN
ap-7596	80	17	)	)	PUNCT
ap-7596	80	18	commuting	commute	VERB
ap-7596	80	19	with	with	ADP
ap-7596	80	20	it	it	PRON
ap-7596	80	21	,	,	PUNCT
ap-7596	80	22	we	we	PRON
ap-7596	80	23	find	find	VERB
ap-7596	80	24	that	that	SCONJ
ap-7596	80	25	only	only	ADV
ap-7596	80	26	two	two	NUM
ap-7596	80	27	such	such	ADJ
ap-7596	80	28	operators	operator	NOUN
ap-7596	80	29	exist	exist	VERB
ap-7596	80	30	(	(	PUNCT
ap-7596	80	31	see	see	VERB
ap-7596	80	32	[	[	X
ap-7596	80	33	10	10	NUM
ap-7596	80	34	]	]	PUNCT
ap-7596	80	35	for	for	ADP
ap-7596	80	36	the	the	DET
ap-7596	80	37	general	general	ADJ
ap-7596	80	38	case	case	NOUN
ap-7596	80	39	)	)	PUNCT
ap-7596	80	40	,	,	PUNCT
ap-7596	80	41	given	give	VERB
ap-7596	80	42	by	by	ADP
ap-7596	80	43	a1	a1	NOUN
ap-7596	80	44	=	=	SYM
ap-7596	80	45	x4	x4	PROPN
ap-7596	80	46	−	−	NOUN
ap-7596	80	47	x3	x3	ADJ
ap-7596	80	48	−	−	PROPN
ap-7596	80	49	x6	x6	PROPN
ap-7596	80	50	+	+	CCONJ
ap-7596	80	51	x1(1	x1(1	PROPN
ap-7596	81	1	+	+	CCONJ
ap-7596	82	1	x3	x3	ADJ
ap-7596	82	2	+	+	CCONJ
ap-7596	82	3	x6	x6	NOUN
ap-7596	82	4	)	)	PUNCT
ap-7596	83	1	+	+	CCONJ
ap-7596	83	2	(	(	PUNCT
ap-7596	83	3	x3	x3	ADJ
ap-7596	83	4	+	+	CCONJ
ap-7596	83	5	x6)x4	x6)x4	ADJ
ap-7596	83	6	,	,	PUNCT
ap-7596	83	7	b1	b1	NOUN
ap-7596	83	8	=	=	SYM
ap-7596	83	9	−4x1	−4x1	NUM
ap-7596	83	10	−	−	PROPN
ap-7596	83	11	x2	x2	PROPN
ap-7596	84	1	+	+	CCONJ
ap-7596	84	2	x6	x6	PROPN
ap-7596	85	1	+	+	CCONJ
ap-7596	85	2	x1x2	x1x2	PUNCT
ap-7596	86	1	+	+	CCONJ
ap-7596	86	2	x1x3	x1x3	NUM
ap-7596	87	1	−	−	X
ap-7596	87	2	x1x6	x1x6	INTJ
ap-7596	88	1	−	−	PROPN
ap-7596	88	2	x6x4	x6x4	NOUN
ap-7596	88	3	.	.	PUNCT
ap-7596	89	1	these	these	DET
ap-7596	89	2	polynomials	polynomial	NOUN
ap-7596	89	3	are	be	AUX
ap-7596	89	4	not	not	PART
ap-7596	89	5	independent	independent	ADJ
ap-7596	89	6	,	,	PUNCT
ap-7596	89	7	as	as	SCONJ
ap-7596	89	8	they	they	PRON
ap-7596	89	9	satisfy	satisfy	VERB
ap-7596	89	10	the	the	DET
ap-7596	89	11	relation	relation	NOUN
ap-7596	89	12	a1	a1	NOUN
ap-7596	90	1	+	+	SYM
ap-7596	90	2	b1	b1	NOUN
ap-7596	90	3	+	+	CCONJ
ap-7596	90	4	1	1	NUM
ap-7596	90	5	4	4	NUM
ap-7596	90	6	h1	h1	NOUN
ap-7596	90	7	=	=	SYM
ap-7596	90	8	0	0	NUM
ap-7596	90	9	.	.	PUNCT
ap-7596	91	1	now	now	ADV
ap-7596	91	2	,	,	PUNCT
ap-7596	91	3	if	if	SCONJ
ap-7596	91	4	we	we	PRON
ap-7596	91	5	extend	extend	VERB
ap-7596	91	6	the	the	DET
ap-7596	91	7	analysis	analysis	NOUN
ap-7596	91	8	to	to	ADP
ap-7596	91	9	cubic	cubic	ADJ
ap-7596	91	10	polynomials	polynomial	NOUN
ap-7596	91	11	in	in	ADP
ap-7596	91	12	u(r	u(r	NOUN
ap-7596	91	13	)	)	PUNCT
ap-7596	91	14	,	,	PUNCT
ap-7596	91	15	we	we	PRON
ap-7596	91	16	find	find	VERB
ap-7596	91	17	the	the	DET
ap-7596	91	18	following	follow	VERB
ap-7596	91	19	operator	operator	NOUN
ap-7596	91	20	c1	c1	NOUN
ap-7596	91	21	that	that	PRON
ap-7596	91	22	commutes	commute	VERB
ap-7596	91	23	with	with	ADP
ap-7596	91	24	h1	h1	PROPN
ap-7596	91	25	:	:	PUNCT
ap-7596	91	26	c1	c1	NOUN
ap-7596	91	27	=	=	PROPN
ap-7596	92	1	3x1	3x1	NUM
ap-7596	92	2	−	−	NUM
ap-7596	92	3	2x3	2x3	NUM
ap-7596	92	4	−	−	PROPN
ap-7596	92	5	x5	x5	NOUN
ap-7596	92	6	−	−	PROPN
ap-7596	92	7	4x6	4x6	NUM
ap-7596	93	1	+	+	CCONJ
ap-7596	93	2	2x1x3	2x1x3	NUM
ap-7596	94	1	+	+	CCONJ
ap-7596	94	2	4x1x6	4x1x6	NUM
ap-7596	95	1	+	+	CCONJ
ap-7596	95	2	x2	x2	NOUN
ap-7596	95	3	3	3	NUM
ap-7596	95	4	+	+	CCONJ
ap-7596	95	5	x2x4	x2x4	X
ap-7596	96	1	+	+	CCONJ
ap-7596	96	2	x2	x2	PROPN
ap-7596	96	3	3	3	NUM
ap-7596	96	4	−	−	NOUN
ap-7596	96	5	x3x5	x3x5	PROPN
ap-7596	97	1	+	+	CCONJ
ap-7596	97	2	x3x6	x3x6	PUNCT
ap-7596	98	1	+	+	CCONJ
ap-7596	98	2	x6x4	x6x4	NUM
ap-7596	99	1	−	−	PROPN
ap-7596	100	1	x6x5	x6x5	INTJ
ap-7596	100	2	−	−	NOUN
ap-7596	100	3	x1x2	x1x2	NOUN
ap-7596	100	4	3	3	NUM
ap-7596	100	5	−	−	NOUN
ap-7596	100	6	x1x3x6	x1x3x6	PUNCT
ap-7596	101	1	+	+	CCONJ
ap-7596	101	2	x2x3x4	x2x3x4	PROPN
ap-7596	101	3	+	+	X
ap-7596	102	1	x2x6x4	x2x6x4	PROPN
ap-7596	102	2	.	.	PUNCT
ap-7596	103	1	the	the	DET
ap-7596	103	2	operators	operator	NOUN
ap-7596	103	3	a1	a1	VERB
ap-7596	103	4	and	and	CCONJ
ap-7596	103	5	c1	c1	PROPN
ap-7596	103	6	generate	generate	VERB
ap-7596	103	7	a	a	DET
ap-7596	103	8	finitedimensional	finitedimensional	ADJ
ap-7596	103	9	polynomial	polynomial	ADJ
ap-7596	103	10	algebra	algebra	NOUN
ap-7596	103	11	in	in	ADP
ap-7596	103	12	u(r	u(r	NOUN
ap-7596	103	13	)	)	PUNCT
ap-7596	103	14	,	,	PUNCT
ap-7596	103	15	with	with	ADP
ap-7596	103	16	explicit	explicit	ADJ
ap-7596	103	17	nonvanishing	nonvanishe	VERB
ap-7596	103	18	commutators	commutator	NOUN
ap-7596	104	1	[	[	X
ap-7596	104	2	a1	a1	NOUN
ap-7596	104	3	,	,	PUNCT
ap-7596	104	4	c1	c1	NOUN
ap-7596	104	5	]	]	PUNCT
ap-7596	104	6	=	=	SYM
ap-7596	104	7	d1	d1	PROPN
ap-7596	104	8	,	,	PUNCT
ap-7596	104	9	[	[	X
ap-7596	104	10	a1	a1	NOUN
ap-7596	104	11	,	,	PUNCT
ap-7596	104	12	d1	d1	NOUN
ap-7596	104	13	]	]	PUNCT
ap-7596	104	14	=	=	SYM
ap-7596	104	15	d1	d1	PROPN
ap-7596	104	16	,	,	PUNCT
ap-7596	104	17	[	[	X
ap-7596	104	18	b1	b1	NOUN
ap-7596	104	19	,	,	PUNCT
ap-7596	104	20	c1	c1	NOUN
ap-7596	104	21	]	]	PUNCT
ap-7596	104	22	=	=	SYM
ap-7596	104	23	−d1	−d1	NOUN
ap-7596	104	24	,	,	PUNCT
ap-7596	104	25	[	[	X
ap-7596	104	26	c1	c1	NOUN
ap-7596	104	27	,	,	PUNCT
ap-7596	104	28	d1	d1	PROPN
ap-7596	104	29	]	]	PUNCT
ap-7596	104	30	=	=	SYM
ap-7596	104	31	1	1	NUM
ap-7596	104	32	2{b1	2{b1	NUM
ap-7596	104	33	,	,	PUNCT
ap-7596	104	34	d1	d1	NOUN
ap-7596	104	35	}	}	PUNCT
ap-7596	104	36	−	−	PROPN
ap-7596	104	37	1	1	NUM
ap-7596	104	38	2{a1	2{a1	NUM
ap-7596	104	39	,	,	PUNCT
ap-7596	104	40	d1	d1	NOUN
ap-7596	104	41	}	}	PUNCT
ap-7596	104	42	−	−	PROPN
ap-7596	104	43	12a1	12a1	NUM
ap-7596	105	1	−	−	NOUN
ap-7596	105	2	12a1	12a1	NUM
ap-7596	106	1	+	+	CCONJ
ap-7596	106	2	4b1	4b1	NUM
ap-7596	106	3	+	+	CCONJ
ap-7596	106	4	4c1	4c1	NUM
ap-7596	106	5	−	−	NOUN
ap-7596	106	6	2{a1	2{a1	NUM
ap-7596	106	7	,	,	PUNCT
ap-7596	106	8	b1	b1	NOUN
ap-7596	106	9	}	}	PUNCT
ap-7596	106	10	,	,	PUNCT
ap-7596	106	11	where	where	SCONJ
ap-7596	106	12	{	{	PUNCT
ap-7596	106	13	◦	◦	NOUN
ap-7596	106	14	,	,	PUNCT
ap-7596	106	15	◦	◦	NOUN
ap-7596	106	16	}	}	PUNCT
ap-7596	106	17	is	be	AUX
ap-7596	106	18	the	the	DET
ap-7596	106	19	anticommutator	anticommutator	NOUN
ap-7596	106	20	.	.	PUNCT
ap-7596	107	1	now	now	ADV
ap-7596	107	2	,	,	PUNCT
ap-7596	107	3	as	as	SCONJ
ap-7596	107	4	the	the	DET
ap-7596	107	5	operators	operator	NOUN
ap-7596	107	6	h1	h1	VERB
ap-7596	107	7	,	,	PUNCT
ap-7596	107	8	a1	a1	PROPN
ap-7596	107	9	,	,	PUNCT
ap-7596	107	10	c1	c1	PROPN
ap-7596	107	11	commute	commute	NOUN
ap-7596	107	12	at	at	ADP
ap-7596	107	13	the	the	DET
ap-7596	107	14	algebraic	algebraic	ADJ
ap-7596	107	15	level	level	NOUN
ap-7596	107	16	,	,	PUNCT
ap-7596	107	17	for	for	ADP
ap-7596	107	18	any	any	DET
ap-7596	107	19	realization	realization	NOUN
ap-7596	107	20	of	of	ADP
ap-7596	107	21	r	r	NOUN
ap-7596	107	22	by	by	ADP
ap-7596	107	23	vector	vector	NOUN
ap-7596	107	24	fields	field	NOUN
ap-7596	107	25	they	they	PRON
ap-7596	107	26	give	give	VERB
ap-7596	107	27	rise	rise	NOUN
ap-7596	107	28	to	to	ADP
ap-7596	107	29	a	a	DET
ap-7596	107	30	hamiltonian	hamiltonian	ADJ
ap-7596	107	31	system	system	NOUN
ap-7596	107	32	possessing	possess	VERB
ap-7596	107	33	a	a	DET
ap-7596	107	34	quadratic	quadratic	ADJ
ap-7596	107	35	and	and	CCONJ
ap-7596	107	36	a	a	DET
ap-7596	107	37	cubic	cubic	ADJ
ap-7596	107	38	integral	integral	ADJ
ap-7596	107	39	,	,	PUNCT
ap-7596	107	40	respectively.1	respectively.1	PROPN
ap-7596	107	41	for	for	ADP
ap-7596	107	42	the	the	DET
ap-7596	107	43	particular	particular	ADJ
ap-7596	107	44	realization	realization	NOUN
ap-7596	107	45	(	(	PUNCT
ap-7596	107	46	6	6	NUM
ap-7596	107	47	)	)	PUNCT
ap-7596	107	48	,	,	PUNCT
ap-7596	107	49	it	it	PRON
ap-7596	107	50	follows	follow	VERB
ap-7596	107	51	that	that	SCONJ
ap-7596	107	52	the	the	DET
ap-7596	107	53	resulting	result	VERB
ap-7596	107	54	system	system	NOUN
ap-7596	107	55	is	be	AUX
ap-7596	107	56	actually	actually	ADV
ap-7596	107	57	equivalent	equivalent	ADJ
ap-7596	107	58	to	to	ADP
ap-7596	107	59	the	the	DET
ap-7596	107	60	initial	initial	ADJ
ap-7596	107	61	one	one	NUM
ap-7596	107	62	(	(	PUNCT
ap-7596	107	63	7	7	NUM
ap-7596	107	64	)	)	PUNCT
ap-7596	107	65	,	,	PUNCT
ap-7596	107	66	as	as	ADP
ap-7596	107	67	the	the	DET
ap-7596	107	68	image	image	NOUN
ap-7596	107	69	of	of	ADP
ap-7596	107	70	the	the	DET
ap-7596	107	71	ideal	ideal	NOUN
ap-7596	107	72	j	j	PROPN
ap-7596	107	73	generated	generate	VERB
ap-7596	107	74	by	by	ADP
ap-7596	107	75	a1	a1	PROPN
ap-7596	107	76	,	,	PUNCT
ap-7596	107	77	b1	b1	NOUN
ap-7596	107	78	,	,	PUNCT
ap-7596	107	79	c1	c1	PROPN
ap-7596	107	80	,	,	PUNCT
ap-7596	107	81	d1	d1	PROPN
ap-7596	107	82	is	be	AUX
ap-7596	107	83	properly	properly	ADV
ap-7596	107	84	contained	contain	VERB
ap-7596	107	85	in	in	ADP
ap-7596	107	86	the	the	DET
ap-7596	107	87	ideal	ideal	NOUN
ap-7596	107	88	spanned	span	VERB
ap-7596	107	89	by	by	ADP
ap-7596	107	90	φ1	φ1	PROPN
ap-7596	107	91	and	and	CCONJ
ap-7596	107	92	φ2	φ2	PROPN
ap-7596	107	93	,	,	PUNCT
ap-7596	107	94	thus	thus	ADV
ap-7596	107	95	being	be	AUX
ap-7596	107	96	functionally	functionally	ADV
ap-7596	107	97	dependent	dependent	ADJ
ap-7596	107	98	on	on	ADP
ap-7596	107	99	these	these	DET
ap-7596	107	100	integrals	integral	NOUN
ap-7596	107	101	.	.	PUNCT
ap-7596	108	1	1provided	1provided	NUM
ap-7596	108	2	that	that	SCONJ
ap-7596	108	3	the	the	DET
ap-7596	108	4	transformed	transform	VERB
ap-7596	108	5	operators	operator	NOUN
ap-7596	108	6	are	be	AUX
ap-7596	108	7	independent	independent	ADJ
ap-7596	108	8	.	.	PUNCT
ap-7596	109	1	3	3	X
ap-7596	109	2	.	.	X
ap-7596	109	3	commutants	commutant	NOUN
ap-7596	109	4	in	in	ADP
ap-7596	109	5	enveloping	envelop	VERB
ap-7596	109	6	algebras	algebra	NOUN
ap-7596	109	7	and	and	CCONJ
ap-7596	109	8	coadjoint	coadjoint	NOUN
ap-7596	109	9	representations	representation	NOUN
ap-7596	109	10	a	a	DET
ap-7596	109	11	second	second	ADJ
ap-7596	109	12	algebraic	algebraic	ADJ
ap-7596	109	13	approach	approach	NOUN
ap-7596	109	14	,	,	PUNCT
ap-7596	109	15	of	of	ADP
ap-7596	109	16	a	a	DET
ap-7596	109	17	more	more	ADV
ap-7596	109	18	general	general	ADJ
ap-7596	109	19	nature	nature	NOUN
ap-7596	109	20	,	,	PUNCT
ap-7596	109	21	can	can	AUX
ap-7596	109	22	be	be	AUX
ap-7596	109	23	proposed	propose	VERB
ap-7596	109	24	considering	consider	VERB
ap-7596	109	25	chain	chain	NOUN
ap-7596	109	26	reductions	reduction	NOUN
ap-7596	109	27	g′	g′	PROPN
ap-7596	109	28	⊂	⊂	PROPN
ap-7596	109	29	g	g	PROPN
ap-7596	109	30	of	of	ADP
ap-7596	109	31	(	(	PUNCT
ap-7596	109	32	reductive	reductive	ADJ
ap-7596	109	33	)	)	PUNCT
ap-7596	109	34	lie	lie	NOUN
ap-7596	109	35	algebras	algebra	NOUN
ap-7596	109	36	,	,	PUNCT
ap-7596	109	37	and	and	CCONJ
ap-7596	109	38	analyzing	analyze	VERB
ap-7596	109	39	the	the	DET
ap-7596	109	40	structure	structure	NOUN
ap-7596	109	41	of	of	ADP
ap-7596	109	42	the	the	DET
ap-7596	109	43	commutant	commutant	NOUN
ap-7596	109	44	of	of	ADP
ap-7596	109	45	g′	g′	NOUN
ap-7596	109	46	in	in	ADP
ap-7596	109	47	the	the	DET
ap-7596	109	48	enveloping	enveloping	NOUN
ap-7596	109	49	algebra	algebra	NOUN
ap-7596	109	50	u(g	u(g	PROPN
ap-7596	109	51	)	)	PUNCT
ap-7596	109	52	,	,	PUNCT
ap-7596	109	53	in	in	ADP
ap-7596	109	54	order	order	NOUN
ap-7596	109	55	to	to	PART
ap-7596	109	56	identify	identify	VERB
ap-7596	109	57	polynomial	polynomial	ADJ
ap-7596	109	58	(	(	PUNCT
ap-7596	109	59	in	in	ADP
ap-7596	109	60	particular	particular	ADJ
ap-7596	109	61	,	,	PUNCT
ap-7596	109	62	quadratic	quadratic	ADJ
ap-7596	109	63	)	)	PUNCT
ap-7596	109	64	subalgebras	subalgebra	NOUN
ap-7596	110	1	[	[	X
ap-7596	110	2	9	9	NUM
ap-7596	110	3	]	]	PUNCT
ap-7596	110	4	.	.	PUNCT
ap-7596	111	1	in	in	ADP
ap-7596	111	2	the	the	DET
ap-7596	111	3	generic	generic	ADJ
ap-7596	111	4	analysis	analysis	NOUN
ap-7596	111	5	of	of	ADP
ap-7596	111	6	commutants	commutant	NOUN
ap-7596	111	7	,	,	PUNCT
ap-7596	111	8	elements	element	NOUN
ap-7596	111	9	of	of	ADP
ap-7596	111	10	the	the	DET
ap-7596	111	11	theory	theory	NOUN
ap-7596	111	12	the	the	DET
ap-7596	111	13	coadjoint	coadjoint	NOUN
ap-7596	111	14	representation	representation	NOUN
ap-7596	111	15	of	of	ADP
ap-7596	111	16	lie	lie	NOUN
ap-7596	111	17	algebras	algebra	NOUN
ap-7596	111	18	can	can	AUX
ap-7596	111	19	be	be	AUX
ap-7596	111	20	used	use	VERB
ap-7596	111	21	,	,	PUNCT
ap-7596	111	22	in	in	ADP
ap-7596	111	23	order	order	NOUN
ap-7596	111	24	to	to	PART
ap-7596	111	25	simplify	simplify	VERB
ap-7596	111	26	some	some	PRON
ap-7596	111	27	of	of	ADP
ap-7596	111	28	the	the	DET
ap-7596	111	29	computations	computation	NOUN
ap-7596	111	30	in	in	ADP
ap-7596	111	31	enveloping	envelop	VERB
ap-7596	111	32	algebras	algebra	NOUN
ap-7596	111	33	.	.	PUNCT
ap-7596	112	1	if	if	SCONJ
ap-7596	112	2	g	g	PROPN
ap-7596	112	3	is	be	AUX
ap-7596	112	4	a	a	DET
ap-7596	112	5	lie	lie	NOUN
ap-7596	112	6	algebra	algebra	NOUN
ap-7596	112	7	with	with	ADP
ap-7596	112	8	generators	generator	NOUN
ap-7596	112	9	{	{	PUNCT
ap-7596	112	10	x1	x1	PROPN
ap-7596	112	11	,	,	PUNCT
ap-7596	112	12	.	.	PUNCT
ap-7596	112	13	.	.	PUNCT
ap-7596	113	1	.	.	PUNCT
ap-7596	114	1	,	,	PUNCT
ap-7596	114	2	xn	xn	X
ap-7596	114	3	}	}	PUNCT
ap-7596	115	1	and	and	CCONJ
ap-7596	115	2	commutators	commutator	VERB
ap-7596	115	3	[	[	X
ap-7596	115	4	xi	xi	X
ap-7596	115	5	,	,	PUNCT
ap-7596	115	6	xj	xj	X
ap-7596	115	7	]	]	PUNCT
ap-7596	116	1	=	=	SYM
ap-7596	116	2	ck	ck	PROPN
ap-7596	116	3	ijxk	ijxk	PROPN
ap-7596	116	4	,	,	PUNCT
ap-7596	116	5	the	the	DET
ap-7596	116	6	xi	xi	PROPN
ap-7596	116	7	’s	’s	PART
ap-7596	116	8	are	be	AUX
ap-7596	116	9	realized	realize	VERB
ap-7596	116	10	in	in	ADP
ap-7596	116	11	the	the	DET
ap-7596	116	12	space	space	NOUN
ap-7596	116	13	c∞	c∞	PROPN
ap-7596	116	14	(	(	PUNCT
ap-7596	116	15	g∗	g∗	PROPN
ap-7596	116	16	)	)	PUNCT
ap-7596	116	17	by	by	ADP
ap-7596	116	18	means	mean	NOUN
ap-7596	116	19	of	of	ADP
ap-7596	116	20	the	the	DET
ap-7596	116	21	first	first	ADJ
ap-7596	116	22	-	-	PUNCT
ap-7596	116	23	order	order	NOUN
ap-7596	116	24	differential	differential	ADJ
ap-7596	116	25	operators	operator	NOUN
ap-7596	116	26	:	:	PUNCT
ap-7596	116	27	x̂i	x̂i	PROPN
ap-7596	116	28	=	=	SYM
ap-7596	116	29	ck	ck	PROPN
ap-7596	116	30	ijxk	ijxk	PROPN
ap-7596	116	31	∂	∂	NUM
ap-7596	116	32	∂xj	∂xj	NOUN
ap-7596	116	33	,	,	PUNCT
ap-7596	116	34	(	(	PUNCT
ap-7596	116	35	8)	8)	NUM
ap-7596	116	36	where	where	SCONJ
ap-7596	116	37	{	{	PUNCT
ap-7596	116	38	x1	x1	ADJ
ap-7596	116	39	,	,	PUNCT
ap-7596	116	40	.	.	PUNCT
ap-7596	116	41	.	.	PUNCT
ap-7596	116	42	.	.	PUNCT
ap-7596	117	1	,	,	PUNCT
ap-7596	117	2	xn	xn	X
ap-7596	117	3	}	}	PUNCT
ap-7596	117	4	are	be	AUX
ap-7596	117	5	the	the	DET
ap-7596	117	6	coordinates	coordinate	NOUN
ap-7596	117	7	of	of	ADP
ap-7596	117	8	a	a	DET
ap-7596	117	9	covector	covector	NOUN
ap-7596	117	10	in	in	ADP
ap-7596	117	11	a	a	DET
ap-7596	117	12	dual	dual	ADJ
ap-7596	117	13	basis	basis	NOUN
ap-7596	117	14	of	of	ADP
ap-7596	117	15	r	r	NOUN
ap-7596	117	16	{	{	PUNCT
ap-7596	117	17	x1	x1	PROPN
ap-7596	117	18	,	,	PUNCT
ap-7596	117	19	.	.	PUNCT
ap-7596	117	20	.	.	PUNCT
ap-7596	118	1	.	.	PUNCT
ap-7596	119	1	,	,	PUNCT
ap-7596	119	2	xn	xn	PROPN
ap-7596	119	3	}	}	PUNCT
ap-7596	119	4	.	.	PUNCT
ap-7596	120	1	the	the	DET
ap-7596	120	2	invariants	invariant	NOUN
ap-7596	120	3	of	of	ADP
ap-7596	120	4	g	g	PROPN
ap-7596	120	5	(	(	PUNCT
ap-7596	120	6	in	in	ADP
ap-7596	120	7	particular	particular	ADJ
ap-7596	120	8	,	,	PUNCT
ap-7596	120	9	the	the	DET
ap-7596	120	10	casimir	casimir	PROPN
ap-7596	120	11	operators	operator	NOUN
ap-7596	120	12	)	)	PUNCT
ap-7596	120	13	correspond	correspond	VERB
ap-7596	120	14	to	to	ADP
ap-7596	120	15	the	the	DET
ap-7596	120	16	solutions	solution	NOUN
ap-7596	120	17	of	of	ADP
ap-7596	120	18	the	the	DET
ap-7596	120	19	following	follow	VERB
ap-7596	120	20	system	system	NOUN
ap-7596	120	21	of	of	ADP
ap-7596	120	22	partial	partial	ADJ
ap-7596	120	23	differential	differential	NOUN
ap-7596	120	24	equations	equation	NOUN
ap-7596	120	25	:	:	PUNCT
ap-7596	121	1	x̂if	x̂if	X
ap-7596	121	2	=	=	SYM
ap-7596	121	3	0	0	NUM
ap-7596	121	4	,	,	PUNCT
ap-7596	121	5	1	1	NUM
ap-7596	121	6	≤	≤	NUM
ap-7596	121	7	i	i	PRON
ap-7596	121	8	≤	≤	ADJ
ap-7596	121	9	n.	n.	NOUN
ap-7596	121	10	(	(	PUNCT
ap-7596	121	11	9	9	NUM
ap-7596	121	12	)	)	PUNCT
ap-7596	121	13	for	for	ADP
ap-7596	121	14	an	an	DET
ap-7596	121	15	embedding	embedding	NOUN
ap-7596	121	16	of	of	ADP
ap-7596	121	17	lie	lie	NOUN
ap-7596	121	18	algebras	algebras	PROPN
ap-7596	121	19	f	f	PROPN
ap-7596	121	20	:	:	PUNCT
ap-7596	121	21	g′	g′	NOUN
ap-7596	121	22	→	→	SYM
ap-7596	121	23	g	g	PROPN
ap-7596	121	24	,	,	PUNCT
ap-7596	121	25	a	a	DET
ap-7596	121	26	basis	basis	NOUN
ap-7596	121	27	{	{	PUNCT
ap-7596	121	28	x1	x1	PROPN
ap-7596	121	29	,	,	PUNCT
ap-7596	121	30	.	.	PUNCT
ap-7596	121	31	.	.	PUNCT
ap-7596	121	32	.	.	PUNCT
ap-7596	121	33	,	,	PUNCT
ap-7596	121	34	xr	xr	X
ap-7596	121	35	}	}	PUNCT
ap-7596	121	36	of	of	ADP
ap-7596	121	37	the	the	DET
ap-7596	121	38	subalgebra	subalgebra	NOUN
ap-7596	121	39	can	can	AUX
ap-7596	121	40	be	be	AUX
ap-7596	121	41	extended	extend	VERB
ap-7596	121	42	to	to	ADP
ap-7596	121	43	a	a	DET
ap-7596	121	44	basis	basis	NOUN
ap-7596	121	45	{	{	PUNCT
ap-7596	121	46	x1	x1	PROPN
ap-7596	121	47	,	,	PUNCT
ap-7596	121	48	.	.	PUNCT
ap-7596	121	49	.	.	PUNCT
ap-7596	122	1	.	.	PUNCT
ap-7596	123	1	,	,	PUNCT
ap-7596	123	2	xn	xn	X
ap-7596	123	3	}	}	PUNCT
ap-7596	123	4	of	of	ADP
ap-7596	123	5	g.	g.	PROPN
ap-7596	123	6	therefore	therefore	ADV
ap-7596	123	7	,	,	PUNCT
ap-7596	123	8	we	we	PRON
ap-7596	123	9	can	can	AUX
ap-7596	123	10	consider	consider	VERB
ap-7596	123	11	the	the	DET
ap-7596	123	12	subsystem	subsystem	NOUN
ap-7596	123	13	formed	form	VERB
ap-7596	123	14	by	by	ADP
ap-7596	123	15	the	the	DET
ap-7596	123	16	first	first	ADJ
ap-7596	123	17	r	r	NOUN
ap-7596	123	18	equations	equation	NOUN
ap-7596	123	19	of	of	ADP
ap-7596	123	20	(	(	PUNCT
ap-7596	123	21	9	9	NUM
ap-7596	123	22	)	)	PUNCT
ap-7596	123	23	,	,	PUNCT
ap-7596	123	24	corresponding	correspond	VERB
ap-7596	123	25	to	to	ADP
ap-7596	123	26	the	the	DET
ap-7596	123	27	generators	generator	NOUN
ap-7596	123	28	of	of	ADP
ap-7596	123	29	the	the	DET
ap-7596	123	30	subalgebra	subalgebra	NOUN
ap-7596	123	31	g′.	g′.	VERB
ap-7596	123	32	the	the	DET
ap-7596	123	33	solutions	solution	NOUN
ap-7596	123	34	of	of	ADP
ap-7596	123	35	this	this	DET
ap-7596	123	36	subsystem	subsystem	NOUN
ap-7596	123	37	,	,	PUNCT
ap-7596	123	38	that	that	SCONJ
ap-7596	123	39	in	in	ADP
ap-7596	123	40	particular	particular	ADJ
ap-7596	123	41	encompass	encompass	VERB
ap-7596	123	42	the	the	DET
ap-7596	123	43	invariants	invariant	NOUN
ap-7596	123	44	of	of	ADP
ap-7596	123	45	g′	g′	NOUN
ap-7596	123	46	,	,	PUNCT
ap-7596	123	47	are	be	AUX
ap-7596	123	48	usually	usually	ADV
ap-7596	123	49	called	call	VERB
ap-7596	123	50	subgroup	subgroup	NOUN
ap-7596	123	51	scalars	scalar	VERB
ap-7596	124	1	[	[	X
ap-7596	124	2	18	18	NUM
ap-7596	124	3	]	]	PUNCT
ap-7596	124	4	.	.	PUNCT
ap-7596	125	1	by	by	ADP
ap-7596	125	2	means	mean	NOUN
ap-7596	125	3	of	of	ADP
ap-7596	125	4	the	the	DET
ap-7596	125	5	standard	standard	ADJ
ap-7596	125	6	symmetrization	symmetrization	NOUN
ap-7596	125	7	map	map	NOUN
ap-7596	125	8	λ	λ	INTJ
ap-7596	125	9	(	(	PUNCT
ap-7596	125	10	xi1	xi1	PROPN
ap-7596	125	11	.	.	PUNCT
ap-7596	125	12	.	.	PUNCT
ap-7596	125	13	.	.	PUNCT
ap-7596	126	1	xip	xip	X
ap-7596	126	2	)	)	PUNCT
ap-7596	127	1	=	=	SYM
ap-7596	127	2	1	1	NUM
ap-7596	127	3	p	p	NOUN
ap-7596	127	4	!	!	PUNCT
ap-7596	128	1	∑	∑	PROPN
ap-7596	128	2	σ∈sp	σ∈sp	PROPN
ap-7596	128	3	xσ(i1	xσ(i1	PUNCT
ap-7596	128	4	)	)	PUNCT
ap-7596	128	5	.	.	PUNCT
ap-7596	128	6	.	.	PUNCT
ap-7596	128	7	.	.	PUNCT
ap-7596	129	1	xσ(ip	xσ(ip	PROPN
ap-7596	129	2	)	)	PUNCT
ap-7596	130	1	(	(	PUNCT
ap-7596	130	2	10	10	X
ap-7596	130	3	)	)	PUNCT
ap-7596	130	4	polynomial	polynomial	ADJ
ap-7596	130	5	solutions	solution	NOUN
ap-7596	130	6	of	of	ADP
ap-7596	130	7	the	the	DET
ap-7596	130	8	subsystem	subsystem	NOUN
ap-7596	130	9	correspond	correspond	VERB
ap-7596	130	10	to	to	ADP
ap-7596	130	11	elements	element	NOUN
ap-7596	130	12	in	in	ADP
ap-7596	130	13	the	the	DET
ap-7596	130	14	enveloping	enveloping	NOUN
ap-7596	130	15	algebra	algebra	NOUN
ap-7596	130	16	u(g	u(g	PROPN
ap-7596	130	17	)	)	PUNCT
ap-7596	130	18	of	of	ADP
ap-7596	130	19	g	g	PROPN
ap-7596	130	20	that	that	DET
ap-7596	130	21	commute	commute	NOUN
ap-7596	130	22	with	with	ADP
ap-7596	130	23	the	the	DET
ap-7596	130	24	subalgebra	subalgebra	NOUN
ap-7596	130	25	g′.	g′.	X
ap-7596	130	26	if	if	SCONJ
ap-7596	130	27	we	we	PRON
ap-7596	130	28	now	now	ADV
ap-7596	130	29	define	define	VERB
ap-7596	130	30	an	an	DET
ap-7596	130	31	algebraic	algebraic	ADJ
ap-7596	130	32	hamiltonian	hamiltonian	ADJ
ap-7596	130	33	h	h	NOUN
ap-7596	131	1	=	=	NOUN
ap-7596	131	2	h	h	PROPN
ap-7596	131	3	(	(	PUNCT
ap-7596	131	4	x1	x1	PROPN
ap-7596	131	5	,	,	PUNCT
ap-7596	131	6	.	.	PUNCT
ap-7596	131	7	.	.	PUNCT
ap-7596	131	8	.	.	PUNCT
ap-7596	132	1	,	,	PUNCT
ap-7596	132	2	xr	xr	PROPN
ap-7596	132	3	)	)	PUNCT
ap-7596	132	4	∈	∈	PROPN
ap-7596	132	5	u(g′	u(g′	PROPN
ap-7596	132	6	)	)	PUNCT
ap-7596	132	7	,	,	PUNCT
ap-7596	132	8	(	(	PUNCT
ap-7596	132	9	11	11	NUM
ap-7596	132	10	)	)	PUNCT
ap-7596	132	11	in	in	ADP
ap-7596	132	12	terms	term	NOUN
ap-7596	132	13	of	of	ADP
ap-7596	132	14	the	the	DET
ap-7596	132	15	subalgebra	subalgebra	NOUN
ap-7596	132	16	generators	generator	NOUN
ap-7596	132	17	,	,	PUNCT
ap-7596	132	18	the	the	DET
ap-7596	132	19	commutant	commutant	NOUN
ap-7596	132	20	cu(g)(h	cu(g)(h	NUM
ap-7596	132	21	)	)	PUNCT
ap-7596	133	1	=	=	PRON
ap-7596	133	2	{	{	PUNCT
ap-7596	133	3	u	u	NOUN
ap-7596	133	4	∈	∈	PROPN
ap-7596	133	5	u(g	u(g	PROPN
ap-7596	133	6	)	)	PUNCT
ap-7596	134	1	|	|	ADV
ap-7596	135	1	[	[	X
ap-7596	135	2	h	h	NOUN
ap-7596	135	3	,	,	PUNCT
ap-7596	135	4	u	u	NOUN
ap-7596	135	5	]	]	X
ap-7596	135	6	=	=	SYM
ap-7596	135	7	0	0	X
ap-7596	135	8	}	}	PUNCT
ap-7596	135	9	certainly	certainly	ADV
ap-7596	135	10	includes	include	VERB
ap-7596	135	11	the	the	DET
ap-7596	135	12	solutions	solution	NOUN
ap-7596	135	13	of	of	ADP
ap-7596	135	14	(	(	PUNCT
ap-7596	135	15	9	9	NUM
ap-7596	135	16	)	)	PUNCT
ap-7596	135	17	common	common	ADJ
ap-7596	135	18	to	to	ADP
ap-7596	135	19	the	the	DET
ap-7596	135	20	g′-generators	g′-generators	PROPN
ap-7596	135	21	,	,	PUNCT
ap-7596	135	22	i.e.	i.e.	X
ap-7596	135	23	cu(g)(h	cu(g)(h	PRON
ap-7596	135	24	)	)	PUNCT
ap-7596	135	25	⊃	⊃	PROPN
ap-7596	135	26	{	{	PUNCT
ap-7596	135	27	λ(φ	λ(φ	NOUN
ap-7596	135	28	)	)	PUNCT
ap-7596	135	29	|	|	ADV
ap-7596	135	30	x̂1(φ	x̂1(φ	VERB
ap-7596	135	31	)	)	PUNCT
ap-7596	135	32	=	=	SYM
ap-7596	135	33	·	·	PUNCT
ap-7596	135	34	·	·	PUNCT
ap-7596	135	35	·	·	PUNCT
ap-7596	136	1	=	=	SYM
ap-7596	136	2	x̂r(φ	x̂r(φ	PROPN
ap-7596	136	3	)	)	PUNCT
ap-7596	137	1	=	=	SYM
ap-7596	137	2	0	0	NUM
ap-7596	137	3	}	}	PUNCT
ap-7596	137	4	,	,	PUNCT
ap-7596	137	5	where	where	SCONJ
ap-7596	137	6	φ(x1	φ(x1	NOUN
ap-7596	137	7	,	,	PUNCT
ap-7596	137	8	.	.	PUNCT
ap-7596	137	9	.	.	PUNCT
ap-7596	137	10	.	.	PUNCT
ap-7596	138	1	,	,	PUNCT
ap-7596	138	2	xn	xn	X
ap-7596	138	3	)	)	PUNCT
ap-7596	138	4	∈	∈	PROPN
ap-7596	138	5	c∞	c∞	PROPN
ap-7596	138	6	(	(	PUNCT
ap-7596	138	7	g∗	g∗	PROPN
ap-7596	138	8	)	)	PUNCT
ap-7596	138	9	.	.	PUNCT
ap-7596	139	1	depending	depend	VERB
ap-7596	139	2	on	on	ADP
ap-7596	139	3	the	the	DET
ap-7596	139	4	structure	structure	NOUN
ap-7596	139	5	of	of	ADP
ap-7596	139	6	g	g	PROPN
ap-7596	139	7	and	and	CCONJ
ap-7596	139	8	the	the	DET
ap-7596	139	9	subalgebra	subalgebra	PROPN
ap-7596	139	10	g′	g′	PROPN
ap-7596	139	11	,	,	PUNCT
ap-7596	139	12	as	as	ADV
ap-7596	139	13	well	well	ADV
ap-7596	139	14	as	as	ADP
ap-7596	139	15	on	on	ADP
ap-7596	139	16	the	the	DET
ap-7596	139	17	choice	choice	NOUN
ap-7596	139	18	of	of	ADP
ap-7596	139	19	h	h	NOUN
ap-7596	139	20	,	,	PUNCT
ap-7596	139	21	two	two	NUM
ap-7596	139	22	possible	possible	ADJ
ap-7596	139	23	cases	case	NOUN
ap-7596	139	24	arise	arise	VERB
ap-7596	139	25	for	for	ADP
ap-7596	139	26	a	a	DET
ap-7596	139	27	polynomial	polynomial	ADJ
ap-7596	139	28	p	p	X
ap-7596	139	29	∈	∈	PROPN
ap-7596	139	30	cu(g)(h	cu(g)(h	NUM
ap-7596	139	31	):	):	PUNCT
ap-7596	139	32	18	18	NUM
ap-7596	139	33	vol	vol	NOUN
ap-7596	139	34	.	.	PUNCT
ap-7596	140	1	62	62	NUM
ap-7596	140	2	no	no	INTJ
ap-7596	140	3	.	.	PUNCT
ap-7596	141	1	1/2022	1/2022	NUM
ap-7596	141	2	on	on	ADP
ap-7596	141	3	some	some	DET
ap-7596	141	4	algebraic	algebraic	ADJ
ap-7596	141	5	formulations	formulation	NOUN
ap-7596	141	6	.	.	PUNCT
ap-7596	141	7	.	.	PUNCT
ap-7596	141	8	.	.	PUNCT
ap-7596	142	1	(	(	PUNCT
ap-7596	142	2	1	1	NUM
ap-7596	142	3	.	.	PUNCT
ap-7596	142	4	)	)	PUNCT
ap-7596	143	1	p	p	NOUN
ap-7596	143	2	commutes	commute	NOUN
ap-7596	143	3	with	with	ADP
ap-7596	143	4	all	all	DET
ap-7596	143	5	x1	x1	PROPN
ap-7596	143	6	,	,	PUNCT
ap-7596	143	7	.	.	PUNCT
ap-7596	143	8	.	.	PUNCT
ap-7596	143	9	.	.	PUNCT
ap-7596	144	1	,	,	PUNCT
ap-7596	144	2	xr	xr	PROPN
ap-7596	144	3	.	.	PUNCT
ap-7596	145	1	(	(	PUNCT
ap-7596	145	2	2	2	NUM
ap-7596	145	3	.	.	PUNCT
ap-7596	145	4	)	)	PUNCT
ap-7596	146	1	there	there	PRON
ap-7596	146	2	is	be	VERB
ap-7596	146	3	an	an	DET
ap-7596	146	4	index	index	NOUN
ap-7596	146	5	k0	k0	NOUN
ap-7596	146	6	with	with	ADP
ap-7596	146	7	[	[	X
ap-7596	146	8	p	p	X
ap-7596	146	9	,	,	PUNCT
ap-7596	146	10	xk0	xk0	PROPN
ap-7596	146	11	]	]	PUNCT
ap-7596	147	1	̸=	̸=	PROPN
ap-7596	147	2	0	0	NUM
ap-7596	147	3	.	.	PUNCT
ap-7596	148	1	polynomials	polynomial	VERB
ap-7596	148	2	p	p	NOUN
ap-7596	148	3	in	in	ADP
ap-7596	148	4	the	the	DET
ap-7596	148	5	first	first	ADJ
ap-7596	148	6	case	case	NOUN
ap-7596	148	7	actually	actually	ADV
ap-7596	148	8	commute	commute	VERB
ap-7596	148	9	with	with	ADP
ap-7596	148	10	the	the	DET
ap-7596	148	11	hamiltonian	hamiltonian	ADJ
ap-7596	148	12	h	h	NOUN
ap-7596	148	13	,	,	PUNCT
ap-7596	148	14	and	and	CCONJ
ap-7596	148	15	thus	thus	ADV
ap-7596	148	16	belong	belong	VERB
ap-7596	148	17	to	to	ADP
ap-7596	148	18	the	the	DET
ap-7596	148	19	two	two	NUM
ap-7596	148	20	-	-	PUNCT
ap-7596	148	21	sided	side	VERB
ap-7596	148	22	ideal	ideal	ADJ
ap-7596	148	23	⟨i⟩	⟨i⟩	PROPN
ap-7596	148	24	generated	generate	VERB
ap-7596	148	25	by	by	ADP
ap-7596	148	26	the	the	DET
ap-7596	148	27	set	set	NOUN
ap-7596	148	28	i	i	NOUN
ap-7596	148	29	=	=	SYM
ap-7596	148	30	{	{	PUNCT
ap-7596	148	31	j1	j1	PROPN
ap-7596	148	32	,	,	PUNCT
ap-7596	148	33	.	.	PUNCT
ap-7596	148	34	.	.	PUNCT
ap-7596	149	1	.	.	PUNCT
ap-7596	150	1	,	,	PUNCT
ap-7596	150	2	js	js	ADP
ap-7596	150	3	}	}	PUNCT
ap-7596	150	4	of	of	ADP
ap-7596	150	5	elements	element	NOUN
ap-7596	150	6	corresponding	correspond	VERB
ap-7596	150	7	to	to	ADP
ap-7596	150	8	the	the	DET
ap-7596	150	9	symmetrization	symmetrization	NOUN
ap-7596	150	10	of	of	ADP
ap-7596	150	11	independent	independent	ADJ
ap-7596	150	12	polynomials	polynomial	NOUN
ap-7596	150	13	satisfying	satisfy	VERB
ap-7596	150	14	the	the	DET
ap-7596	150	15	subsystem	subsystem	NOUN
ap-7596	150	16	of	of	ADP
ap-7596	150	17	(	(	PUNCT
ap-7596	150	18	9	9	X
ap-7596	150	19	)	)	PUNCT
ap-7596	150	20	corresponding	correspond	VERB
ap-7596	150	21	to	to	ADP
ap-7596	150	22	g′.	g′.	NOUN
ap-7596	150	23	for	for	ADP
ap-7596	150	24	these	these	DET
ap-7596	150	25	elements	element	NOUN
ap-7596	150	26	,	,	PUNCT
ap-7596	150	27	it	it	PRON
ap-7596	150	28	follows	follow	VERB
ap-7596	150	29	at	at	ADP
ap-7596	150	30	once	once	ADV
ap-7596	150	31	that	that	PRON
ap-7596	150	32	[	[	X
ap-7596	150	33	jk	jk	PROPN
ap-7596	150	34	,	,	PUNCT
ap-7596	150	35	jℓ	jℓ	PROPN
ap-7596	150	36	]	]	PUNCT
ap-7596	150	37	belongs	belong	VERB
ap-7596	150	38	to	to	ADP
ap-7596	150	39	i.	i.	PROPN
ap-7596	150	40	in	in	ADP
ap-7596	150	41	the	the	DET
ap-7596	150	42	general	general	ADJ
ap-7596	150	43	case	case	NOUN
ap-7596	150	44	,	,	PUNCT
ap-7596	150	45	the	the	DET
ap-7596	150	46	hamiltonian	hamiltonian	ADJ
ap-7596	150	47	h	h	NOUN
ap-7596	150	48	does	do	AUX
ap-7596	150	49	not	not	PART
ap-7596	150	50	commute	commute	VERB
ap-7596	150	51	with	with	ADP
ap-7596	150	52	all	all	DET
ap-7596	150	53	xj	xj	NOUN
ap-7596	150	54	-	-	NOUN
ap-7596	150	55	generators	generator	NOUN
ap-7596	150	56	,	,	PUNCT
ap-7596	150	57	and	and	CCONJ
ap-7596	150	58	in	in	ADP
ap-7596	150	59	order	order	NOUN
ap-7596	150	60	to	to	PART
ap-7596	150	61	find	find	VERB
ap-7596	150	62	the	the	DET
ap-7596	150	63	commutant	commutant	NOUN
ap-7596	150	64	cu(g)(h	cu(g)(h	NUM
ap-7596	150	65	)	)	PUNCT
ap-7596	150	66	,	,	PUNCT
ap-7596	150	67	we	we	PRON
ap-7596	150	68	can	can	AUX
ap-7596	150	69	restrict	restrict	VERB
ap-7596	150	70	the	the	DET
ap-7596	150	71	analysis	analysis	NOUN
ap-7596	150	72	to	to	ADP
ap-7596	150	73	the	the	DET
ap-7596	150	74	determination	determination	NOUN
ap-7596	150	75	of	of	ADP
ap-7596	150	76	a	a	DET
ap-7596	150	77	basis	basis	NOUN
ap-7596	150	78	of	of	ADP
ap-7596	150	79	the	the	DET
ap-7596	150	80	factor	factor	NOUN
ap-7596	150	81	module	module	NOUN
ap-7596	150	82	cu(g)(h)/⟨i⟩.	cu(g)(h)/⟨i⟩.	PROPN
ap-7596	150	83	although	although	SCONJ
ap-7596	150	84	the	the	DET
ap-7596	150	85	problem	problem	NOUN
ap-7596	150	86	is	be	AUX
ap-7596	150	87	computationally	computationally	ADV
ap-7596	150	88	cumbersome	cumbersome	ADJ
ap-7596	150	89	,	,	PUNCT
ap-7596	150	90	certain	certain	ADJ
ap-7596	150	91	algorithms	algorithm	NOUN
ap-7596	150	92	in	in	ADP
ap-7596	150	93	terms	term	NOUN
ap-7596	150	94	of	of	ADP
ap-7596	150	95	gröbner	gröbner	NOUN
ap-7596	150	96	bases	basis	NOUN
ap-7596	150	97	have	have	AUX
ap-7596	150	98	been	be	AUX
ap-7596	150	99	developed	develop	VERB
ap-7596	150	100	that	that	PRON
ap-7596	150	101	allow	allow	VERB
ap-7596	150	102	its	its	PRON
ap-7596	150	103	precise	precise	ADJ
ap-7596	150	104	determination	determination	NOUN
ap-7596	150	105	[	[	X
ap-7596	150	106	19	19	NUM
ap-7596	150	107	]	]	PUNCT
ap-7596	150	108	.	.	PUNCT
ap-7596	151	1	a	a	DET
ap-7596	151	2	(	(	PUNCT
ap-7596	151	3	restricted	restrict	VERB
ap-7596	151	4	)	)	PUNCT
ap-7596	151	5	systematic	systematic	ADJ
ap-7596	151	6	procedure	procedure	NOUN
ap-7596	151	7	that	that	PRON
ap-7596	151	8	circumvents	circumvent	VERB
ap-7596	151	9	the	the	DET
ap-7596	151	10	above	above	ADV
ap-7596	151	11	-	-	PUNCT
ap-7596	151	12	mentioned	mention	VERB
ap-7596	151	13	obstruction	obstruction	NOUN
ap-7596	151	14	and	and	CCONJ
ap-7596	151	15	allows	allow	VERB
ap-7596	151	16	us	we	PRON
ap-7596	151	17	to	to	PART
ap-7596	151	18	analyze	analyze	VERB
ap-7596	151	19	polynomial	polynomial	ADJ
ap-7596	151	20	algebras	algebra	NOUN
ap-7596	151	21	with	with	ADP
ap-7596	151	22	respect	respect	NOUN
ap-7596	151	23	to	to	ADP
ap-7596	151	24	a	a	DET
ap-7596	151	25	reduction	reduction	NOUN
ap-7596	151	26	chain	chain	NOUN
ap-7596	151	27	g′	g′	NOUN
ap-7596	151	28	⊂	⊂	PROPN
ap-7596	151	29	g	g	PROPN
ap-7596	151	30	can	can	AUX
ap-7596	151	31	be	be	AUX
ap-7596	151	32	proposed	propose	VERB
ap-7596	151	33	starting	start	VERB
ap-7596	151	34	from	from	ADP
ap-7596	151	35	the	the	DET
ap-7596	151	36	polynomials	polynomial	NOUN
ap-7596	151	37	in	in	ADP
ap-7596	151	38	u(g	u(g	ADJ
ap-7596	151	39	)	)	PUNCT
ap-7596	151	40	that	that	PRON
ap-7596	151	41	commute	commute	VERB
ap-7596	151	42	with	with	ADP
ap-7596	151	43	all	all	DET
ap-7596	151	44	the	the	DET
ap-7596	151	45	generators	generator	NOUN
ap-7596	151	46	intervening	intervene	VERB
ap-7596	151	47	in	in	ADP
ap-7596	151	48	the	the	DET
ap-7596	151	49	expression	expression	NOUN
ap-7596	151	50	of	of	ADP
ap-7596	151	51	the	the	DET
ap-7596	151	52	algebraic	algebraic	ADJ
ap-7596	151	53	hamiltonian	hamiltonian	PROPN
ap-7596	151	54	h	h	PROPN
ap-7596	151	55	∈	∈	PROPN
ap-7596	151	56	u(g′	u(g′	PROPN
ap-7596	151	57	)	)	PUNCT
ap-7596	151	58	.	.	PUNCT
ap-7596	152	1	more	more	ADV
ap-7596	152	2	precisely	precisely	ADV
ap-7596	152	3	,	,	PUNCT
ap-7596	152	4	if	if	SCONJ
ap-7596	152	5	the	the	DET
ap-7596	152	6	hamiltonian	hamiltonian	ADJ
ap-7596	152	7	h	h	NOUN
ap-7596	152	8	is	be	AUX
ap-7596	152	9	given	give	VERB
ap-7596	152	10	as	as	ADP
ap-7596	152	11	a	a	DET
ap-7596	152	12	polynomial	polynomial	ADJ
ap-7596	152	13	p	p	NOUN
ap-7596	152	14	(	(	PUNCT
ap-7596	152	15	xi1	xi1	PROPN
ap-7596	152	16	,	,	PUNCT
ap-7596	152	17	.	.	PUNCT
ap-7596	152	18	.	.	PUNCT
ap-7596	152	19	.	.	PUNCT
ap-7596	153	1	,	,	PUNCT
ap-7596	153	2	xis	xis	PROPN
ap-7596	153	3	)	)	PUNCT
ap-7596	153	4	in	in	ADP
ap-7596	153	5	terms	term	NOUN
ap-7596	153	6	of	of	ADP
ap-7596	153	7	the	the	DET
ap-7596	153	8	generators	generator	NOUN
ap-7596	153	9	of	of	ADP
ap-7596	153	10	the	the	DET
ap-7596	153	11	subalgebra	subalgebra	PROPN
ap-7596	153	12	g′	g′	NOUN
ap-7596	153	13	with	with	ADP
ap-7596	153	14	basis	basis	NOUN
ap-7596	153	15	{	{	PUNCT
ap-7596	153	16	x1	x1	PROPN
ap-7596	153	17	,	,	PUNCT
ap-7596	153	18	.	.	PUNCT
ap-7596	153	19	.	.	PUNCT
ap-7596	153	20	.	.	PUNCT
ap-7596	154	1	,	,	PUNCT
ap-7596	154	2	xr	xr	PROPN
ap-7596	154	3	}	}	PUNCT
ap-7596	154	4	,	,	PUNCT
ap-7596	154	5	we	we	PRON
ap-7596	154	6	consider	consider	VERB
ap-7596	154	7	the	the	DET
ap-7596	154	8	subsystem	subsystem	NOUN
ap-7596	154	9	of	of	ADP
ap-7596	154	10	(	(	PUNCT
ap-7596	154	11	9	9	NUM
ap-7596	154	12	)	)	PUNCT
ap-7596	154	13	given	give	VERB
ap-7596	154	14	by	by	ADP
ap-7596	154	15	x̂ij	x̂ij	PROPN
ap-7596	154	16	f	f	PROPN
ap-7596	154	17	(	(	PUNCT
ap-7596	154	18	x1	x1	PROPN
ap-7596	154	19	,	,	PUNCT
ap-7596	154	20	.	.	PUNCT
ap-7596	154	21	.	.	PUNCT
ap-7596	155	1	.	.	PUNCT
ap-7596	156	1	,	,	PUNCT
ap-7596	156	2	xn	xn	X
ap-7596	156	3	)	)	PUNCT
ap-7596	157	1	=	=	SYM
ap-7596	157	2	0	0	NUM
ap-7596	157	3	,	,	PUNCT
ap-7596	157	4	1	1	NUM
ap-7596	157	5	≤	≤	NUM
ap-7596	157	6	j	j	PROPN
ap-7596	157	7	≤	≤	PROPN
ap-7596	157	8	s.	s.	PROPN
ap-7596	157	9	we	we	PRON
ap-7596	157	10	then	then	ADV
ap-7596	157	11	extract	extract	VERB
ap-7596	157	12	a	a	DET
ap-7596	157	13	maximal	maximal	ADJ
ap-7596	157	14	set	set	NOUN
ap-7596	157	15	of	of	ADP
ap-7596	157	16	independent	independent	ADJ
ap-7596	157	17	polynomial	polynomial	ADJ
ap-7596	157	18	solutions	solution	NOUN
ap-7596	157	19	{	{	PUNCT
ap-7596	157	20	q1	q1	NOUN
ap-7596	157	21	,	,	PUNCT
ap-7596	157	22	.	.	PUNCT
ap-7596	157	23	.	.	PUNCT
ap-7596	158	1	.	.	PUNCT
ap-7596	159	1	,	,	PUNCT
ap-7596	159	2	qp	qp	ADP
ap-7596	159	3	}	}	PUNCT
ap-7596	159	4	of	of	ADP
ap-7596	159	5	(	(	PUNCT
ap-7596	159	6	9	9	NUM
ap-7596	159	7	)	)	PUNCT
ap-7596	159	8	,	,	PUNCT
ap-7596	159	9	which	which	PRON
ap-7596	159	10	in	in	ADP
ap-7596	159	11	the	the	DET
ap-7596	159	12	reductive	reductive	ADJ
ap-7596	159	13	case	case	NOUN
ap-7596	159	14	forms	form	VERB
ap-7596	159	15	an	an	DET
ap-7596	159	16	integrity	integrity	NOUN
ap-7596	159	17	basis	basis	NOUN
ap-7596	159	18	for	for	ADP
ap-7596	159	19	the	the	DET
ap-7596	159	20	solutions	solution	NOUN
ap-7596	159	21	.	.	PUNCT
ap-7596	160	1	symmetrizing	symmetrize	VERB
ap-7596	160	2	these	these	DET
ap-7596	160	3	functions	function	NOUN
ap-7596	160	4	we	we	PRON
ap-7596	160	5	obtain	obtain	VERB
ap-7596	160	6	elements	element	NOUN
ap-7596	160	7	mj	mj	VERB
ap-7596	160	8	in	in	ADP
ap-7596	160	9	the	the	DET
ap-7596	160	10	commutant	commutant	NOUN
ap-7596	160	11	cu(g)(h	cu(g)(h	NUM
ap-7596	160	12	)	)	PUNCT
ap-7596	160	13	.	.	PUNCT
ap-7596	161	1	starting	start	VERB
ap-7596	161	2	from	from	ADP
ap-7596	161	3	the	the	DET
ap-7596	161	4	set	set	NOUN
ap-7596	161	5	of	of	ADP
ap-7596	161	6	polynomials	polynomial	NOUN
ap-7596	161	7	s	s	AUX
ap-7596	161	8	=	=	PUNCT
ap-7596	161	9	{	{	PUNCT
ap-7596	161	10	h	h	NOUN
ap-7596	161	11	,	,	PUNCT
ap-7596	161	12	m1	m1	PROPN
ap-7596	161	13	,	,	PUNCT
ap-7596	161	14	.	.	PUNCT
ap-7596	161	15	.	.	PUNCT
ap-7596	162	1	.	.	PUNCT
ap-7596	163	1	,	,	PUNCT
ap-7596	163	2	mp	mp	PROPN
ap-7596	163	3	}	}	PUNCT
ap-7596	163	4	,	,	PUNCT
ap-7596	163	5	we	we	PRON
ap-7596	163	6	inspect	inspect	VERB
ap-7596	163	7	their	their	PRON
ap-7596	163	8	commutators	commutator	NOUN
ap-7596	163	9	and	and	CCONJ
ap-7596	163	10	determine	determine	VERB
ap-7596	163	11	whether	whether	SCONJ
ap-7596	163	12	,	,	PUNCT
ap-7596	163	13	either	either	CCONJ
ap-7596	163	14	adjoining	adjoin	VERB
ap-7596	163	15	new	new	ADJ
ap-7596	163	16	(	(	PUNCT
ap-7596	163	17	dependent	dependent	ADJ
ap-7596	163	18	)	)	PUNCT
ap-7596	163	19	elements	element	NOUN
ap-7596	163	20	to	to	ADP
ap-7596	163	21	s	s	PRON
ap-7596	163	22	or	or	CCONJ
ap-7596	163	23	discarding	discard	VERB
ap-7596	163	24	some	some	DET
ap-7596	163	25	elements	element	NOUN
ap-7596	163	26	of	of	ADP
ap-7596	163	27	s	s	PROPN
ap-7596	163	28	,	,	PUNCT
ap-7596	163	29	a	a	DET
ap-7596	163	30	finite	finite	ADJ
ap-7596	163	31	-	-	ADJ
ap-7596	163	32	dimensional	dimensional	ADJ
ap-7596	163	33	quadratic	quadratic	ADJ
ap-7596	163	34	algebra	algebra	NOUN
ap-7596	163	35	a	a	PRON
ap-7596	163	36	can	can	AUX
ap-7596	163	37	be	be	AUX
ap-7596	163	38	found	find	VERB
ap-7596	163	39	.	.	PUNCT
ap-7596	164	1	although	although	SCONJ
ap-7596	164	2	there	there	PRON
ap-7596	164	3	is	be	VERB
ap-7596	164	4	some	some	DET
ap-7596	164	5	ambiguity	ambiguity	NOUN
ap-7596	164	6	in	in	ADP
ap-7596	164	7	the	the	DET
ap-7596	164	8	construction	construction	NOUN
ap-7596	164	9	,	,	PUNCT
ap-7596	164	10	as	as	SCONJ
ap-7596	164	11	there	there	PRON
ap-7596	164	12	is	be	VERB
ap-7596	164	13	no	no	DET
ap-7596	164	14	quadratic	quadratic	ADJ
ap-7596	164	15	algebra	algebra	NOUN
ap-7596	164	16	“	"	PUNCT
ap-7596	164	17	canonically	canonically	ADV
ap-7596	164	18	"	"	PUNCT
ap-7596	164	19	associated	associate	VERB
ap-7596	164	20	to	to	ADP
ap-7596	164	21	the	the	DET
ap-7596	164	22	reduction	reduction	NOUN
ap-7596	164	23	chain	chain	NOUN
ap-7596	164	24	g′	g′	NOUN
ap-7596	164	25	⊂	⊂	PROPN
ap-7596	164	26	g	g	PROPN
ap-7596	164	27	,	,	PUNCT
ap-7596	164	28	it	it	PRON
ap-7596	164	29	provides	provide	VERB
ap-7596	164	30	an	an	DET
ap-7596	164	31	alternative	alternative	ADJ
ap-7596	164	32	method	method	NOUN
ap-7596	164	33	that	that	PRON
ap-7596	164	34	does	do	AUX
ap-7596	164	35	not	not	PART
ap-7596	164	36	require	require	VERB
ap-7596	164	37	a	a	DET
ap-7596	164	38	specific	specific	ADJ
ap-7596	164	39	realization	realization	NOUN
ap-7596	164	40	by	by	ADP
ap-7596	164	41	vector	vector	NOUN
ap-7596	164	42	fields	field	NOUN
ap-7596	164	43	,	,	PUNCT
ap-7596	164	44	as	as	SCONJ
ap-7596	164	45	the	the	DET
ap-7596	164	46	integrability	integrability	NOUN
ap-7596	164	47	condition	condition	NOUN
ap-7596	164	48	is	be	AUX
ap-7596	164	49	guaranteed	guarantee	VERB
ap-7596	164	50	by	by	ADP
ap-7596	164	51	the	the	DET
ap-7596	164	52	commutant	commutant	NOUN
ap-7596	164	53	.	.	PUNCT
ap-7596	165	1	this	this	DET
ap-7596	165	2	ansatz	ansatz	ADJ
ap-7596	165	3	has	have	AUX
ap-7596	165	4	been	be	AUX
ap-7596	165	5	successfully	successfully	ADV
ap-7596	165	6	applied	apply	VERB
ap-7596	165	7	in	in	ADP
ap-7596	165	8	[	[	X
ap-7596	165	9	9	9	NUM
ap-7596	165	10	]	]	PUNCT
ap-7596	165	11	to	to	ADP
ap-7596	165	12	the	the	DET
ap-7596	165	13	enveloping	enveloping	NOUN
ap-7596	165	14	algebra	algebra	NOUN
ap-7596	165	15	of	of	ADP
ap-7596	165	16	the	the	DET
ap-7596	165	17	schrödinger	schrödinger	ADJ
ap-7596	165	18	algebras	algebra	NOUN
ap-7596	165	19	ŝ(n	ŝ(n	NOUN
ap-7596	165	20	)	)	PUNCT
ap-7596	165	21	for	for	ADP
ap-7596	165	22	arbitrary	arbitrary	ADJ
ap-7596	165	23	values	value	NOUN
ap-7596	165	24	of	of	ADP
ap-7596	165	25	n	n	PRON
ap-7596	165	26	≥	≥	NOUN
ap-7596	165	27	1	1	NUM
ap-7596	165	28	and	and	CCONJ
ap-7596	165	29	various	various	ADJ
ap-7596	165	30	choices	choice	NOUN
ap-7596	165	31	of	of	ADP
ap-7596	165	32	algebraic	algebraic	ADJ
ap-7596	165	33	hamiltonian	hamiltonian	NOUN
ap-7596	165	34	,	,	PUNCT
ap-7596	165	35	showing	show	VERB
ap-7596	165	36	that	that	SCONJ
ap-7596	165	37	the	the	DET
ap-7596	165	38	construction	construction	NOUN
ap-7596	165	39	is	be	AUX
ap-7596	165	40	formally	formally	ADV
ap-7596	165	41	of	of	ADP
ap-7596	165	42	use	use	NOUN
ap-7596	165	43	for	for	ADP
ap-7596	165	44	the	the	DET
ap-7596	165	45	analysis	analysis	NOUN
ap-7596	165	46	of	of	ADP
ap-7596	165	47	hidden	hide	VERB
ap-7596	165	48	algebras	algebra	NOUN
ap-7596	165	49	that	that	PRON
ap-7596	165	50	are	be	AUX
ap-7596	165	51	not	not	PART
ap-7596	165	52	reductive	reductive	ADJ
ap-7596	165	53	.	.	PUNCT
ap-7596	166	1	4	4	X
ap-7596	166	2	.	.	X
ap-7596	166	3	virtual	virtual	ADJ
ap-7596	166	4	copies	copy	NOUN
ap-7596	166	5	in	in	ADP
ap-7596	166	6	enveloping	envelop	VERB
ap-7596	166	7	algebras	algebra	NOUN
ap-7596	166	8	in	in	ADP
ap-7596	166	9	the	the	DET
ap-7596	166	10	solution	solution	NOUN
ap-7596	166	11	of	of	ADP
ap-7596	166	12	the	the	DET
ap-7596	166	13	embedding	embed	VERB
ap-7596	166	14	problem	problem	NOUN
ap-7596	166	15	into	into	ADP
ap-7596	166	16	enveloping	envelop	VERB
ap-7596	166	17	algebras	algebra	NOUN
ap-7596	166	18	for	for	ADP
ap-7596	166	19	semisimple	semisimple	NOUN
ap-7596	166	20	algebras	algebra	NOUN
ap-7596	166	21	,	,	PUNCT
ap-7596	166	22	the	the	DET
ap-7596	166	23	vanishing	vanishing	NOUN
ap-7596	166	24	of	of	ADP
ap-7596	166	25	the	the	DET
ap-7596	166	26	first	first	ADJ
ap-7596	166	27	cohomology	cohomology	NOUN
ap-7596	166	28	group	group	NOUN
ap-7596	166	29	with	with	ADP
ap-7596	166	30	values	value	NOUN
ap-7596	166	31	in	in	ADP
ap-7596	166	32	u(g	u(g	NOUN
ap-7596	166	33	)	)	PUNCT
ap-7596	166	34	plays	play	VERB
ap-7596	166	35	an	an	DET
ap-7596	166	36	important	important	ADJ
ap-7596	166	37	role	role	NOUN
ap-7596	166	38	,	,	PUNCT
ap-7596	166	39	as	as	SCONJ
ap-7596	166	40	it	it	PRON
ap-7596	166	41	allows	allow	VERB
ap-7596	166	42	to	to	PART
ap-7596	166	43	provide	provide	VERB
ap-7596	166	44	a	a	DET
ap-7596	166	45	general	general	ADJ
ap-7596	166	46	solution	solution	NOUN
ap-7596	166	47	for	for	ADP
ap-7596	166	48	the	the	DET
ap-7596	166	49	perturbation	perturbation	NOUN
ap-7596	166	50	problem	problem	NOUN
ap-7596	167	1	[	[	X
ap-7596	167	2	16	16	NUM
ap-7596	167	3	]	]	PUNCT
ap-7596	167	4	.	.	PUNCT
ap-7596	168	1	for	for	ADP
ap-7596	168	2	nonsemisimple	nonsemisimple	ADJ
ap-7596	168	3	lie	lie	NOUN
ap-7596	168	4	algebras	algebra	NOUN
ap-7596	168	5	,	,	PUNCT
ap-7596	168	6	the	the	DET
ap-7596	168	7	application	application	NOUN
ap-7596	168	8	of	of	ADP
ap-7596	168	9	the	the	DET
ap-7596	168	10	procedure	procedure	NOUN
ap-7596	168	11	is	be	AUX
ap-7596	168	12	quite	quite	ADV
ap-7596	168	13	complicated	complicated	ADJ
ap-7596	168	14	for	for	ADP
ap-7596	168	15	both	both	DET
ap-7596	168	16	computational	computational	ADJ
ap-7596	168	17	reasons	reason	NOUN
ap-7596	168	18	and	and	CCONJ
ap-7596	168	19	the	the	DET
ap-7596	168	20	currently	currently	ADV
ap-7596	168	21	incomplete	incomplete	ADJ
ap-7596	168	22	understanding	understanding	NOUN
ap-7596	168	23	of	of	ADP
ap-7596	168	24	the	the	DET
ap-7596	168	25	precise	precise	ADJ
ap-7596	168	26	structure	structure	NOUN
ap-7596	168	27	of	of	ADP
ap-7596	168	28	the	the	DET
ap-7596	168	29	corresponding	corresponding	ADJ
ap-7596	168	30	enveloping	enveloping	NOUN
ap-7596	168	31	algebras	algebra	NOUN
ap-7596	168	32	.	.	PUNCT
ap-7596	169	1	however	however	ADV
ap-7596	169	2	,	,	PUNCT
ap-7596	169	3	for	for	ADP
ap-7596	169	4	certain	certain	ADJ
ap-7596	169	5	types	type	NOUN
ap-7596	169	6	of	of	ADP
ap-7596	169	7	semidirect	semidirect	NOUN
ap-7596	169	8	sums	sum	NOUN
ap-7596	169	9	of	of	ADP
ap-7596	169	10	simple	simple	ADJ
ap-7596	169	11	and	and	CCONJ
ap-7596	169	12	solvable	solvable	ADJ
ap-7596	169	13	lie	lie	NOUN
ap-7596	169	14	algebras	algebra	NOUN
ap-7596	169	15	,	,	PUNCT
ap-7596	169	16	some	some	DET
ap-7596	169	17	analogous	analogous	ADJ
ap-7596	169	18	statements	statement	NOUN
ap-7596	169	19	may	may	AUX
ap-7596	169	20	be	be	AUX
ap-7596	169	21	proposed	propose	VERB
ap-7596	169	22	,	,	PUNCT
ap-7596	169	23	providing	provide	VERB
ap-7596	169	24	copies	copy	NOUN
ap-7596	169	25	of	of	ADP
ap-7596	169	26	semisimple	semisimple	NOUN
ap-7596	169	27	lie	lie	NOUN
ap-7596	169	28	algebras	algebra	NOUN
ap-7596	169	29	in	in	ADP
ap-7596	169	30	the	the	DET
ap-7596	169	31	enveloping	enveloping	NOUN
ap-7596	169	32	algebra	algebra	NOUN
ap-7596	169	33	of	of	ADP
ap-7596	169	34	a	a	DET
ap-7596	169	35	semidirect	semidirect	NOUN
ap-7596	169	36	sum	sum	NOUN
ap-7596	169	37	,	,	PUNCT
ap-7596	169	38	up	up	ADP
ap-7596	169	39	to	to	ADP
ap-7596	169	40	a	a	DET
ap-7596	169	41	polynomial	polynomial	ADJ
ap-7596	169	42	factor	factor	NOUN
ap-7596	169	43	.	.	PUNCT
ap-7596	170	1	supposed	suppose	VERB
ap-7596	170	2	that	that	PRON
ap-7596	170	3	s	s	VERB
ap-7596	170	4	is	be	AUX
ap-7596	170	5	the	the	DET
ap-7596	170	6	levi	levi	PROPN
ap-7596	170	7	subalgebra	subalgebra	NOUN
ap-7596	170	8	of	of	ADP
ap-7596	170	9	a	a	DET
ap-7596	170	10	semidirect	semidirect	NOUN
ap-7596	170	11	sum	sum	NOUN
ap-7596	170	12	g	g	PROPN
ap-7596	170	13	=	=	SYM
ap-7596	170	14	s	s	NOUN
ap-7596	170	15	−→⊕γr	−→⊕γr	NOUN
ap-7596	170	16	,	,	PUNCT
ap-7596	170	17	we	we	PRON
ap-7596	170	18	seek	seek	VERB
ap-7596	170	19	for	for	ADP
ap-7596	170	20	elements	element	NOUN
ap-7596	170	21	of	of	ADP
ap-7596	170	22	degree	degree	NOUN
ap-7596	170	23	d	d	X
ap-7596	170	24	≥	≥	NUM
ap-7596	170	25	2	2	NUM
ap-7596	170	26	in	in	ADP
ap-7596	170	27	the	the	DET
ap-7596	170	28	generators	generator	NOUN
ap-7596	170	29	in	in	ADP
ap-7596	170	30	u(g	u(g	ADJ
ap-7596	170	31	)	)	PUNCT
ap-7596	170	32	that	that	PRON
ap-7596	170	33	transform	transform	VERB
ap-7596	170	34	according	accord	VERB
ap-7596	170	35	to	to	ADP
ap-7596	170	36	the	the	DET
ap-7596	170	37	structure	structure	NOUN
ap-7596	170	38	tensor	tensor	NOUN
ap-7596	170	39	of	of	ADP
ap-7596	170	40	s	s	PROPN
ap-7596	170	41	,	,	PUNCT
ap-7596	170	42	up	up	ADP
ap-7596	170	43	to	to	ADP
ap-7596	170	44	a	a	DET
ap-7596	170	45	(	(	PUNCT
ap-7596	170	46	polynomial	polynomial	ADJ
ap-7596	170	47	)	)	PUNCT
ap-7596	170	48	factor	factor	NOUN
ap-7596	170	49	.	.	PUNCT
ap-7596	171	1	the	the	DET
ap-7596	171	2	procedure	procedure	NOUN
ap-7596	171	3	can	can	AUX
ap-7596	171	4	be	be	AUX
ap-7596	171	5	summarized	summarize	VERB
ap-7596	171	6	as	as	SCONJ
ap-7596	171	7	follows	follow	VERB
ap-7596	171	8	:	:	PUNCT
ap-7596	171	9	consider	consider	VERB
ap-7596	171	10	a	a	DET
ap-7596	171	11	basis	basis	NOUN
ap-7596	171	12	{	{	PUNCT
ap-7596	171	13	x1	x1	PROPN
ap-7596	171	14	,	,	PUNCT
ap-7596	171	15	.	.	PUNCT
ap-7596	171	16	.	.	PUNCT
ap-7596	172	1	.	.	PUNCT
ap-7596	173	1	,	,	PUNCT
ap-7596	173	2	xn	xn	X
ap-7596	173	3	}	}	PUNCT
ap-7596	173	4	of	of	ADP
ap-7596	173	5	s	s	PRON
ap-7596	173	6	with	with	ADP
ap-7596	173	7	commmutators	commmutator	NOUN
ap-7596	173	8	[	[	X
ap-7596	173	9	xi	xi	X
ap-7596	173	10	,	,	PUNCT
ap-7596	173	11	xj	xj	X
ap-7596	173	12	]	]	PUNCT
ap-7596	174	1	=	=	SYM
ap-7596	174	2	ck	ck	PROPN
ap-7596	174	3	ijxk	ijxk	PROPN
ap-7596	174	4	.	.	PUNCT
ap-7596	175	1	(	(	PUNCT
ap-7596	175	2	12	12	NUM
ap-7596	175	3	)	)	PUNCT
ap-7596	175	4	and	and	CCONJ
ap-7596	175	5	extend	extend	VERB
ap-7596	175	6	it	it	PRON
ap-7596	175	7	to	to	ADP
ap-7596	175	8	a	a	DET
ap-7596	175	9	basis	basis	NOUN
ap-7596	175	10	{	{	PUNCT
ap-7596	175	11	x1	x1	PROPN
ap-7596	175	12	,	,	PUNCT
ap-7596	175	13	.	.	PUNCT
ap-7596	175	14	.	.	PUNCT
ap-7596	175	15	.	.	PUNCT
ap-7596	176	1	,	,	PUNCT
ap-7596	176	2	xn	xn	PROPN
ap-7596	176	3	,	,	PUNCT
ap-7596	176	4	y1	y1	NOUN
ap-7596	176	5	,	,	PUNCT
ap-7596	176	6	.	.	PUNCT
ap-7596	176	7	.	.	PUNCT
ap-7596	177	1	.	.	PUNCT
ap-7596	178	1	,	,	PUNCT
ap-7596	178	2	ym	ym	NOUN
ap-7596	178	3	}	}	PUNCT
ap-7596	178	4	of	of	ADP
ap-7596	178	5	of	of	ADP
ap-7596	178	6	the	the	DET
ap-7596	178	7	semidirect	semidirect	NOUN
ap-7596	178	8	sum	sum	NOUN
ap-7596	178	9	g.	g.	NOUN
ap-7596	178	10	we	we	PRON
ap-7596	178	11	now	now	ADV
ap-7596	178	12	define	define	VERB
ap-7596	178	13	operators	operator	NOUN
ap-7596	178	14	x	x	PUNCT
ap-7596	179	1	′	′	NUM
ap-7596	180	1	i	i	PRON
ap-7596	180	2	=	=	SYM
ap-7596	180	3	xi	xi	PROPN
ap-7596	180	4	r	r	PROPN
ap-7596	180	5	(	(	PUNCT
ap-7596	180	6	y1	y1	PROPN
ap-7596	180	7	,	,	PUNCT
ap-7596	180	8	.	.	PUNCT
ap-7596	180	9	.	.	PUNCT
ap-7596	180	10	.	.	PUNCT
ap-7596	181	1	,	,	PUNCT
ap-7596	181	2	ym	ym	PROPN
ap-7596	181	3	)	)	PUNCT
ap-7596	182	1	+	+	NUM
ap-7596	182	2	pi	pi	NOUN
ap-7596	182	3	(	(	PUNCT
ap-7596	182	4	y1	y1	INTJ
ap-7596	182	5	,	,	PUNCT
ap-7596	182	6	.	.	PUNCT
ap-7596	182	7	.	.	PUNCT
ap-7596	183	1	.	.	PUNCT
ap-7596	184	1	,	,	PUNCT
ap-7596	184	2	ym	ym	PROPN
ap-7596	184	3	)	)	PUNCT
ap-7596	184	4	(	(	PUNCT
ap-7596	184	5	13	13	NUM
ap-7596	184	6	)	)	PUNCT
ap-7596	184	7	in	in	ADP
ap-7596	184	8	u(g	u(g	PROPN
ap-7596	184	9	)	)	PUNCT
ap-7596	184	10	,	,	PUNCT
ap-7596	184	11	where	where	SCONJ
ap-7596	184	12	pi	pi	NOUN
ap-7596	184	13	and	and	CCONJ
ap-7596	184	14	r	r	NOUN
ap-7596	184	15	are	be	AUX
ap-7596	184	16	still	still	ADV
ap-7596	184	17	undetermined	undetermined	ADJ
ap-7596	184	18	polynomials	polynomial	NOUN
ap-7596	184	19	.	.	PUNCT
ap-7596	185	1	in	in	ADP
ap-7596	185	2	order	order	NOUN
ap-7596	185	3	to	to	PART
ap-7596	185	4	simplify	simplify	VERB
ap-7596	185	5	computations	computation	NOUN
ap-7596	185	6	,	,	PUNCT
ap-7596	185	7	they	they	PRON
ap-7596	185	8	can	can	AUX
ap-7596	185	9	be	be	AUX
ap-7596	185	10	considered	consider	VERB
ap-7596	185	11	as	as	ADP
ap-7596	185	12	homogeneous	homogeneous	ADJ
ap-7596	185	13	polynomials	polynomial	NOUN
ap-7596	185	14	of	of	ADP
ap-7596	185	15	degrees	degree	NOUN
ap-7596	185	16	k	k	PROPN
ap-7596	185	17	and	and	CCONJ
ap-7596	185	18	k	k	PROPN
ap-7596	185	19	−1	−1	NOUN
ap-7596	185	20	respectively	respectively	ADV
ap-7596	185	21	,	,	PUNCT
ap-7596	185	22	so	so	SCONJ
ap-7596	185	23	that	that	SCONJ
ap-7596	185	24	x	x	X
ap-7596	186	1	′	′	NOUN
ap-7596	186	2	i	i	PRON
ap-7596	186	3	is	be	AUX
ap-7596	186	4	homogeneous	homogeneous	ADJ
ap-7596	186	5	of	of	ADP
ap-7596	186	6	degree	degree	NOUN
ap-7596	186	7	k.	k.	PROPN
ap-7596	187	1	we	we	PRON
ap-7596	187	2	require	require	VERB
ap-7596	187	3	that	that	SCONJ
ap-7596	187	4	these	these	DET
ap-7596	187	5	operators	operator	NOUN
ap-7596	187	6	commute	commute	VERB
ap-7596	187	7	with	with	ADP
ap-7596	187	8	the	the	DET
ap-7596	187	9	generators	generator	NOUN
ap-7596	187	10	yk	yk	PROPN
ap-7596	187	11	of	of	ADP
ap-7596	187	12	the	the	DET
ap-7596	187	13	radical	radical	ADJ
ap-7596	187	14	r	r	NOUN
ap-7596	187	15	,	,	PUNCT
ap-7596	187	16	so	so	SCONJ
ap-7596	187	17	that	that	SCONJ
ap-7596	187	18	the	the	DET
ap-7596	187	19	identity	identity	NOUN
ap-7596	187	20	[	[	X
ap-7596	187	21	x	x	X
ap-7596	187	22	′	′	NUM
ap-7596	187	23	i	i	PRON
ap-7596	187	24	,	,	PUNCT
ap-7596	187	25	yj	yj	PROPN
ap-7596	187	26	]	]	X
ap-7596	187	27	=	=	SYM
ap-7596	187	28	0	0	NUM
ap-7596	187	29	,	,	PUNCT
ap-7596	187	30	1	1	NUM
ap-7596	187	31	≤	≤	NUM
ap-7596	187	32	i	i	PRON
ap-7596	187	33	≤	≤	PROPN
ap-7596	187	34	n	n	CCONJ
ap-7596	187	35	,	,	PUNCT
ap-7596	187	36	1	1	NUM
ap-7596	187	37	≤	≤	NUM
ap-7596	187	38	j	j	PROPN
ap-7596	187	39	≤	≤	NOUN
ap-7596	187	40	m	m	VERB
ap-7596	187	41	is	be	AUX
ap-7596	187	42	satisfied	satisfied	ADJ
ap-7596	187	43	for	for	ADP
ap-7596	187	44	all	all	DET
ap-7596	187	45	indices	index	NOUN
ap-7596	187	46	.	.	PUNCT
ap-7596	188	1	expanding	expand	VERB
ap-7596	188	2	the	the	DET
ap-7596	188	3	latter	latter	ADJ
ap-7596	188	4	leads	lead	VERB
ap-7596	188	5	to	to	ADP
ap-7596	188	6	the	the	DET
ap-7596	188	7	expression	expression	NOUN
ap-7596	189	1	[	[	X
ap-7596	189	2	x	x	X
ap-7596	189	3	′	′	NUM
ap-7596	189	4	i	i	PRON
ap-7596	189	5	,	,	PUNCT
ap-7596	189	6	yj	yj	PROPN
ap-7596	189	7	]	]	PUNCT
ap-7596	189	8	=	=	PUNCT
ap-7596	190	1	[	[	X
ap-7596	190	2	xir	xir	PROPN
ap-7596	190	3	,	,	PUNCT
ap-7596	190	4	yj	yj	PROPN
ap-7596	190	5	]	]	PUNCT
ap-7596	190	6	+	+	CCONJ
ap-7596	191	1	[	[	X
ap-7596	191	2	pi	pi	NOUN
ap-7596	191	3	,	,	PUNCT
ap-7596	191	4	yj	yj	PROPN
ap-7596	191	5	]	]	X
ap-7596	192	1	=	=	X
ap-7596	192	2	xi	xi	X
ap-7596	192	3	[	[	X
ap-7596	192	4	r	r	X
ap-7596	192	5	,	,	PUNCT
ap-7596	192	6	yj	yj	X
ap-7596	192	7	]	]	PUNCT
ap-7596	193	1	+	+	CCONJ
ap-7596	193	2	[	[	X
ap-7596	193	3	xi	xi	X
ap-7596	193	4	,	,	PUNCT
ap-7596	193	5	yj	yj	X
ap-7596	193	6	]	]	X
ap-7596	193	7	r	r	NOUN
ap-7596	193	8	+	+	NUM
ap-7596	194	1	[	[	X
ap-7596	194	2	pi	pi	NOUN
ap-7596	194	3	,	,	PUNCT
ap-7596	194	4	yj	yj	PROPN
ap-7596	194	5	]	]	PUNCT
ap-7596	194	6	.	.	PUNCT
ap-7596	195	1	taking	take	VERB
ap-7596	195	2	into	into	ADP
ap-7596	195	3	account	account	NOUN
ap-7596	195	4	the	the	DET
ap-7596	195	5	homogeneity	homogeneity	NOUN
ap-7596	195	6	degree	degree	NOUN
ap-7596	195	7	of	of	ADP
ap-7596	195	8	the	the	DET
ap-7596	195	9	terms	term	NOUN
ap-7596	195	10	with	with	ADP
ap-7596	195	11	respect	respect	NOUN
ap-7596	195	12	to	to	ADP
ap-7596	195	13	the	the	DET
ap-7596	195	14	generators	generator	NOUN
ap-7596	195	15	of	of	ADP
ap-7596	195	16	s	s	PRON
ap-7596	195	17	and	and	CCONJ
ap-7596	195	18	the	the	DET
ap-7596	195	19	representation	representation	NOUN
ap-7596	195	20	space	space	NOUN
ap-7596	195	21	,	,	PUNCT
ap-7596	195	22	it	it	PRON
ap-7596	195	23	follows	follow	VERB
ap-7596	195	24	that	that	PRON
ap-7596	195	25	xi	xi	X
ap-7596	196	1	[	[	X
ap-7596	196	2	r	r	X
ap-7596	196	3	,	,	PUNCT
ap-7596	196	4	yj	yj	PROPN
ap-7596	196	5	]	]	PUNCT
ap-7596	196	6	can	can	AUX
ap-7596	196	7	be	be	AUX
ap-7596	196	8	seen	see	VERB
ap-7596	196	9	as	as	ADP
ap-7596	196	10	a	a	DET
ap-7596	196	11	polynomial	polynomial	NOUN
ap-7596	196	12	of	of	ADP
ap-7596	196	13	degree	degree	NOUN
ap-7596	196	14	(	(	PUNCT
ap-7596	196	15	k	k	NOUN
ap-7596	196	16	−	−	PROPN
ap-7596	196	17	1	1	NUM
ap-7596	196	18	)	)	PUNCT
ap-7596	196	19	in	in	ADP
ap-7596	196	20	the	the	DET
ap-7596	196	21	variables	variable	NOUN
ap-7596	196	22	{	{	PUNCT
ap-7596	196	23	y1	y1	NOUN
ap-7596	196	24	,	,	PUNCT
ap-7596	196	25	.	.	PUNCT
ap-7596	196	26	.	.	PUNCT
ap-7596	197	1	.	.	PUNCT
ap-7596	198	1	,	,	PUNCT
ap-7596	198	2	ym	ym	PROPN
ap-7596	198	3	}	}	PUNCT
ap-7596	198	4	.	.	PUNCT
ap-7596	199	1	on	on	ADP
ap-7596	199	2	the	the	DET
ap-7596	199	3	other	other	ADJ
ap-7596	199	4	hand	hand	NOUN
ap-7596	199	5	the	the	DET
ap-7596	199	6	terms	term	NOUN
ap-7596	199	7	of	of	ADP
ap-7596	199	8	[	[	X
ap-7596	199	9	xi	xi	PROPN
ap-7596	199	10	,	,	PUNCT
ap-7596	199	11	yj	yj	X
ap-7596	199	12	]	]	X
ap-7596	199	13	r	r	NOUN
ap-7596	199	14	+	+	NUM
ap-7596	200	1	[	[	X
ap-7596	200	2	pi	pi	NOUN
ap-7596	200	3	,	,	PUNCT
ap-7596	200	4	yj	yj	PROPN
ap-7596	200	5	]	]	PUNCT
ap-7596	200	6	have	have	VERB
ap-7596	200	7	degree	degree	NOUN
ap-7596	200	8	k	k	NOUN
ap-7596	200	9	,	,	PUNCT
ap-7596	200	10	allowing	allow	VERB
ap-7596	200	11	us	we	PRON
ap-7596	200	12	to	to	PART
ap-7596	200	13	further	far	ADV
ap-7596	200	14	separate	separate	VERB
ap-7596	200	15	the	the	DET
ap-7596	200	16	commutator	commutator	NOUN
ap-7596	200	17	as	as	ADP
ap-7596	200	18	[	[	X
ap-7596	200	19	r	r	X
ap-7596	200	20	,	,	PUNCT
ap-7596	200	21	yj	yj	X
ap-7596	200	22	]	]	X
ap-7596	200	23	=	=	PUNCT
ap-7596	200	24	0	0	NUM
ap-7596	200	25	,	,	PUNCT
ap-7596	200	26	[	[	X
ap-7596	200	27	xi	xi	X
ap-7596	200	28	,	,	PUNCT
ap-7596	200	29	yj	yj	X
ap-7596	200	30	]	]	X
ap-7596	201	1	r	r	NOUN
ap-7596	202	1	+	+	NUM
ap-7596	203	1	[	[	X
ap-7596	203	2	pi	pi	NOUN
ap-7596	203	3	,	,	PUNCT
ap-7596	203	4	yj	yj	PROPN
ap-7596	203	5	]	]	X
ap-7596	203	6	=	=	PUNCT
ap-7596	204	1	0	0	X
ap-7596	204	2	.	.	PUNCT
ap-7596	205	1	(	(	PUNCT
ap-7596	205	2	14	14	NUM
ap-7596	205	3	)	)	PUNCT
ap-7596	205	4	from	from	ADP
ap-7596	205	5	the	the	DET
ap-7596	205	6	first	first	ADJ
ap-7596	205	7	equation	equation	NOUN
ap-7596	205	8	we	we	PRON
ap-7596	205	9	conclude	conclude	VERB
ap-7596	205	10	that	that	SCONJ
ap-7596	205	11	the	the	DET
ap-7596	205	12	factor	factor	NOUN
ap-7596	205	13	r	r	NOUN
ap-7596	205	14	commutes	commute	NOUN
ap-7596	205	15	with	with	ADP
ap-7596	205	16	all	all	DET
ap-7596	205	17	generators	generator	NOUN
ap-7596	205	18	yi	yi	PROPN
ap-7596	205	19	,	,	PUNCT
ap-7596	205	20	thus	thus	ADV
ap-7596	205	21	defines	define	VERB
ap-7596	205	22	an	an	DET
ap-7596	205	23	invariant	invariant	NOUN
ap-7596	205	24	of	of	ADP
ap-7596	205	25	the	the	DET
ap-7596	205	26	solvable	solvable	ADJ
ap-7596	205	27	lie	lie	NOUN
ap-7596	205	28	algebra	algebra	PROPN
ap-7596	205	29	r.	r.	NOUN
ap-7596	205	30	we	we	PRON
ap-7596	205	31	further	far	ADV
ap-7596	205	32	require	require	VERB
ap-7596	205	33	that	that	SCONJ
ap-7596	205	34	the	the	DET
ap-7596	205	35	operators	operator	NOUN
ap-7596	205	36	x	x	PUNCT
ap-7596	205	37	′	′	NOUN
ap-7596	205	38	i	i	PRON
ap-7596	205	39	transform	transform	VERB
ap-7596	205	40	by	by	ADP
ap-7596	205	41	the	the	DET
ap-7596	205	42	action	action	NOUN
ap-7596	205	43	of	of	ADP
ap-7596	205	44	s	s	PRON
ap-7596	205	45	as	as	ADP
ap-7596	205	46	the	the	DET
ap-7596	205	47	generators	generator	NOUN
ap-7596	205	48	of	of	ADP
ap-7596	205	49	the	the	DET
ap-7596	205	50	latter	latter	ADJ
ap-7596	205	51	algebra	algebra	NOUN
ap-7596	205	52	,	,	PUNCT
ap-7596	206	1	i.e.	i.e.	X
ap-7596	206	2	[	[	X
ap-7596	206	3	x	x	X
ap-7596	206	4	′	′	NUM
ap-7596	206	5	i	i	PRON
ap-7596	206	6	,	,	PUNCT
ap-7596	206	7	xj	xj	PROPN
ap-7596	206	8	]	]	PUNCT
ap-7596	207	1	=	=	PUNCT
ap-7596	208	1	[	[	X
ap-7596	208	2	xi	xi	X
ap-7596	208	3	,	,	PUNCT
ap-7596	208	4	xj	xj	PROPN
ap-7596	208	5	]	]	PUNCT
ap-7596	208	6	′	′	NUM
ap-7596	208	7	:	:	PUNCT
ap-7596	209	1	=	=	PUNCT
ap-7596	209	2	ck	ck	INTJ
ap-7596	209	3	ij	ij	INTJ
ap-7596	209	4	(	(	PUNCT
ap-7596	209	5	xkr	xkr	PROPN
ap-7596	209	6	+	+	CCONJ
ap-7596	209	7	pk	pk	NOUN
ap-7596	209	8	)	)	PUNCT
ap-7596	209	9	.	.	PUNCT
ap-7596	210	1	(	(	PUNCT
ap-7596	210	2	15	15	NUM
ap-7596	210	3	)	)	PUNCT
ap-7596	210	4	as	as	SCONJ
ap-7596	210	5	this	this	DET
ap-7596	210	6	relation	relation	NOUN
ap-7596	210	7	must	must	AUX
ap-7596	210	8	hold	hold	VERB
ap-7596	210	9	for	for	ADP
ap-7596	210	10	all	all	DET
ap-7596	210	11	the	the	DET
ap-7596	210	12	generators	generator	NOUN
ap-7596	210	13	of	of	ADP
ap-7596	210	14	the	the	DET
ap-7596	210	15	semidirect	semidirect	NOUN
ap-7596	210	16	sum	sum	NOUN
ap-7596	210	17	g	g	NOUN
ap-7596	210	18	,	,	PUNCT
ap-7596	210	19	further	further	ADJ
ap-7596	210	20	structural	structural	ADJ
ap-7596	210	21	constraints	constraint	NOUN
ap-7596	210	22	on	on	ADP
ap-7596	210	23	the	the	DET
ap-7596	210	24	polynomials	polynomial	NOUN
ap-7596	210	25	r	r	NOUN
ap-7596	210	26	and	and	CCONJ
ap-7596	210	27	pi	pi	NOUN
ap-7596	210	28	are	be	AUX
ap-7596	210	29	obtained	obtain	VERB
ap-7596	210	30	.	.	PUNCT
ap-7596	211	1	expanding	expand	VERB
ap-7596	211	2	the	the	DET
ap-7596	211	3	left	left	ADJ
ap-7596	211	4	-	-	PUNCT
ap-7596	211	5	hand	hand	NOUN
ap-7596	211	6	term	term	NOUN
ap-7596	211	7	of	of	ADP
ap-7596	211	8	condition	condition	NOUN
ap-7596	211	9	(	(	PUNCT
ap-7596	211	10	15	15	NUM
ap-7596	211	11	)	)	PUNCT
ap-7596	211	12	yields	yield	NOUN
ap-7596	212	1	[	[	X
ap-7596	212	2	x	x	X
ap-7596	212	3	′	′	NUM
ap-7596	212	4	i	i	PRON
ap-7596	212	5	,	,	PUNCT
ap-7596	212	6	xj	xj	PROPN
ap-7596	212	7	]	]	PUNCT
ap-7596	213	1	=	=	PUNCT
ap-7596	214	1	[	[	X
ap-7596	214	2	xi	xi	X
ap-7596	214	3	,	,	PUNCT
ap-7596	214	4	xj	xj	X
ap-7596	214	5	]	]	PUNCT
ap-7596	214	6	r	r	NOUN
ap-7596	214	7	−	−	PROPN
ap-7596	214	8	xi	xi	PROPN
ap-7596	215	1	[	[	X
ap-7596	215	2	xj	xj	X
ap-7596	215	3	,	,	PUNCT
ap-7596	215	4	r	r	X
ap-7596	215	5	]	]	PUNCT
ap-7596	215	6	+	+	CCONJ
ap-7596	216	1	[	[	X
ap-7596	216	2	pi	pi	X
ap-7596	216	3	,	,	PUNCT
ap-7596	216	4	xj	xj	PROPN
ap-7596	216	5	]	]	PUNCT
ap-7596	216	6	.	.	PUNCT
ap-7596	217	1	19	19	NUM
ap-7596	217	2	rutwig	rutwig	PROPN
ap-7596	217	3	campoamor	campoamor	NOUN
ap-7596	217	4	-	-	PUNCT
ap-7596	217	5	stursberg	stursberg	PROPN
ap-7596	217	6	acta	acta	PROPN
ap-7596	217	7	polytechnica	polytechnica	PROPN
ap-7596	217	8	as	as	SCONJ
ap-7596	217	9	the	the	DET
ap-7596	217	10	yj	yj	PROPN
ap-7596	217	11	are	be	AUX
ap-7596	217	12	the	the	DET
ap-7596	217	13	generators	generator	NOUN
ap-7596	217	14	of	of	ADP
ap-7596	217	15	the	the	DET
ap-7596	217	16	representation	representation	NOUN
ap-7596	217	17	space	space	NOUN
ap-7596	217	18	γ	γ	PROPN
ap-7596	217	19	,	,	PUNCT
ap-7596	217	20	it	it	PRON
ap-7596	217	21	follows	follow	VERB
ap-7596	217	22	that	that	SCONJ
ap-7596	217	23	the	the	DET
ap-7596	217	24	term	term	NOUN
ap-7596	217	25	[	[	X
ap-7596	217	26	xi	xi	X
ap-7596	217	27	,	,	PUNCT
ap-7596	217	28	xj	xj	X
ap-7596	217	29	]	]	PUNCT
ap-7596	218	1	r	r	NOUN
ap-7596	218	2	−	−	PROPN
ap-7596	218	3	xi	xi	PROPN
ap-7596	219	1	[	[	X
ap-7596	219	2	xj	xj	X
ap-7596	219	3	,	,	PUNCT
ap-7596	219	4	r	r	X
ap-7596	219	5	]	]	X
ap-7596	219	6	is	be	AUX
ap-7596	219	7	linear	linear	ADJ
ap-7596	219	8	in	in	ADP
ap-7596	219	9	the	the	DET
ap-7596	219	10	generators	generator	NOUN
ap-7596	219	11	of	of	ADP
ap-7596	219	12	s	s	PRON
ap-7596	219	13	and	and	CCONJ
ap-7596	219	14	of	of	ADP
ap-7596	219	15	degree	degree	NOUN
ap-7596	219	16	(	(	PUNCT
ap-7596	219	17	k	k	NOUN
ap-7596	219	18	−1	−1	NOUN
ap-7596	219	19	)	)	PUNCT
ap-7596	219	20	in	in	ADP
ap-7596	219	21	the	the	DET
ap-7596	219	22	yj	yj	PROPN
ap-7596	219	23	’s	’s	ADV
ap-7596	219	24	,	,	PUNCT
ap-7596	219	25	while	while	SCONJ
ap-7596	219	26	[	[	X
ap-7596	219	27	pi	pi	X
ap-7596	219	28	,	,	PUNCT
ap-7596	219	29	xj	xj	PROPN
ap-7596	219	30	]	]	PUNCT
ap-7596	219	31	does	do	AUX
ap-7596	219	32	not	not	PART
ap-7596	219	33	involve	involve	VERB
ap-7596	219	34	generators	generator	NOUN
ap-7596	219	35	of	of	ADP
ap-7596	219	36	s.	s.	PROPN
ap-7596	219	37	comparing	compare	VERB
ap-7596	219	38	now	now	ADV
ap-7596	219	39	with	with	ADP
ap-7596	219	40	the	the	DET
ap-7596	219	41	right	right	ADJ
ap-7596	219	42	-	-	PUNCT
ap-7596	219	43	hand	hand	NOUN
ap-7596	219	44	side	side	NOUN
ap-7596	219	45	of	of	ADP
ap-7596	219	46	(	(	PUNCT
ap-7596	219	47	15	15	NUM
ap-7596	219	48	)	)	PUNCT
ap-7596	219	49	,	,	PUNCT
ap-7596	219	50	the	the	DET
ap-7596	219	51	condition	condition	NOUN
ap-7596	219	52	again	again	ADV
ap-7596	219	53	separates	separate	VERB
ap-7596	219	54	into	into	ADP
ap-7596	219	55	two	two	NUM
ap-7596	219	56	parts	part	NOUN
ap-7596	219	57	:	:	PUNCT
ap-7596	220	1	[	[	X
ap-7596	220	2	xi	xi	X
ap-7596	220	3	,	,	PUNCT
ap-7596	220	4	xj	xj	X
ap-7596	220	5	]	]	PUNCT
ap-7596	220	6	r	r	NOUN
ap-7596	220	7	−	−	PROPN
ap-7596	220	8	xi	xi	PROPN
ap-7596	221	1	[	[	X
ap-7596	221	2	xj	xj	X
ap-7596	221	3	,	,	PUNCT
ap-7596	221	4	r	r	X
ap-7596	221	5	]	]	X
ap-7596	221	6	=	=	PUNCT
ap-7596	221	7	ck	ck	PRON
ap-7596	221	8	ijxkr	ijxkr	NOUN
ap-7596	221	9	,	,	PUNCT
ap-7596	221	10	[	[	X
ap-7596	221	11	pi	pi	NOUN
ap-7596	221	12	,	,	PUNCT
ap-7596	221	13	xj	xj	X
ap-7596	221	14	]	]	PUNCT
ap-7596	222	1	=	=	PUNCT
ap-7596	222	2	ck	ck	ADJ
ap-7596	222	3	ijpk	ijpk	NOUN
ap-7596	222	4	.	.	PUNCT
ap-7596	223	1	(	(	PUNCT
ap-7596	223	2	16	16	NUM
ap-7596	223	3	)	)	PUNCT
ap-7596	223	4	simplifying	simplify	VERB
ap-7596	223	5	the	the	DET
ap-7596	223	6	first	first	ADJ
ap-7596	223	7	equations	equation	NOUN
ap-7596	223	8	shows	show	VERB
ap-7596	223	9	that	that	SCONJ
ap-7596	223	10	xi	xi	PROPN
ap-7596	224	1	[	[	X
ap-7596	224	2	xj	xj	X
ap-7596	224	3	,	,	PUNCT
ap-7596	224	4	r	r	X
ap-7596	224	5	]	]	X
ap-7596	224	6	=	=	SYM
ap-7596	224	7	0	0	NUM
ap-7596	224	8	,	,	PUNCT
ap-7596	224	9	hence	hence	ADV
ap-7596	224	10	implying	imply	VERB
ap-7596	224	11	that	that	SCONJ
ap-7596	224	12	r	r	NOUN
ap-7596	224	13	also	also	ADV
ap-7596	224	14	commutes	commute	VERB
ap-7596	224	15	with	with	ADP
ap-7596	224	16	the	the	DET
ap-7596	224	17	generators	generator	NOUN
ap-7596	224	18	of	of	ADP
ap-7596	224	19	the	the	DET
ap-7596	224	20	lie	lie	NOUN
ap-7596	224	21	algebra	algebra	NOUN
ap-7596	224	22	.	.	PUNCT
ap-7596	225	1	as	as	SCONJ
ap-7596	225	2	r	r	NOUN
ap-7596	225	3	corresponds	correspond	VERB
ap-7596	225	4	simultaneously	simultaneously	ADV
ap-7596	225	5	to	to	ADP
ap-7596	225	6	an	an	DET
ap-7596	225	7	invariant	invariant	ADJ
ap-7596	225	8	polynomial	polynomial	NOUN
ap-7596	225	9	of	of	ADP
ap-7596	225	10	the	the	DET
ap-7596	225	11	radical	radical	NOUN
ap-7596	225	12	,	,	PUNCT
ap-7596	225	13	it	it	PRON
ap-7596	225	14	must	must	AUX
ap-7596	225	15	correspond	correspond	VERB
ap-7596	225	16	to	to	ADP
ap-7596	225	17	an	an	DET
ap-7596	225	18	invariant	invariant	NOUN
ap-7596	225	19	of	of	ADP
ap-7596	225	20	g	g	PROPN
ap-7596	225	21	that	that	PRON
ap-7596	225	22	depends	depend	VERB
ap-7596	225	23	only	only	ADV
ap-7596	225	24	on	on	ADP
ap-7596	225	25	the	the	DET
ap-7596	225	26	generators	generator	NOUN
ap-7596	225	27	of	of	ADP
ap-7596	225	28	its	its	PRON
ap-7596	225	29	maximal	maximal	ADJ
ap-7596	225	30	solvable	solvable	NOUN
ap-7596	225	31	ideal.2	ideal.2	PROPN
ap-7596	225	32	the	the	DET
ap-7596	225	33	second	second	ADJ
ap-7596	225	34	equation	equation	NOUN
ap-7596	225	35	shows	show	VERB
ap-7596	225	36	that	that	SCONJ
ap-7596	225	37	the	the	DET
ap-7596	225	38	polynomials	polynomial	NOUN
ap-7596	225	39	pi	pi	NOUN
ap-7596	225	40	transform	transform	VERB
ap-7596	225	41	according	accord	VERB
ap-7596	225	42	to	to	ADP
ap-7596	225	43	the	the	DET
ap-7596	225	44	adjoint	adjoint	NOUN
ap-7596	225	45	representation	representation	NOUN
ap-7596	225	46	of	of	ADP
ap-7596	225	47	the	the	DET
ap-7596	225	48	semisimple	semisimple	NOUN
ap-7596	225	49	lie	lie	NOUN
ap-7596	225	50	algebra	algebra	NOUN
ap-7596	225	51	s.	s.	PROPN
ap-7596	225	52	supposed	suppose	VERB
ap-7596	225	53	that	that	SCONJ
ap-7596	225	54	all	all	DET
ap-7596	225	55	the	the	DET
ap-7596	225	56	conditions	condition	NOUN
ap-7596	225	57	are	be	AUX
ap-7596	225	58	satisfied	satisfied	ADJ
ap-7596	225	59	,	,	PUNCT
ap-7596	225	60	we	we	PRON
ap-7596	225	61	obtain	obtain	VERB
ap-7596	225	62	the	the	DET
ap-7596	225	63	commutators	commutator	NOUN
ap-7596	225	64	of	of	ADP
ap-7596	225	65	the	the	DET
ap-7596	225	66	operators	operator	NOUN
ap-7596	225	67	x	x	PUNCT
ap-7596	226	1	′	′	NUM
ap-7596	226	2	i	i	PRON
ap-7596	226	3	in	in	ADP
ap-7596	226	4	the	the	DET
ap-7596	226	5	enveloping	enveloping	NOUN
ap-7596	226	6	algebra	algebra	NOUN
ap-7596	226	7	u(g	u(g	ADP
ap-7596	226	8	)	)	PUNCT
ap-7596	226	9	as	as	ADP
ap-7596	226	10	[	[	PUNCT
ap-7596	226	11	x	x	X
ap-7596	226	12	′	′	NUM
ap-7596	226	13	i	i	PRON
ap-7596	226	14	,	,	PUNCT
ap-7596	226	15	x	x	PUNCT
ap-7596	226	16	′	′	NUM
ap-7596	226	17	j	j	NOUN
ap-7596	226	18	]	]	X
ap-7596	227	1	=	=	PUNCT
ap-7596	228	1	[	[	X
ap-7596	228	2	xir	xir	NOUN
ap-7596	228	3	+	+	CCONJ
ap-7596	228	4	pi	pi	PROPN
ap-7596	228	5	,	,	PUNCT
ap-7596	228	6	xjr	xjr	PROPN
ap-7596	229	1	+	+	CCONJ
ap-7596	229	2	pj	pj	PROPN
ap-7596	229	3	]	]	PUNCT
ap-7596	230	1	=	=	PUNCT
ap-7596	231	1	[	[	X
ap-7596	231	2	xir	xir	NOUN
ap-7596	231	3	+	+	CCONJ
ap-7596	231	4	pi	pi	PROPN
ap-7596	231	5	,	,	PUNCT
ap-7596	231	6	xjr	xjr	PROPN
ap-7596	231	7	]	]	PUNCT
ap-7596	232	1	+	+	CCONJ
ap-7596	233	1	[	[	X
ap-7596	233	2	xir	xir	NOUN
ap-7596	233	3	+	+	CCONJ
ap-7596	233	4	pi	pi	PROPN
ap-7596	233	5	,	,	PUNCT
ap-7596	233	6	pj	pj	PROPN
ap-7596	233	7	]	]	PUNCT
ap-7596	233	8	=	=	PUNCT
ap-7596	233	9	ck	ck	ADJ
ap-7596	233	10	ijxkr2	ijxkr2	NOUN
ap-7596	233	11	+	+	CCONJ
ap-7596	233	12	ck	ck	PRON
ap-7596	233	13	ijpkr	ijpkr	NOUN
ap-7596	234	1	+	+	X
ap-7596	235	1	[	[	X
ap-7596	235	2	x	x	X
ap-7596	235	3	′	′	NUM
ap-7596	235	4	i	i	PRON
ap-7596	235	5	,	,	PUNCT
ap-7596	235	6	pj	pj	PROPN
ap-7596	235	7	]	]	PUNCT
ap-7596	235	8	.	.	PUNCT
ap-7596	236	1	(	(	PUNCT
ap-7596	236	2	17	17	NUM
ap-7596	236	3	)	)	PUNCT
ap-7596	236	4	as	as	ADP
ap-7596	236	5	the	the	PRON
ap-7596	236	6	x	x	NOUN
ap-7596	236	7	′	′	NUM
ap-7596	237	1	i	i	PRON
ap-7596	237	2	commute	commute	VERB
ap-7596	237	3	with	with	ADP
ap-7596	237	4	the	the	DET
ap-7596	237	5	yj	yj	PROPN
ap-7596	237	6	,	,	PUNCT
ap-7596	237	7	it	it	PRON
ap-7596	237	8	follows	follow	VERB
ap-7596	237	9	from	from	ADP
ap-7596	237	10	equation	equation	NOUN
ap-7596	237	11	(	(	PUNCT
ap-7596	237	12	17	17	NUM
ap-7596	237	13	)	)	PUNCT
ap-7596	237	14	that	that	SCONJ
ap-7596	238	1	[	[	X
ap-7596	238	2	x	x	X
ap-7596	238	3	′	′	NUM
ap-7596	238	4	i	i	PRON
ap-7596	238	5	,	,	PUNCT
ap-7596	238	6	pj	pj	PROPN
ap-7596	238	7	]	]	PUNCT
ap-7596	238	8	=	=	SYM
ap-7596	238	9	0	0	PUNCT
ap-7596	238	10	and	and	CCONJ
ap-7596	238	11	therefore	therefore	ADV
ap-7596	238	12	that	that	SCONJ
ap-7596	238	13	[	[	PUNCT
ap-7596	238	14	x	x	SYM
ap-7596	238	15	′	′	NUM
ap-7596	239	1	i	i	PRON
ap-7596	239	2	,	,	PUNCT
ap-7596	239	3	x	x	PUNCT
ap-7596	239	4	′	′	NUM
ap-7596	239	5	j	j	NOUN
ap-7596	239	6	]	]	X
ap-7596	240	1	=	=	PUNCT
ap-7596	241	1	[	[	X
ap-7596	241	2	xi	xi	X
ap-7596	241	3	,	,	PUNCT
ap-7596	241	4	xj	xj	PROPN
ap-7596	241	5	]	]	PUNCT
ap-7596	241	6	′	′	NUM
ap-7596	241	7	r	r	NOUN
ap-7596	241	8	,	,	PUNCT
ap-7596	241	9	showing	show	VERB
ap-7596	241	10	that	that	SCONJ
ap-7596	241	11	the	the	DET
ap-7596	241	12	operators	operator	NOUN
ap-7596	241	13	reproduce	reproduce	VERB
ap-7596	241	14	the	the	DET
ap-7596	241	15	commutators	commutator	NOUN
ap-7596	241	16	of	of	ADP
ap-7596	241	17	s	s	PROPN
ap-7596	241	18	,	,	PUNCT
ap-7596	241	19	up	up	ADP
ap-7596	241	20	to	to	ADP
ap-7596	241	21	the	the	DET
ap-7596	241	22	invariant	invariant	ADJ
ap-7596	241	23	factor	factor	NOUN
ap-7596	241	24	r.	r.	NOUN
ap-7596	241	25	it	it	PRON
ap-7596	241	26	should	should	AUX
ap-7596	241	27	be	be	AUX
ap-7596	241	28	emphasized	emphasize	VERB
ap-7596	241	29	that	that	SCONJ
ap-7596	241	30	r	r	NOUN
ap-7596	241	31	is	be	AUX
ap-7596	241	32	not	not	PART
ap-7596	241	33	necessarily	necessarily	ADV
ap-7596	241	34	a	a	DET
ap-7596	241	35	central	central	ADJ
ap-7596	241	36	element	element	NOUN
ap-7596	241	37	,	,	PUNCT
ap-7596	241	38	but	but	CCONJ
ap-7596	241	39	an	an	DET
ap-7596	241	40	invariant	invariant	NOUN
ap-7596	241	41	of	of	ADP
ap-7596	241	42	g	g	PROPN
ap-7596	241	43	that	that	PRON
ap-7596	241	44	solely	solely	ADV
ap-7596	241	45	depends	depend	VERB
ap-7596	241	46	on	on	ADP
ap-7596	241	47	the	the	DET
ap-7596	241	48	generators	generator	NOUN
ap-7596	241	49	of	of	ADP
ap-7596	241	50	the	the	DET
ap-7596	241	51	characteristic	characteristic	ADJ
ap-7596	241	52	representation	representation	NOUN
ap-7596	241	53	γ	γ	X
ap-7596	241	54	.	.	PUNCT
ap-7596	242	1	it	it	PRON
ap-7596	242	2	follows	follow	VERB
ap-7596	242	3	in	in	ADP
ap-7596	242	4	particular	particular	ADJ
ap-7596	242	5	from	from	ADP
ap-7596	242	6	this	this	DET
ap-7596	242	7	construction	construction	NOUN
ap-7596	242	8	that	that	SCONJ
ap-7596	242	9	the	the	DET
ap-7596	242	10	operators	operator	NOUN
ap-7596	242	11	{	{	PUNCT
ap-7596	242	12	r	r	NOUN
ap-7596	242	13	,	,	PUNCT
ap-7596	242	14	x	x	NOUN
ap-7596	242	15	′	′	NUM
ap-7596	242	16	1	1	NUM
ap-7596	242	17	,	,	PUNCT
ap-7596	242	18	.	.	PUNCT
ap-7596	242	19	.	.	PUNCT
ap-7596	242	20	.	.	PUNCT
ap-7596	243	1	,	,	PUNCT
ap-7596	243	2	x	x	X
ap-7596	243	3	′	′	NOUN
ap-7596	243	4	n	n	CCONJ
ap-7596	243	5	}	}	PUNCT
ap-7596	243	6	generate	generate	VERB
ap-7596	243	7	a	a	DET
ap-7596	243	8	finite	finite	ADJ
ap-7596	243	9	dimensional	dimensional	ADJ
ap-7596	243	10	quadratic	quadratic	ADJ
ap-7596	243	11	algebra	algebra	NOUN
ap-7596	243	12	a	a	PRON
ap-7596	243	13	in	in	ADP
ap-7596	243	14	the	the	DET
ap-7596	243	15	enveloping	enveloping	NOUN
ap-7596	243	16	algebra	algebra	NOUN
ap-7596	243	17	u(g	u(g	PROPN
ap-7596	243	18	)	)	PUNCT
ap-7596	243	19	,	,	PUNCT
ap-7596	243	20	with	with	ADP
ap-7596	243	21	commutators	commutator	NOUN
ap-7596	243	22	[	[	X
ap-7596	243	23	r	r	X
ap-7596	243	24	,	,	PUNCT
ap-7596	243	25	x	x	NOUN
ap-7596	243	26	′	′	NUM
ap-7596	244	1	i	i	NOUN
ap-7596	244	2	]	]	X
ap-7596	244	3	=	=	PUNCT
ap-7596	244	4	0	0	NUM
ap-7596	244	5	,	,	PUNCT
ap-7596	244	6	[	[	PUNCT
ap-7596	244	7	x	x	SYM
ap-7596	244	8	′	′	NUM
ap-7596	245	1	i	i	PRON
ap-7596	245	2	,	,	PUNCT
ap-7596	245	3	x	x	PUNCT
ap-7596	245	4	′	′	NUM
ap-7596	245	5	j	j	NOUN
ap-7596	245	6	]	]	X
ap-7596	246	1	=	=	PUNCT
ap-7596	246	2	ck	ck	INTJ
ap-7596	246	3	ijx	ijx	NOUN
ap-7596	246	4	′	′	NUM
ap-7596	246	5	kr	kr	PROPN
ap-7596	246	6	,	,	PUNCT
ap-7596	246	7	1	1	NUM
ap-7596	246	8	≤	≤	NUM
ap-7596	246	9	i	i	PROPN
ap-7596	246	10	,	,	PUNCT
ap-7596	246	11	j	j	PROPN
ap-7596	246	12	,	,	PUNCT
ap-7596	246	13	k	k	PROPN
ap-7596	246	14	≤	≤	PROPN
ap-7596	246	15	n.	n.	NOUN
ap-7596	246	16	under	under	ADP
ap-7596	246	17	some	some	DET
ap-7596	246	18	specific	specific	ADJ
ap-7596	246	19	conditions	condition	NOUN
ap-7596	246	20	,	,	PUNCT
ap-7596	246	21	these	these	DET
ap-7596	246	22	so	so	ADV
ap-7596	246	23	-	-	PUNCT
ap-7596	246	24	called	call	VERB
ap-7596	246	25	virtual	virtual	ADJ
ap-7596	246	26	copies	copy	NOUN
ap-7596	246	27	of	of	ADP
ap-7596	246	28	semisimple	semisimple	NOUN
ap-7596	246	29	lie	lie	NOUN
ap-7596	246	30	algebras	algebra	NOUN
ap-7596	246	31	in	in	ADP
ap-7596	246	32	enveloping	envelop	VERB
ap-7596	246	33	algebras	algebra	NOUN
ap-7596	246	34	can	can	AUX
ap-7596	246	35	be	be	AUX
ap-7596	246	36	used	use	VERB
ap-7596	246	37	to	to	PART
ap-7596	246	38	construct	construct	VERB
ap-7596	246	39	(	(	PUNCT
ap-7596	246	40	formal	formal	ADJ
ap-7596	246	41	)	)	PUNCT
ap-7596	246	42	hamiltonians	hamiltonian	NOUN
ap-7596	246	43	with	with	ADP
ap-7596	246	44	first	first	ADJ
ap-7596	246	45	integrals	integral	NOUN
ap-7596	246	46	given	give	VERB
ap-7596	246	47	by	by	ADP
ap-7596	246	48	some	some	PRON
ap-7596	246	49	of	of	ADP
ap-7596	246	50	the	the	DET
ap-7596	246	51	operators	operator	NOUN
ap-7596	246	52	x	x	PUNCT
ap-7596	246	53	′	′	NUM
ap-7596	246	54	i.	i.	NOUN
ap-7596	246	55	let	let	VERB
ap-7596	246	56	us	we	PRON
ap-7596	246	57	outline	outline	VERB
ap-7596	246	58	one	one	NUM
ap-7596	246	59	possibility	possibility	NOUN
ap-7596	246	60	,	,	PUNCT
ap-7596	246	61	based	base	VERB
ap-7596	246	62	on	on	ADP
ap-7596	246	63	the	the	DET
ap-7596	246	64	branching	branch	VERB
ap-7596	246	65	rules	rule	NOUN
ap-7596	246	66	of	of	ADP
ap-7596	246	67	representations	representation	NOUN
ap-7596	246	68	of	of	ADP
ap-7596	246	69	semisimple	semisimple	ADJ
ap-7596	246	70	lie	lie	NOUN
ap-7596	246	71	algebras	algebra	NOUN
ap-7596	246	72	.	.	PUNCT
ap-7596	247	1	to	to	ADP
ap-7596	247	2	this	this	DET
ap-7596	247	3	extent	extent	NOUN
ap-7596	247	4	,	,	PUNCT
ap-7596	247	5	we	we	PRON
ap-7596	247	6	fix	fix	VERB
ap-7596	247	7	a	a	DET
ap-7596	247	8	semisimple	semisimple	ADJ
ap-7596	247	9	subalgebra	subalgebra	NOUN
ap-7596	247	10	s′	s′	NUM
ap-7596	247	11	of	of	ADP
ap-7596	247	12	the	the	DET
ap-7596	247	13	levi	levi	PROPN
ap-7596	247	14	factor	factor	NOUN
ap-7596	247	15	s	s	PROPN
ap-7596	247	16	of	of	ADP
ap-7596	247	17	the	the	DET
ap-7596	247	18	semidirect	semidirect	NOUN
ap-7596	247	19	sum	sum	NOUN
ap-7596	247	20	g.	g.	PROPN
ap-7596	247	21	further	far	ADV
ap-7596	247	22	suppose	suppose	VERB
ap-7596	247	23	that	that	SCONJ
ap-7596	247	24	the	the	DET
ap-7596	247	25	adjoint	adjoint	PROPN
ap-7596	247	26	representation	representation	NOUN
ap-7596	247	27	ad(s	ad(s	NOUN
ap-7596	247	28	)	)	PUNCT
ap-7596	247	29	decomposes	decompose	NOUN
ap-7596	247	30	,	,	PUNCT
ap-7596	247	31	as	as	ADP
ap-7596	247	32	a	a	DET
ap-7596	247	33	representation	representation	NOUN
ap-7596	247	34	of	of	ADP
ap-7596	247	35	s′	s′	PROPN
ap-7596	247	36	,	,	PUNCT
ap-7596	247	37	as	as	SCONJ
ap-7596	247	38	follows	follow	VERB
ap-7596	247	39	ad(s	ad(s	NUM
ap-7596	247	40	)	)	PUNCT
ap-7596	248	1	↓	↓	PROPN
ap-7596	248	2	ad(s′	ad(s′	PROPN
ap-7596	248	3	)	)	PUNCT
ap-7596	248	4	+	+	NUM
ap-7596	248	5	γ1	γ1	NOUN
ap-7596	248	6	+	+	CCONJ
ap-7596	248	7	·	·	PUNCT
ap-7596	248	8	·	·	PUNCT
ap-7596	248	9	·	·	PUNCT
ap-7596	249	1	+	+	CCONJ
ap-7596	249	2	γs	γs	VERB
ap-7596	249	3	,	,	PUNCT
ap-7596	249	4	(	(	PUNCT
ap-7596	249	5	18	18	NUM
ap-7596	249	6	)	)	PUNCT
ap-7596	249	7	2this	2this	NUM
ap-7596	249	8	fact	fact	NOUN
ap-7596	249	9	actually	actually	ADV
ap-7596	249	10	provides	provide	VERB
ap-7596	249	11	information	information	NOUN
ap-7596	249	12	concerning	concern	VERB
ap-7596	249	13	the	the	DET
ap-7596	249	14	dimension	dimension	NOUN
ap-7596	249	15	of	of	ADP
ap-7596	249	16	the	the	DET
ap-7596	249	17	characteristic	characteristic	ADJ
ap-7596	249	18	representation	representation	NOUN
ap-7596	249	19	γ	γ	NOUN
ap-7596	249	20	in	in	ADP
ap-7596	249	21	the	the	DET
ap-7596	249	22	semidirect	semidirect	NOUN
ap-7596	249	23	sum	sum	NOUN
ap-7596	249	24	.	.	PUNCT
ap-7596	250	1	where	where	SCONJ
ap-7596	250	2	γ	γ	PROPN
ap-7596	250	3	=	=	SYM
ap-7596	250	4	γ1	γ1	PROPN
ap-7596	250	5	+	+	CCONJ
ap-7596	250	6	·	·	PUNCT
ap-7596	250	7	·	·	PUNCT
ap-7596	250	8	·	·	PUNCT
ap-7596	250	9	+	+	CCONJ
ap-7596	250	10	γs	γs	VERB
ap-7596	250	11	is	be	AUX
ap-7596	250	12	the	the	DET
ap-7596	250	13	so	so	ADV
ap-7596	250	14	-	-	PUNCT
ap-7596	250	15	called	call	VERB
ap-7596	250	16	characteristic	characteristic	ADJ
ap-7596	250	17	representation	representation	NOUN
ap-7596	251	1	[	[	X
ap-7596	251	2	20	20	NUM
ap-7596	251	3	]	]	PUNCT
ap-7596	251	4	.	.	PUNCT
ap-7596	252	1	suppose	suppose	VERB
ap-7596	252	2	that	that	SCONJ
ap-7596	252	3	the	the	DET
ap-7596	252	4	trivial	trivial	ADJ
ap-7596	252	5	representation	representation	NOUN
ap-7596	252	6	γ0	γ0	NOUN
ap-7596	252	7	of	of	ADP
ap-7596	252	8	s′	s′	PROPN
ap-7596	252	9	has	have	VERB
ap-7596	252	10	multiplicity	multiplicity	NOUN
ap-7596	252	11	k	k	PROPN
ap-7596	252	12	>	>	X
ap-7596	252	13	0	0	PUNCT
ap-7596	252	14	in	in	ADP
ap-7596	252	15	the	the	DET
ap-7596	252	16	decomposition	decomposition	NOUN
ap-7596	252	17	(	(	PUNCT
ap-7596	252	18	18	18	NUM
ap-7596	252	19	)	)	PUNCT
ap-7596	252	20	.	.	PUNCT
ap-7596	253	1	this	this	PRON
ap-7596	253	2	means	mean	VERB
ap-7596	253	3	specifically	specifically	ADV
ap-7596	253	4	that	that	SCONJ
ap-7596	253	5	we	we	PRON
ap-7596	253	6	can	can	AUX
ap-7596	253	7	find	find	VERB
ap-7596	253	8	k	k	PROPN
ap-7596	253	9	generators	generator	NOUN
ap-7596	253	10	{	{	PUNCT
ap-7596	253	11	x̃1	x̃1	PROPN
ap-7596	253	12	,	,	PUNCT
ap-7596	253	13	.	.	PUNCT
ap-7596	253	14	.	.	PUNCT
ap-7596	253	15	.	.	PUNCT
ap-7596	254	1	,	,	PUNCT
ap-7596	254	2	x̃k	x̃k	ADP
ap-7596	254	3	}	}	PUNCT
ap-7596	254	4	of	of	ADP
ap-7596	254	5	s	s	PRON
ap-7596	254	6	that	that	DET
ap-7596	254	7	commute	commute	NOUN
ap-7596	254	8	with	with	ADP
ap-7596	254	9	the	the	DET
ap-7596	254	10	subalgebra	subalgebra	NOUN
ap-7596	254	11	s′.	s′.	PROPN
ap-7596	254	12	now	now	ADV
ap-7596	254	13	,	,	PUNCT
ap-7596	254	14	by	by	ADP
ap-7596	254	15	condition	condition	NOUN
ap-7596	254	16	(	(	PUNCT
ap-7596	254	17	15	15	NUM
ap-7596	254	18	)	)	PUNCT
ap-7596	254	19	,	,	PUNCT
ap-7596	254	20	for	for	ADP
ap-7596	254	21	the	the	DET
ap-7596	254	22	corresponding	correspond	VERB
ap-7596	254	23	operators	operator	NOUN
ap-7596	254	24	x̃s	x̃s	PROPN
ap-7596	254	25	(	(	PUNCT
ap-7596	254	26	1	1	NUM
ap-7596	254	27	≤	≤	PROPN
ap-7596	254	28	s	s	PART
ap-7596	254	29	≤	≤	NUM
ap-7596	254	30	k	k	X
ap-7596	254	31	)	)	PUNCT
ap-7596	255	1	we	we	PRON
ap-7596	255	2	have	have	VERB
ap-7596	255	3	that	that	PRON
ap-7596	255	4	[	[	PUNCT
ap-7596	256	1	x̃	x̃	PROPN
ap-7596	256	2	′	′	NUM
ap-7596	256	3	i	i	PROPN
ap-7596	256	4	,	,	PUNCT
ap-7596	256	5	z	z	X
ap-7596	256	6	]	]	PUNCT
ap-7596	257	1	=	=	PUNCT
ap-7596	257	2	[	[	PUNCT
ap-7596	257	3	x̃i	x̃i	PROPN
ap-7596	257	4	,	,	PUNCT
ap-7596	257	5	z	z	NOUN
ap-7596	257	6	]	]	PUNCT
ap-7596	257	7	′	′	NUM
ap-7596	257	8	=	=	SYM
ap-7596	257	9	0	0	NUM
ap-7596	257	10	,	,	PUNCT
ap-7596	257	11	z	z	PROPN
ap-7596	257	12	∈	∈	PROPN
ap-7596	257	13	s′	s′	NOUN
ap-7596	257	14	,	,	PUNCT
ap-7596	257	15	(	(	PUNCT
ap-7596	257	16	19	19	NUM
ap-7596	257	17	)	)	PUNCT
ap-7596	257	18	from	from	ADP
ap-7596	257	19	which	which	PRON
ap-7596	257	20	it	it	PRON
ap-7596	257	21	follows	follow	VERB
ap-7596	257	22	that	that	SCONJ
ap-7596	257	23	for	for	ADP
ap-7596	257	24	any	any	DET
ap-7596	257	25	algebraic	algebraic	ADJ
ap-7596	257	26	hamiltonian	hamiltonian	ADJ
ap-7596	257	27	h	h	PROPN
ap-7596	257	28	∈	∈	PROPN
ap-7596	257	29	u(s′	u(s′	PROPN
ap-7596	257	30	)	)	PUNCT
ap-7596	257	31	the	the	DET
ap-7596	257	32	integrability	integrability	NOUN
ap-7596	257	33	condition	condition	NOUN
ap-7596	257	34	[	[	PUNCT
ap-7596	257	35	x̃	x̃	PROPN
ap-7596	257	36	′	′	NUM
ap-7596	258	1	i	i	PROPN
ap-7596	258	2	,	,	PUNCT
ap-7596	258	3	h	h	NOUN
ap-7596	258	4	]	]	PUNCT
ap-7596	259	1	=	=	PUNCT
ap-7596	260	1	[	[	X
ap-7596	260	2	r	r	X
ap-7596	260	3	,	,	PUNCT
ap-7596	260	4	h	h	NOUN
ap-7596	260	5	]	]	X
ap-7596	260	6	=	=	SYM
ap-7596	260	7	0	0	NUM
ap-7596	260	8	,	,	PUNCT
ap-7596	260	9	1	1	NUM
ap-7596	260	10	≤	≤	NUM
ap-7596	260	11	i	i	NOUN
ap-7596	261	1	≤	≤	NOUN
ap-7596	261	2	k	k	X
ap-7596	261	3	(	(	PUNCT
ap-7596	261	4	20	20	NUM
ap-7596	261	5	)	)	PUNCT
ap-7596	261	6	is	be	AUX
ap-7596	261	7	satisfied	satisfied	ADJ
ap-7596	261	8	.	.	PUNCT
ap-7596	262	1	on	on	ADP
ap-7596	262	2	the	the	DET
ap-7596	262	3	other	other	ADJ
ap-7596	262	4	hand	hand	NOUN
ap-7596	262	5	,	,	PUNCT
ap-7596	262	6	by	by	ADP
ap-7596	262	7	condition	condition	NOUN
ap-7596	262	8	(	(	PUNCT
ap-7596	262	9	17	17	NUM
ap-7596	262	10	)	)	PUNCT
ap-7596	262	11	,	,	PUNCT
ap-7596	262	12	it	it	PRON
ap-7596	262	13	is	be	AUX
ap-7596	262	14	straightforward	straightforward	ADJ
ap-7596	262	15	to	to	PART
ap-7596	262	16	verify	verify	VERB
ap-7596	262	17	that	that	SCONJ
ap-7596	262	18	[	[	PUNCT
ap-7596	262	19	h	h	NOUN
ap-7596	262	20	,	,	PUNCT
ap-7596	262	21	[	[	PUNCT
ap-7596	262	22	x̃	x̃	PROPN
ap-7596	262	23	′	′	NUM
ap-7596	263	1	i	i	PRON
ap-7596	263	2	,	,	PUNCT
ap-7596	263	3	x̃	x̃	PROPN
ap-7596	263	4	′	′	NUM
ap-7596	264	1	j	j	NOUN
ap-7596	265	1	]	]	X
ap-7596	265	2	]	]	X
ap-7596	265	3	=	=	PUNCT
ap-7596	265	4	0	0	X
ap-7596	265	5	.	.	PUNCT
ap-7596	266	1	(	(	PUNCT
ap-7596	266	2	21	21	NUM
ap-7596	266	3	)	)	PUNCT
ap-7596	266	4	this	this	DET
ap-7596	266	5	last	last	ADJ
ap-7596	266	6	identity	identity	NOUN
ap-7596	266	7	implies	imply	VERB
ap-7596	266	8	that	that	SCONJ
ap-7596	266	9	the	the	DET
ap-7596	266	10	terms	term	NOUN
ap-7596	266	11	appearing	appear	VERB
ap-7596	266	12	in	in	ADP
ap-7596	266	13	the	the	DET
ap-7596	266	14	commutator	commutator	NOUN
ap-7596	266	15	[	[	PUNCT
ap-7596	266	16	x̃	x̃	PROPN
ap-7596	266	17	′	′	NUM
ap-7596	266	18	i	i	PRON
ap-7596	266	19	,	,	PUNCT
ap-7596	266	20	x̃	x̃	PROPN
ap-7596	266	21	′	′	NUM
ap-7596	267	1	j	j	PROPN
ap-7596	267	2	]	]	PUNCT
ap-7596	267	3	also	also	ADV
ap-7596	267	4	transform	transform	VERB
ap-7596	267	5	according	accord	VERB
ap-7596	267	6	to	to	ADP
ap-7596	267	7	the	the	DET
ap-7596	267	8	trivial	trivial	ADJ
ap-7596	267	9	representation	representation	NOUN
ap-7596	267	10	of	of	ADP
ap-7596	267	11	the	the	DET
ap-7596	267	12	subalgebra	subalgebra	NOUN
ap-7596	267	13	s′.	s′.	INTJ
ap-7596	267	14	we	we	PRON
ap-7596	267	15	conclude	conclude	VERB
ap-7596	267	16	that	that	SCONJ
ap-7596	267	17	the	the	DET
ap-7596	267	18	set	set	NOUN
ap-7596	267	19	{	{	PUNCT
ap-7596	267	20	r	r	NOUN
ap-7596	267	21	,	,	PUNCT
ap-7596	267	22	x̃	x̃	PROPN
ap-7596	267	23	′	′	NUM
ap-7596	267	24	1	1	NUM
ap-7596	267	25	,	,	PUNCT
ap-7596	267	26	.	.	PUNCT
ap-7596	267	27	.	.	PUNCT
ap-7596	267	28	.	.	PUNCT
ap-7596	268	1	,	,	PUNCT
ap-7596	269	1	x̃	x̃	PROPN
ap-7596	269	2	′	′	NUM
ap-7596	270	1	k	k	NOUN
ap-7596	270	2	}	}	PUNCT
ap-7596	270	3	generates	generate	VERB
ap-7596	270	4	a	a	DET
ap-7596	270	5	finite	finite	ADJ
ap-7596	270	6	-	-	ADJ
ap-7596	270	7	dimensional	dimensional	ADJ
ap-7596	270	8	quadratic	quadratic	ADJ
ap-7596	270	9	algebra	algebra	NOUN
ap-7596	270	10	in	in	ADP
ap-7596	270	11	the	the	DET
ap-7596	270	12	enveloping	enveloping	NOUN
ap-7596	270	13	algebra	algebra	NOUN
ap-7596	270	14	u(g	u(g	ADP
ap-7596	270	15	)	)	PUNCT
ap-7596	270	16	that	that	PRON
ap-7596	270	17	are	be	AUX
ap-7596	270	18	(	(	PUNCT
ap-7596	270	19	formal	formal	ADJ
ap-7596	270	20	)	)	PUNCT
ap-7596	270	21	first	first	ADJ
ap-7596	270	22	integrals	integral	NOUN
ap-7596	270	23	for	for	ADP
ap-7596	270	24	the	the	DET
ap-7596	270	25	hamiltonian	hamiltonian	ADJ
ap-7596	270	26	h.	h.	PROPN
ap-7596	270	27	whether	whether	SCONJ
ap-7596	270	28	or	or	CCONJ
ap-7596	270	29	not	not	PART
ap-7596	270	30	these	these	DET
ap-7596	270	31	integrals	integral	NOUN
ap-7596	270	32	are	be	AUX
ap-7596	270	33	sufficient	sufficient	ADJ
ap-7596	270	34	for	for	ADP
ap-7596	270	35	guaranteeing	guarantee	VERB
ap-7596	270	36	(	(	PUNCT
ap-7596	270	37	super-)integrability	super-)integrability	NOUN
ap-7596	270	38	,	,	PUNCT
ap-7596	270	39	essentially	essentially	ADV
ap-7596	270	40	depends	depend	VERB
ap-7596	270	41	on	on	ADP
ap-7596	270	42	the	the	DET
ap-7596	270	43	subalgebra	subalgebra	NOUN
ap-7596	270	44	s′	s′	VERB
ap-7596	270	45	and	and	CCONJ
ap-7596	270	46	the	the	DET
ap-7596	270	47	associated	associated	ADJ
ap-7596	270	48	branching	branch	VERB
ap-7596	270	49	rule	rule	NOUN
ap-7596	270	50	.	.	PUNCT
ap-7596	271	1	in	in	ADP
ap-7596	271	2	any	any	DET
ap-7596	271	3	case	case	NOUN
ap-7596	271	4	,	,	PUNCT
ap-7596	271	5	the	the	DET
ap-7596	271	6	preceding	precede	VERB
ap-7596	271	7	construction	construction	NOUN
ap-7596	271	8	determines	determine	VERB
ap-7596	271	9	the	the	DET
ap-7596	271	10	maximal	maximal	ADJ
ap-7596	271	11	number	number	NOUN
ap-7596	271	12	of	of	ADP
ap-7596	271	13	operators	operator	NOUN
ap-7596	271	14	x	x	PUNCT
ap-7596	272	1	′	′	NUM
ap-7596	272	2	i	i	PRON
ap-7596	272	3	that	that	PRON
ap-7596	272	4	commute	commute	VERB
ap-7596	272	5	with	with	ADP
ap-7596	272	6	the	the	DET
ap-7596	272	7	hamiltonian	hamiltonian	ADJ
ap-7596	272	8	h	h	NOUN
ap-7596	272	9	,	,	PUNCT
ap-7596	272	10	independently	independently	ADV
ap-7596	272	11	of	of	ADP
ap-7596	272	12	any	any	DET
ap-7596	272	13	realization	realization	NOUN
ap-7596	272	14	of	of	ADP
ap-7596	272	15	the	the	DET
ap-7596	272	16	hidden	hide	VERB
ap-7596	272	17	algebra	algebra	NOUN
ap-7596	272	18	g	g	NOUN
ap-7596	272	19	by	by	ADP
ap-7596	272	20	first	first	ADJ
ap-7596	272	21	-	-	PUNCT
ap-7596	272	22	order	order	NOUN
ap-7596	272	23	differential	differential	NOUN
ap-7596	272	24	operators	operator	NOUN
ap-7596	272	25	.	.	PUNCT
ap-7596	273	1	for	for	ADP
ap-7596	273	2	the	the	DET
ap-7596	273	3	case	case	NOUN
ap-7596	273	4	where	where	SCONJ
ap-7596	273	5	the	the	DET
ap-7596	273	6	characteristic	characteristic	ADJ
ap-7596	273	7	representation	representation	NOUN
ap-7596	273	8	γ	γ	NOUN
ap-7596	273	9	does	do	AUX
ap-7596	273	10	not	not	PART
ap-7596	273	11	contain	contain	VERB
ap-7596	273	12	the	the	DET
ap-7596	273	13	trivial	trivial	ADJ
ap-7596	273	14	representation	representation	NOUN
ap-7596	273	15	of	of	ADP
ap-7596	273	16	the	the	DET
ap-7596	273	17	subalgebra	subalgebra	NOUN
ap-7596	273	18	s′	s′	X
ap-7596	273	19	,	,	PUNCT
ap-7596	273	20	i.e.	i.e.	X
ap-7596	273	21	,	,	PUNCT
ap-7596	273	22	when	when	SCONJ
ap-7596	273	23	no	no	DET
ap-7596	273	24	generators	generator	NOUN
ap-7596	273	25	of	of	ADP
ap-7596	273	26	s	s	PRON
ap-7596	273	27	simultaneously	simultaneously	ADV
ap-7596	273	28	commute	commute	VERB
ap-7596	273	29	with	with	ADP
ap-7596	273	30	the	the	DET
ap-7596	273	31	elements	element	NOUN
ap-7596	273	32	of	of	ADP
ap-7596	273	33	s′	s′	PROPN
ap-7596	273	34	,	,	PUNCT
ap-7596	273	35	the	the	DET
ap-7596	273	36	integrability	integrability	NOUN
ap-7596	273	37	condition	condition	NOUN
ap-7596	273	38	for	for	ADP
ap-7596	273	39	the	the	DET
ap-7596	273	40	operators	operator	NOUN
ap-7596	273	41	would	would	AUX
ap-7596	273	42	not	not	PART
ap-7596	273	43	be	be	AUX
ap-7596	273	44	a	a	DET
ap-7596	273	45	consequence	consequence	NOUN
ap-7596	273	46	of	of	ADP
ap-7596	273	47	the	the	DET
ap-7596	273	48	structure	structure	NOUN
ap-7596	273	49	of	of	ADP
ap-7596	273	50	the	the	DET
ap-7596	273	51	enveloping	enveloping	NOUN
ap-7596	273	52	algebra	algebra	NOUN
ap-7596	273	53	,	,	PUNCT
ap-7596	273	54	but	but	CCONJ
ap-7596	273	55	the	the	DET
ap-7596	273	56	specific	specific	ADJ
ap-7596	273	57	consequence	consequence	NOUN
ap-7596	273	58	of	of	ADP
ap-7596	273	59	a	a	DET
ap-7596	273	60	realization	realization	NOUN
ap-7596	273	61	of	of	ADP
ap-7596	273	62	g	g	NOUN
ap-7596	273	63	,	,	PUNCT
ap-7596	273	64	relating	relate	VERB
ap-7596	273	65	this	this	DET
ap-7596	273	66	approach	approach	NOUN
ap-7596	273	67	with	with	ADP
ap-7596	273	68	the	the	DET
ap-7596	273	69	first	first	ADJ
ap-7596	273	70	algebraic	algebraic	ADJ
ap-7596	273	71	formulation	formulation	NOUN
ap-7596	273	72	.	.	PUNCT
ap-7596	274	1	we	we	PRON
ap-7596	274	2	finally	finally	ADV
ap-7596	274	3	observe	observe	VERB
ap-7596	274	4	that	that	SCONJ
ap-7596	274	5	the	the	DET
ap-7596	274	6	construction	construction	NOUN
ap-7596	274	7	presented	present	VERB
ap-7596	274	8	here	here	ADV
ap-7596	274	9	,	,	PUNCT
ap-7596	274	10	that	that	PRON
ap-7596	274	11	depends	depend	VERB
ap-7596	274	12	essentially	essentially	ADV
ap-7596	274	13	on	on	ADP
ap-7596	274	14	the	the	DET
ap-7596	274	15	homogeneity	homogeneity	NOUN
ap-7596	274	16	of	of	ADP
ap-7596	274	17	the	the	DET
ap-7596	274	18	operators	operator	NOUN
ap-7596	274	19	x	x	PUNCT
ap-7596	275	1	′	′	NUM
ap-7596	275	2	i	i	PRON
ap-7596	275	3	,	,	PUNCT
ap-7596	275	4	is	be	AUX
ap-7596	275	5	specially	specially	ADV
ap-7596	275	6	suitable	suitable	ADJ
ap-7596	275	7	for	for	ADP
ap-7596	275	8	semidirect	semidirect	NOUN
ap-7596	275	9	sums	sum	NOUN
ap-7596	275	10	admitting	admit	VERB
ap-7596	275	11	a	a	DET
ap-7596	275	12	nonvanishing	nonvanishe	VERB
ap-7596	275	13	centre	centre	NOUN
ap-7596	275	14	and	and	CCONJ
ap-7596	275	15	the	the	DET
ap-7596	275	16	class	class	NOUN
ap-7596	275	17	of	of	ADP
ap-7596	275	18	one	one	NUM
ap-7596	275	19	-	-	PUNCT
ap-7596	275	20	dimensional	dimensional	ADJ
ap-7596	275	21	non	non	ADJ
ap-7596	275	22	-	-	ADJ
ap-7596	275	23	central	central	ADJ
ap-7596	275	24	extensions	extension	NOUN
ap-7596	275	25	of	of	ADP
ap-7596	275	26	double	double	ADJ
ap-7596	275	27	inhomogeneous	inhomogeneous	ADJ
ap-7596	275	28	lie	lie	NOUN
ap-7596	275	29	algebras	algebra	NOUN
ap-7596	275	30	[	[	X
ap-7596	275	31	21	21	NUM
ap-7596	275	32	,	,	PUNCT
ap-7596	275	33	22	22	NUM
ap-7596	275	34	]	]	PUNCT
ap-7596	275	35	,	,	PUNCT
ap-7596	275	36	while	while	SCONJ
ap-7596	275	37	the	the	DET
ap-7596	275	38	argument	argument	NOUN
ap-7596	275	39	is	be	AUX
ap-7596	275	40	not	not	PART
ap-7596	275	41	valid	valid	ADJ
ap-7596	275	42	whenever	whenever	SCONJ
ap-7596	275	43	the	the	DET
ap-7596	275	44	levi	levi	PROPN
ap-7596	275	45	factor	factor	NOUN
ap-7596	275	46	s	s	PART
ap-7596	275	47	and	and	CCONJ
ap-7596	275	48	the	the	DET
ap-7596	275	49	radical	radical	ADJ
ap-7596	275	50	do	do	AUX
ap-7596	275	51	not	not	PART
ap-7596	275	52	have	have	VERB
ap-7596	275	53	nonconstant	nonconstant	ADJ
ap-7596	275	54	invariants	invariant	NOUN
ap-7596	275	55	in	in	ADP
ap-7596	275	56	common	common	ADJ
ap-7596	275	57	.	.	PUNCT
ap-7596	276	1	due	due	ADP
ap-7596	276	2	to	to	ADP
ap-7596	276	3	this	this	DET
ap-7596	276	4	obstruction	obstruction	NOUN
ap-7596	276	5	,	,	PUNCT
ap-7596	276	6	it	it	PRON
ap-7596	276	7	is	be	AUX
ap-7596	276	8	formally	formally	ADV
ap-7596	276	9	conceivable	conceivable	ADJ
ap-7596	276	10	to	to	PART
ap-7596	276	11	propose	propose	VERB
ap-7596	276	12	a	a	DET
ap-7596	276	13	generalized	generalized	ADJ
ap-7596	276	14	construction	construction	NOUN
ap-7596	276	15	by	by	ADP
ap-7596	276	16	skipping	skip	VERB
ap-7596	276	17	the	the	DET
ap-7596	276	18	homogeneity	homogeneity	NOUN
ap-7596	276	19	assumption	assumption	NOUN
ap-7596	276	20	.	.	PUNCT
ap-7596	277	1	it	it	PRON
ap-7596	277	2	should	should	AUX
ap-7596	277	3	however	however	ADV
ap-7596	277	4	be	be	AUX
ap-7596	277	5	taken	take	VERB
ap-7596	277	6	into	into	ADP
ap-7596	277	7	account	account	NOUN
ap-7596	277	8	that	that	SCONJ
ap-7596	277	9	using	use	VERB
ap-7596	277	10	operators	operator	NOUN
ap-7596	277	11	of	of	ADP
ap-7596	277	12	different	different	ADJ
ap-7596	277	13	degrees	degree	NOUN
ap-7596	277	14	in	in	ADP
ap-7596	277	15	(	(	PUNCT
ap-7596	277	16	13	13	NUM
ap-7596	277	17	)	)	PUNCT
ap-7596	277	18	may	may	AUX
ap-7596	277	19	lead	lead	VERB
ap-7596	277	20	to	to	ADP
ap-7596	277	21	incompatibilities	incompatibility	NOUN
ap-7596	277	22	in	in	ADP
ap-7596	277	23	the	the	DET
ap-7596	277	24	commutators	commutator	NOUN
ap-7596	277	25	,	,	PUNCT
ap-7596	277	26	as	as	SCONJ
ap-7596	277	27	equations	equation	NOUN
ap-7596	277	28	(	(	PUNCT
ap-7596	277	29	14)-(16	14)-(16	NOUN
ap-7596	277	30	)	)	PUNCT
ap-7596	277	31	cease	cease	NOUN
ap-7596	277	32	to	to	PART
ap-7596	277	33	hold	hold	VERB
ap-7596	277	34	,	,	PUNCT
ap-7596	277	35	and	and	CCONJ
ap-7596	277	36	more	more	ADV
ap-7596	277	37	general	general	ADJ
ap-7596	277	38	constraints	constraint	NOUN
ap-7596	277	39	depending	depend	VERB
ap-7596	277	40	on	on	ADP
ap-7596	277	41	the	the	DET
ap-7596	277	42	particular	particular	ADJ
ap-7596	277	43	degrees	degree	NOUN
ap-7596	277	44	of	of	ADP
ap-7596	277	45	each	each	DET
ap-7596	277	46	pi	pi	NOUN
ap-7596	277	47	would	would	AUX
ap-7596	277	48	be	be	AUX
ap-7596	277	49	required	require	VERB
ap-7596	277	50	.	.	PUNCT
ap-7596	278	1	if	if	SCONJ
ap-7596	278	2	and	and	CCONJ
ap-7596	278	3	under	under	ADP
ap-7596	278	4	what	what	PRON
ap-7596	278	5	specific	specific	ADJ
ap-7596	278	6	assumptions	assumption	NOUN
ap-7596	278	7	a	a	DET
ap-7596	278	8	solution	solution	NOUN
ap-7596	278	9	can	can	AUX
ap-7596	278	10	be	be	AUX
ap-7596	278	11	found	find	VERB
ap-7596	278	12	for	for	ADP
ap-7596	278	13	a	a	DET
ap-7596	278	14	generalized	generalized	ADJ
ap-7596	278	15	inhomogeneous	inhomogeneous	ADJ
ap-7596	278	16	set	set	NOUN
ap-7596	278	17	of	of	ADP
ap-7596	278	18	generators	generator	NOUN
ap-7596	278	19	(	(	PUNCT
ap-7596	278	20	13	13	NUM
ap-7596	278	21	)	)	PUNCT
ap-7596	278	22	,	,	PUNCT
ap-7596	278	23	is	be	AUX
ap-7596	278	24	still	still	ADV
ap-7596	278	25	an	an	DET
ap-7596	278	26	unanswered	unanswered	ADJ
ap-7596	278	27	question	question	NOUN
ap-7596	278	28	that	that	PRON
ap-7596	278	29	is	be	AUX
ap-7596	278	30	currently	currently	ADV
ap-7596	278	31	being	be	AUX
ap-7596	278	32	studied	study	VERB
ap-7596	278	33	in	in	ADP
ap-7596	278	34	detail	detail	NOUN
ap-7596	278	35	.	.	PUNCT
ap-7596	279	1	20	20	NUM
ap-7596	279	2	vol	vol	NOUN
ap-7596	279	3	.	.	PUNCT
ap-7596	280	1	62	62	NUM
ap-7596	280	2	no	no	INTJ
ap-7596	280	3	.	.	PUNCT
ap-7596	281	1	1/2022	1/2022	NUM
ap-7596	281	2	on	on	ADP
ap-7596	281	3	some	some	DET
ap-7596	281	4	algebraic	algebraic	ADJ
ap-7596	281	5	formulations	formulation	NOUN
ap-7596	281	6	.	.	PUNCT
ap-7596	281	7	.	.	PUNCT
ap-7596	281	8	.	.	PUNCT
ap-7596	282	1	5	5	X
ap-7596	282	2	.	.	X
ap-7596	282	3	conclusions	conclusion	NOUN
ap-7596	282	4	two	two	NUM
ap-7596	282	5	possible	possible	ADJ
ap-7596	282	6	approaches	approach	NOUN
ap-7596	282	7	to	to	ADP
ap-7596	282	8	the	the	DET
ap-7596	282	9	problem	problem	NOUN
ap-7596	282	10	of	of	ADP
ap-7596	282	11	determining	determine	VERB
ap-7596	282	12	quadratic	quadratic	ADJ
ap-7596	282	13	algebras	algebra	NOUN
ap-7596	282	14	as	as	SCONJ
ap-7596	282	15	subalgebras	subalgebra	NOUN
ap-7596	282	16	of	of	ADP
ap-7596	282	17	the	the	DET
ap-7596	282	18	enveloping	enveloping	NOUN
ap-7596	282	19	algebra	algebra	NOUN
ap-7596	282	20	of	of	ADP
ap-7596	282	21	a	a	DET
ap-7596	282	22	lie	lie	NOUN
ap-7596	282	23	algebra	algebra	NOUN
ap-7596	282	24	have	have	AUX
ap-7596	282	25	been	be	AUX
ap-7596	282	26	commented	comment	VERB
ap-7596	282	27	.	.	PUNCT
ap-7596	283	1	the	the	DET
ap-7596	283	2	first	first	ADJ
ap-7596	283	3	approach	approach	NOUN
ap-7596	283	4	corresponds	correspond	VERB
ap-7596	283	5	to	to	ADP
ap-7596	283	6	an	an	DET
ap-7596	283	7	algebraic	algebraic	ADJ
ap-7596	283	8	abstraction	abstraction	NOUN
ap-7596	283	9	of	of	ADP
ap-7596	283	10	already	already	ADV
ap-7596	283	11	known	know	VERB
ap-7596	283	12	systems	system	NOUN
ap-7596	283	13	,	,	PUNCT
ap-7596	283	14	which	which	PRON
ap-7596	283	15	are	be	AUX
ap-7596	283	16	analyzed	analyze	VERB
ap-7596	283	17	purely	purely	ADV
ap-7596	283	18	from	from	ADP
ap-7596	283	19	the	the	DET
ap-7596	283	20	perspective	perspective	NOUN
ap-7596	283	21	of	of	ADP
ap-7596	283	22	the	the	DET
ap-7596	283	23	hamiltonian	hamiltonian	NOUN
ap-7596	283	24	and	and	CCONJ
ap-7596	283	25	the	the	DET
ap-7596	283	26	integrals	integral	NOUN
ap-7596	283	27	as	as	ADP
ap-7596	283	28	the	the	DET
ap-7596	283	29	image	image	NOUN
ap-7596	283	30	by	by	ADP
ap-7596	283	31	a	a	DET
ap-7596	283	32	realization	realization	NOUN
ap-7596	283	33	of	of	ADP
ap-7596	283	34	differential	differential	ADJ
ap-7596	283	35	operators	operator	NOUN
ap-7596	283	36	of	of	ADP
ap-7596	283	37	elements	element	NOUN
ap-7596	283	38	in	in	ADP
ap-7596	283	39	some	some	DET
ap-7596	283	40	enveloping	enveloping	NOUN
ap-7596	283	41	algebra	algebra	NOUN
ap-7596	283	42	,	,	PUNCT
ap-7596	283	43	trying	try	VERB
ap-7596	283	44	to	to	PART
ap-7596	283	45	determine	determine	VERB
ap-7596	283	46	to	to	ADP
ap-7596	283	47	which	which	DET
ap-7596	283	48	extent	extent	NOUN
ap-7596	283	49	such	such	ADJ
ap-7596	283	50	integrals	integral	NOUN
ap-7596	283	51	are	be	AUX
ap-7596	283	52	realization	realization	NOUN
ap-7596	283	53	-	-	PUNCT
ap-7596	283	54	dependent	dependent	ADJ
ap-7596	283	55	[	[	X
ap-7596	283	56	10	10	NUM
ap-7596	283	57	]	]	PUNCT
ap-7596	283	58	.	.	PUNCT
ap-7596	284	1	in	in	ADP
ap-7596	284	2	a	a	DET
ap-7596	284	3	the	the	DET
ap-7596	284	4	second	second	ADJ
ap-7596	284	5	algebraic	algebraic	ADJ
ap-7596	284	6	formulation	formulation	NOUN
ap-7596	284	7	,	,	PUNCT
ap-7596	284	8	commutants	commutant	NOUN
ap-7596	284	9	of	of	ADP
ap-7596	284	10	subalgebras	subalgebras	PROPN
ap-7596	284	11	g′	g′	PROPN
ap-7596	284	12	⊂	⊂	PROPN
ap-7596	284	13	g	g	PROPN
ap-7596	284	14	in	in	ADP
ap-7596	284	15	the	the	DET
ap-7596	284	16	enveloping	enveloping	NOUN
ap-7596	284	17	algebra	algebra	NOUN
ap-7596	284	18	of	of	ADP
ap-7596	284	19	g	g	PROPN
ap-7596	284	20	are	be	AUX
ap-7596	284	21	considered	consider	VERB
ap-7596	284	22	,	,	PUNCT
ap-7596	284	23	from	from	ADP
ap-7596	284	24	which	which	PRON
ap-7596	284	25	quadratic	quadratic	ADJ
ap-7596	284	26	algebras	algebra	NOUN
ap-7596	284	27	formed	form	VERB
ap-7596	284	28	by	by	ADP
ap-7596	284	29	polynomials	polynomial	NOUN
ap-7596	284	30	that	that	PRON
ap-7596	284	31	commute	commute	VERB
ap-7596	284	32	with	with	ADP
ap-7596	284	33	a	a	DET
ap-7596	284	34	given	give	VERB
ap-7596	284	35	algebraic	algebraic	ADJ
ap-7596	284	36	hamiltonian	hamiltonian	NOUN
ap-7596	284	37	defined	define	VERB
ap-7596	284	38	in	in	ADP
ap-7596	284	39	u(g′	u(g′	PRON
ap-7596	284	40	)	)	PUNCT
ap-7596	284	41	are	be	AUX
ap-7596	284	42	deduced	deduce	VERB
ap-7596	284	43	.	.	PUNCT
ap-7596	285	1	in	in	ADP
ap-7596	285	2	order	order	NOUN
ap-7596	285	3	to	to	PART
ap-7596	285	4	simplify	simplify	VERB
ap-7596	285	5	the	the	DET
ap-7596	285	6	computations	computation	NOUN
ap-7596	285	7	in	in	ADP
ap-7596	285	8	the	the	DET
ap-7596	285	9	enveloping	enveloping	NOUN
ap-7596	285	10	algebra	algebra	NOUN
ap-7596	285	11	,	,	PUNCT
ap-7596	285	12	distinguished	distinguished	ADJ
ap-7596	285	13	elements	element	NOUN
ap-7596	285	14	in	in	ADP
ap-7596	285	15	the	the	DET
ap-7596	285	16	commutant	commutant	NOUN
ap-7596	285	17	can	can	AUX
ap-7596	285	18	be	be	AUX
ap-7596	285	19	deduced	deduce	VERB
ap-7596	285	20	from	from	ADP
ap-7596	285	21	the	the	DET
ap-7596	285	22	coadjoint	coadjoint	NOUN
ap-7596	285	23	representation	representation	NOUN
ap-7596	285	24	.	.	PUNCT
ap-7596	286	1	for	for	ADP
ap-7596	286	2	the	the	DET
ap-7596	286	3	subalgebras	subalgebras	PROPN
ap-7596	286	4	found	find	VERB
ap-7596	286	5	with	with	ADP
ap-7596	286	6	this	this	DET
ap-7596	286	7	method	method	NOUN
ap-7596	286	8	,	,	PUNCT
ap-7596	286	9	a	a	DET
ap-7596	286	10	realization	realization	NOUN
ap-7596	286	11	by	by	ADP
ap-7596	286	12	vector	vector	NOUN
ap-7596	286	13	fields	field	NOUN
ap-7596	286	14	of	of	ADP
ap-7596	286	15	an	an	DET
ap-7596	286	16	appropriate	appropriate	ADJ
ap-7596	286	17	number	number	NOUN
ap-7596	286	18	of	of	ADP
ap-7596	286	19	variables	variable	NOUN
ap-7596	286	20	automatically	automatically	ADV
ap-7596	286	21	provides	provide	VERB
ap-7596	286	22	a	a	DET
ap-7596	286	23	(	(	PUNCT
ap-7596	286	24	super-)integrable	super-)integrable	ADJ
ap-7596	286	25	system	system	NOUN
ap-7596	286	26	for	for	ADP
ap-7596	286	27	the	the	DET
ap-7596	286	28	given	give	VERB
ap-7596	286	29	hamiltonian	hamiltonian	NOUN
ap-7596	287	1	[	[	X
ap-7596	287	2	9	9	NUM
ap-7596	287	3	]	]	PUNCT
ap-7596	287	4	.	.	PUNCT
ap-7596	288	1	the	the	DET
ap-7596	288	2	method	method	NOUN
ap-7596	288	3	of	of	ADP
ap-7596	288	4	virtual	virtual	ADJ
ap-7596	288	5	copies	copy	NOUN
ap-7596	288	6	,	,	PUNCT
ap-7596	288	7	initially	initially	ADV
ap-7596	288	8	introduced	introduce	VERB
ap-7596	288	9	in	in	ADP
ap-7596	288	10	the	the	DET
ap-7596	288	11	context	context	NOUN
ap-7596	288	12	of	of	ADP
ap-7596	288	13	invariant	invariant	ADJ
ap-7596	288	14	theory	theory	NOUN
ap-7596	288	15	,	,	PUNCT
ap-7596	288	16	provides	provide	VERB
ap-7596	288	17	an	an	DET
ap-7596	288	18	additional	additional	ADJ
ap-7596	288	19	approach	approach	NOUN
ap-7596	288	20	that	that	PRON
ap-7596	288	21	combines	combine	VERB
ap-7596	288	22	elements	element	NOUN
ap-7596	288	23	of	of	ADP
ap-7596	288	24	the	the	DET
ap-7596	288	25	two	two	NUM
ap-7596	288	26	algebraic	algebraic	ADJ
ap-7596	288	27	formulations	formulation	NOUN
ap-7596	288	28	,	,	PUNCT
ap-7596	288	29	and	and	CCONJ
ap-7596	288	30	refers	refer	VERB
ap-7596	288	31	to	to	ADP
ap-7596	288	32	a	a	DET
ap-7596	288	33	number	number	NOUN
ap-7596	288	34	of	of	ADP
ap-7596	288	35	still	still	ADV
ap-7596	288	36	open	open	ADJ
ap-7596	288	37	problems	problem	NOUN
ap-7596	288	38	,	,	PUNCT
ap-7596	288	39	such	such	ADJ
ap-7596	288	40	as	as	ADP
ap-7596	288	41	the	the	DET
ap-7596	288	42	general	general	ADJ
ap-7596	288	43	solution	solution	NOUN
ap-7596	288	44	of	of	ADP
ap-7596	288	45	the	the	DET
ap-7596	288	46	embedding	embed	VERB
ap-7596	288	47	problem	problem	NOUN
ap-7596	288	48	of	of	ADP
ap-7596	288	49	lie	lie	NOUN
ap-7596	288	50	algebras	algebra	NOUN
ap-7596	288	51	into	into	ADP
ap-7596	288	52	enveloping	envelop	VERB
ap-7596	288	53	algebras	algebra	NOUN
ap-7596	289	1	[	[	X
ap-7596	289	2	16	16	NUM
ap-7596	289	3	]	]	X
ap-7596	289	4	,	,	PUNCT
ap-7596	289	5	as	as	ADV
ap-7596	289	6	well	well	ADV
ap-7596	289	7	the	the	DET
ap-7596	289	8	classification	classification	NOUN
ap-7596	289	9	problem	problem	NOUN
ap-7596	289	10	of	of	ADP
ap-7596	289	11	realizations	realization	NOUN
ap-7596	289	12	of	of	ADP
ap-7596	289	13	lie	lie	NOUN
ap-7596	289	14	algebras	algebra	NOUN
ap-7596	289	15	in	in	ADP
ap-7596	289	16	terms	term	NOUN
ap-7596	289	17	of	of	ADP
ap-7596	289	18	differential	differential	ADJ
ap-7596	289	19	operators	operator	NOUN
ap-7596	290	1	[	[	X
ap-7596	290	2	23	23	NUM
ap-7596	290	3	]	]	PUNCT
ap-7596	290	4	.	.	PUNCT
ap-7596	291	1	whether	whether	SCONJ
ap-7596	291	2	these	these	DET
ap-7596	291	3	approaches	approach	NOUN
ap-7596	291	4	are	be	AUX
ap-7596	291	5	compatible	compatible	ADJ
ap-7596	291	6	or	or	CCONJ
ap-7596	291	7	can	can	AUX
ap-7596	291	8	be	be	AUX
ap-7596	291	9	combined	combine	VERB
ap-7596	291	10	with	with	ADP
ap-7596	291	11	other	other	ADJ
ap-7596	291	12	procedures	procedure	NOUN
ap-7596	291	13	like	like	ADP
ap-7596	291	14	the	the	DET
ap-7596	291	15	quadratic	quadratic	ADJ
ap-7596	291	16	deformations	deformation	NOUN
ap-7596	291	17	of	of	ADP
ap-7596	291	18	lie	lie	NOUN
ap-7596	291	19	algebras	algebra	NOUN
ap-7596	291	20	or	or	CCONJ
ap-7596	291	21	the	the	DET
ap-7596	291	22	formalism	formalism	NOUN
ap-7596	291	23	of	of	ADP
ap-7596	291	24	racah	racah	NOUN
ap-7596	291	25	algebras	algebras	PROPN
ap-7596	291	26	(	(	PUNCT
ap-7596	291	27	see	see	VERB
ap-7596	291	28	e.g.	e.g.	ADV
ap-7596	291	29	[	[	X
ap-7596	291	30	8	8	NUM
ap-7596	291	31	,	,	PUNCT
ap-7596	291	32	24	24	NUM
ap-7596	291	33	,	,	PUNCT
ap-7596	291	34	25	25	NUM
ap-7596	291	35	]	]	PUNCT
ap-7596	291	36	and	and	CCONJ
ap-7596	291	37	references	reference	NOUN
ap-7596	291	38	therein	therein	ADV
ap-7596	291	39	)	)	PUNCT
ap-7596	291	40	is	be	AUX
ap-7596	291	41	a	a	DET
ap-7596	291	42	problem	problem	NOUN
ap-7596	291	43	worthy	worthy	ADJ
ap-7596	291	44	to	to	PART
ap-7596	291	45	be	be	AUX
ap-7596	291	46	inspected	inspect	VERB
ap-7596	291	47	.	.	PUNCT
ap-7596	292	1	we	we	PRON
ap-7596	292	2	hope	hope	VERB
ap-7596	292	3	to	to	PART
ap-7596	292	4	report	report	VERB
ap-7596	292	5	on	on	ADP
ap-7596	292	6	some	some	DET
ap-7596	292	7	progress	progress	NOUN
ap-7596	292	8	in	in	ADP
ap-7596	292	9	these	these	DET
ap-7596	292	10	directions	direction	NOUN
ap-7596	292	11	in	in	ADP
ap-7596	292	12	a	a	DET
ap-7596	292	13	near	near	ADJ
ap-7596	292	14	future	future	NOUN
ap-7596	292	15	.	.	PUNCT
ap-7596	293	1	acknowledgements	acknowledgement	NOUN
ap-7596	293	2	the	the	DET
ap-7596	293	3	author	author	NOUN
ap-7596	293	4	is	be	AUX
ap-7596	293	5	indebted	indebte	VERB
ap-7596	293	6	to	to	PART
ap-7596	293	7	alexander	alexander	PROPN
ap-7596	293	8	v.	v.	ADP
ap-7596	293	9	turbiner	turbiner	NOUN
ap-7596	293	10	and	and	CCONJ
ap-7596	293	11	ian	ian	PROPN
ap-7596	293	12	marquette	marquette	PROPN
ap-7596	293	13	for	for	ADP
ap-7596	293	14	valuable	valuable	ADJ
ap-7596	293	15	critical	critical	ADJ
ap-7596	293	16	comments	comment	NOUN
ap-7596	293	17	,	,	PUNCT
ap-7596	293	18	to	to	PART
ap-7596	293	19	artur	artur	PROPN
ap-7596	293	20	sergyeyev	sergyeyev	VERB
ap-7596	293	21	for	for	ADP
ap-7596	293	22	providing	provide	VERB
ap-7596	293	23	reference	reference	NOUN
ap-7596	293	24	[	[	X
ap-7596	293	25	15	15	NUM
ap-7596	293	26	]	]	PUNCT
ap-7596	293	27	,	,	PUNCT
ap-7596	293	28	as	as	ADV
ap-7596	293	29	well	well	ADV
ap-7596	293	30	as	as	ADP
ap-7596	293	31	to	to	ADP
ap-7596	293	32	the	the	DET
ap-7596	293	33	referees	referee	NOUN
ap-7596	293	34	for	for	ADP
ap-7596	293	35	several	several	ADJ
ap-7596	293	36	remarks	remark	NOUN
ap-7596	293	37	that	that	PRON
ap-7596	293	38	have	have	AUX
ap-7596	293	39	greatly	greatly	ADV
ap-7596	293	40	improved	improve	VERB
ap-7596	293	41	the	the	DET
ap-7596	293	42	presentation	presentation	NOUN
ap-7596	293	43	.	.	PUNCT
ap-7596	294	1	during	during	ADP
ap-7596	294	2	the	the	DET
ap-7596	294	3	preparation	preparation	NOUN
ap-7596	294	4	of	of	ADP
ap-7596	294	5	this	this	DET
ap-7596	294	6	work	work	NOUN
ap-7596	294	7	,	,	PUNCT
ap-7596	294	8	the	the	DET
ap-7596	294	9	author	author	NOUN
ap-7596	294	10	was	be	AUX
ap-7596	294	11	financially	financially	ADV
ap-7596	294	12	supported	support	VERB
ap-7596	294	13	by	by	ADP
ap-7596	294	14	the	the	DET
ap-7596	294	15	research	research	NOUN
ap-7596	294	16	grant	grant	NOUN
ap-7596	294	17	pid2019	pid2019	X
ap-7596	294	18	-	-	PUNCT
ap-7596	294	19	106802gbi00	106802gbi00	NUM
ap-7596	294	20	/	/	SYM
ap-7596	294	21	aei/10.13039/501100011033	aei/10.13039/501100011033	PROPN
ap-7596	294	22	(	(	PUNCT
ap-7596	294	23	aei/	aei/	PROPN
ap-7596	294	24	feder	feder	PROPN
ap-7596	294	25	,	,	PUNCT
ap-7596	294	26	ue	ue	PROPN
ap-7596	294	27	)	)	PUNCT
ap-7596	294	28	.	.	PUNCT
ap-7596	295	1	references	reference	NOUN
ap-7596	295	2	[	[	X
ap-7596	295	3	1	1	NUM
ap-7596	295	4	]	]	PUNCT
ap-7596	295	5	a.	a.	NOUN
ap-7596	295	6	m.	m.	NOUN
ap-7596	295	7	perelomov	perelomov	PROPN
ap-7596	295	8	.	.	PUNCT
ap-7596	296	1	integrable	integrable	ADJ
ap-7596	296	2	systems	system	NOUN
ap-7596	296	3	of	of	ADP
ap-7596	296	4	classical	classical	ADJ
ap-7596	296	5	mechanics	mechanic	NOUN
ap-7596	296	6	and	and	CCONJ
ap-7596	296	7	lie	lie	NOUN
ap-7596	296	8	algebras	algebras	PROPN
ap-7596	296	9	.	.	PUNCT
ap-7596	297	1	birkhäuser	birkhäuser	PROPN
ap-7596	297	2	verlag	verlag	PROPN
ap-7596	297	3	,	,	PUNCT
ap-7596	297	4	basel	basel	PROPN
ap-7596	297	5	,	,	PUNCT
ap-7596	297	6	1990	1990	NUM
ap-7596	297	7	.	.	PUNCT
ap-7596	298	1	[	[	X
ap-7596	298	2	2	2	NUM
ap-7596	298	3	]	]	PUNCT
ap-7596	298	4	l.	l.	PROPN
ap-7596	298	5	freidel	freidel	PROPN
ap-7596	298	6	,	,	PUNCT
ap-7596	298	7	j.	j.	PROPN
ap-7596	298	8	m.	m.	PROPN
ap-7596	298	9	maillet	maillet	PROPN
ap-7596	298	10	.	.	PUNCT
ap-7596	299	1	quadratic	quadratic	ADJ
ap-7596	299	2	algebras	algebra	NOUN
ap-7596	299	3	and	and	CCONJ
ap-7596	299	4	integrable	integrable	ADJ
ap-7596	299	5	systems	system	NOUN
ap-7596	299	6	.	.	PUNCT
ap-7596	300	1	physics	physics	NOUN
ap-7596	300	2	letters	letter	NOUN
ap-7596	300	3	b	b	PROPN
ap-7596	300	4	262(2	262(2	NUM
ap-7596	300	5	-	-	SYM
ap-7596	300	6	3):278–284	3):278–284	NUM
ap-7596	300	7	,	,	PUNCT
ap-7596	300	8	1991	1991	NUM
ap-7596	300	9	.	.	PUNCT
ap-7596	301	1	https://doi.org/10.1016/0370-2693(91)91566-e	https://doi.org/10.1016/0370-2693(91)91566-e	NOUN
ap-7596	301	2	.	.	PUNCT
ap-7596	302	1	[	[	X
ap-7596	302	2	3	3	X
ap-7596	302	3	]	]	PUNCT
ap-7596	302	4	p.	p.	NOUN
ap-7596	302	5	tempesta	tempesta	PROPN
ap-7596	302	6	,	,	PUNCT
ap-7596	302	7	a.	a.	NOUN
ap-7596	302	8	v.	v.	PROPN
ap-7596	302	9	turbiner	turbiner	NOUN
ap-7596	302	10	,	,	PUNCT
ap-7596	302	11	p.	p.	PROPN
ap-7596	302	12	winternitz	winternitz	PROPN
ap-7596	302	13	.	.	PUNCT
ap-7596	303	1	exact	exact	ADJ
ap-7596	303	2	solvability	solvability	NOUN
ap-7596	303	3	of	of	ADP
ap-7596	303	4	superintegrable	superintegrable	ADJ
ap-7596	303	5	systems	system	NOUN
ap-7596	303	6	.	.	PUNCT
ap-7596	304	1	journal	journal	PROPN
ap-7596	304	2	of	of	ADP
ap-7596	304	3	mathematical	mathematical	ADJ
ap-7596	304	4	physics	physics	NOUN
ap-7596	304	5	42(9):4248	42(9):4248	PROPN
ap-7596	304	6	,	,	PUNCT
ap-7596	304	7	2001	2001	NUM
ap-7596	304	8	.	.	PUNCT
ap-7596	305	1	https://doi.org/10.1063/1.1386927	https://doi.org/10.1063/1.1386927	X
ap-7596	305	2	.	.	PUNCT
ap-7596	306	1	[	[	X
ap-7596	306	2	4	4	NUM
ap-7596	306	3	]	]	X
ap-7596	306	4	f.	f.	PROPN
ap-7596	306	5	tremblay	tremblay	PROPN
ap-7596	306	6	,	,	PUNCT
ap-7596	306	7	a.	a.	NOUN
ap-7596	306	8	turbiner	turbiner	NOUN
ap-7596	306	9	,	,	PUNCT
ap-7596	306	10	p.	p.	PROPN
ap-7596	306	11	winternitz	winternitz	PROPN
ap-7596	306	12	.	.	PUNCT
ap-7596	307	1	an	an	DET
ap-7596	307	2	infinite	infinite	ADJ
ap-7596	307	3	family	family	NOUN
ap-7596	307	4	of	of	ADP
ap-7596	307	5	solvable	solvable	ADJ
ap-7596	307	6	and	and	CCONJ
ap-7596	307	7	integrable	integrable	ADJ
ap-7596	307	8	quantum	quantum	NOUN
ap-7596	307	9	systems	system	NOUN
ap-7596	307	10	on	on	ADP
ap-7596	307	11	a	a	DET
ap-7596	307	12	plane	plane	NOUN
ap-7596	307	13	.	.	PUNCT
ap-7596	308	1	journal	journal	PROPN
ap-7596	308	2	of	of	ADP
ap-7596	308	3	physics	physics	PROPN
ap-7596	308	4	a	a	PRON
ap-7596	308	5	:	:	PUNCT
ap-7596	308	6	mathematical	mathematical	ADJ
ap-7596	308	7	and	and	CCONJ
ap-7596	308	8	theoretical	theoretical	ADJ
ap-7596	308	9	42(24):242001	42(24):242001	NUM
ap-7596	308	10	,	,	PUNCT
ap-7596	308	11	2009	2009	NUM
ap-7596	308	12	.	.	PUNCT
ap-7596	309	1	https://doi.org/10.1088/1751-8113/42/24/242001	https://doi.org/10.1088/1751-8113/42/24/242001	PROPN
ap-7596	309	2	.	.	PUNCT
ap-7596	310	1	[	[	X
ap-7596	310	2	5	5	X
ap-7596	310	3	]	]	PUNCT
ap-7596	310	4	p.	p.	PROPN
ap-7596	310	5	letourneau	letourneau	PROPN
ap-7596	310	6	,	,	PUNCT
ap-7596	310	7	l.	l.	PROPN
ap-7596	310	8	vinet	vinet	PROPN
ap-7596	310	9	.	.	PUNCT
ap-7596	311	1	superintegrable	superintegrable	ADJ
ap-7596	311	2	systems	system	NOUN
ap-7596	311	3	:	:	PUNCT
ap-7596	311	4	polynomial	polynomial	ADJ
ap-7596	311	5	algebras	algebra	NOUN
ap-7596	311	6	and	and	CCONJ
ap-7596	311	7	quasi	quasi	ADJ
ap-7596	311	8	-	-	ADJ
ap-7596	311	9	exactly	exactly	ADV
ap-7596	311	10	solvable	solvable	ADJ
ap-7596	311	11	hamiltonian	hamiltonian	NOUN
ap-7596	311	12	.	.	PUNCT
ap-7596	312	1	annals	annal	NOUN
ap-7596	312	2	of	of	ADP
ap-7596	312	3	physics	physics	NOUN
ap-7596	312	4	243(1):144–168	243(1):144–168	PROPN
ap-7596	312	5	,	,	PUNCT
ap-7596	312	6	1995	1995	NUM
ap-7596	312	7	.	.	PUNCT
ap-7596	313	1	https://doi.org/10.1006/aphy.1995.1094	https://doi.org/10.1006/aphy.1995.1094	PROPN
ap-7596	313	2	.	.	PUNCT
ap-7596	314	1	[	[	X
ap-7596	314	2	6	6	NUM
ap-7596	314	3	]	]	PUNCT
ap-7596	314	4	w.	w.	PROPN
ap-7596	314	5	miller	miller	PROPN
ap-7596	314	6	,	,	PUNCT
ap-7596	314	7	s.	s.	PROPN
ap-7596	314	8	post	post	PROPN
ap-7596	314	9	,	,	PUNCT
ap-7596	314	10	p.	p.	PROPN
ap-7596	314	11	winternitz	winternitz	PROPN
ap-7596	314	12	.	.	PUNCT
ap-7596	315	1	classical	classical	ADJ
ap-7596	315	2	and	and	CCONJ
ap-7596	315	3	quantum	quantum	ADJ
ap-7596	315	4	superintegrability	superintegrability	NOUN
ap-7596	315	5	with	with	ADP
ap-7596	315	6	applications	application	NOUN
ap-7596	315	7	.	.	PUNCT
ap-7596	316	1	journal	journal	PROPN
ap-7596	316	2	of	of	ADP
ap-7596	316	3	physics	physics	PROPN
ap-7596	316	4	a	a	PRON
ap-7596	316	5	:	:	PUNCT
ap-7596	316	6	mathematical	mathematical	ADJ
ap-7596	316	7	and	and	CCONJ
ap-7596	316	8	theoretical	theoretical	ADJ
ap-7596	316	9	46(42):423001	46(42):423001	NUM
ap-7596	316	10	,	,	PUNCT
ap-7596	316	11	2013	2013	NUM
ap-7596	316	12	.	.	PUNCT
ap-7596	317	1	https://doi.org/10.1088/1751-8113/46/42/423001	https://doi.org/10.1088/1751-8113/46/42/423001	NOUN
ap-7596	317	2	.	.	PUNCT
ap-7596	318	1	[	[	X
ap-7596	318	2	7	7	X
ap-7596	318	3	]	]	X
ap-7596	318	4	c.	c.	NOUN
ap-7596	318	5	daskaloyannis	daskaloyannis	PROPN
ap-7596	318	6	,	,	PUNCT
ap-7596	318	7	y.	y.	PROPN
ap-7596	318	8	tanoudis	tanoudis	PROPN
ap-7596	318	9	.	.	PUNCT
ap-7596	319	1	quadratic	quadratic	ADJ
ap-7596	319	2	algebras	algebra	NOUN
ap-7596	319	3	for	for	ADP
ap-7596	319	4	three	three	NUM
ap-7596	319	5	-	-	PUNCT
ap-7596	319	6	dimensional	dimensional	ADJ
ap-7596	319	7	superintegrable	superintegrable	ADJ
ap-7596	319	8	systems	system	NOUN
ap-7596	319	9	.	.	PUNCT
ap-7596	320	1	physics	physics	PROPN
ap-7596	320	2	of	of	ADP
ap-7596	320	3	atomic	atomic	ADJ
ap-7596	320	4	nuclei	nucleus	NOUN
ap-7596	320	5	73:214–221	73:214–221	PROPN
ap-7596	320	6	,	,	PUNCT
ap-7596	320	7	2010	2010	NUM
ap-7596	320	8	.	.	PUNCT
ap-7596	321	1	https://doi.org/10.1134/s106377881002002x	https://doi.org/10.1134/s106377881002002x	NOUN
ap-7596	321	2	.	.	PUNCT
ap-7596	322	1	[	[	X
ap-7596	322	2	8	8	NUM
ap-7596	322	3	]	]	X
ap-7596	322	4	d.	d.	PROPN
ap-7596	322	5	latini	latini	PROPN
ap-7596	322	6	,	,	PUNCT
ap-7596	322	7	i.	i.	PROPN
ap-7596	322	8	marquette	marquette	PROPN
ap-7596	322	9	,	,	PUNCT
ap-7596	322	10	y.-z	y.-z	PROPN
ap-7596	322	11	.	.	PUNCT
ap-7596	323	1	zhang	zhang	PROPN
ap-7596	323	2	.	.	PUNCT
ap-7596	324	1	embedding	embed	VERB
ap-7596	324	2	of	of	ADP
ap-7596	324	3	the	the	DET
ap-7596	324	4	racah	racah	NOUN
ap-7596	324	5	algebra	algebra	PROPN
ap-7596	324	6	r(n	r(n	PROPN
ap-7596	324	7	)	)	PUNCT
ap-7596	324	8	and	and	CCONJ
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ap-7596	324	10	.	.	PUNCT
ap-7596	325	1	annals	annal	NOUN
ap-7596	325	2	of	of	ADP
ap-7596	325	3	physics	physics	NOUN
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ap-7596	325	5	,	,	PUNCT
ap-7596	325	6	2021	2021	NUM
ap-7596	325	7	.	.	PUNCT
ap-7596	326	1	https://doi.org/10.1016/j.aop.2021.168397	https://doi.org/10.1016/j.aop.2021.168397	X
ap-7596	326	2	.	.	PUNCT
ap-7596	327	1	[	[	X
ap-7596	327	2	9	9	NUM
ap-7596	327	3	]	]	X
ap-7596	327	4	r.	r.	PROPN
ap-7596	327	5	campoamor	campoamor	PROPN
ap-7596	327	6	-	-	PUNCT
ap-7596	327	7	stursberg	stursberg	PROPN
ap-7596	327	8	,	,	PUNCT
ap-7596	327	9	i.	i.	PROPN
ap-7596	327	10	marquette	marquette	PROPN
ap-7596	327	11	.	.	PUNCT
ap-7596	328	1	quadratic	quadratic	ADJ
ap-7596	328	2	algebras	algebra	NOUN
ap-7596	328	3	as	as	ADP
ap-7596	328	4	commutants	commutant	NOUN
ap-7596	328	5	of	of	ADP
ap-7596	328	6	algebraic	algebraic	ADJ
ap-7596	328	7	hamiltonians	hamiltonian	NOUN
ap-7596	328	8	in	in	ADP
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ap-7596	328	10	enveloping	enveloping	NOUN
ap-7596	328	11	algebra	algebra	NOUN
ap-7596	328	12	of	of	ADP
ap-7596	328	13	schrödinger	schrödinger	ADJ
ap-7596	328	14	algebras	algebra	NOUN
ap-7596	328	15	.	.	PUNCT
ap-7596	329	1	annals	annal	NOUN
ap-7596	329	2	of	of	ADP
ap-7596	329	3	physics	physics	NOUN
ap-7596	329	4	437:168694	437:168694	NUM
ap-7596	329	5	,	,	PUNCT
ap-7596	329	6	2022	2022	NUM
ap-7596	329	7	.	.	PUNCT
ap-7596	330	1	https://doi.org/10.1016/j.aop.2021.168694	https://doi.org/10.1016/j.aop.2021.168694	PROPN
ap-7596	330	2	.	.	PUNCT
ap-7596	331	1	[	[	X
ap-7596	331	2	10	10	NUM
ap-7596	331	3	]	]	X
ap-7596	331	4	r.	r.	PROPN
ap-7596	331	5	campoamor	campoamor	PROPN
ap-7596	331	6	-	-	PUNCT
ap-7596	331	7	stursberg	stursberg	PROPN
ap-7596	331	8	,	,	PUNCT
ap-7596	331	9	i.	i.	PROPN
ap-7596	331	10	marquette	marquette	PROPN
ap-7596	331	11	.	.	PUNCT
ap-7596	332	1	hidden	hide	VERB
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ap-7596	332	6	of	of	ADP
ap-7596	332	7	quadratic	quadratic	ADJ
ap-7596	332	8	algebras	algebra	NOUN
ap-7596	332	9	of	of	ADP
ap-7596	332	10	superintegrable	superintegrable	ADJ
ap-7596	332	11	systems	system	NOUN
ap-7596	332	12	.	.	PUNCT
ap-7596	333	1	annals	annal	NOUN
ap-7596	333	2	of	of	ADP
ap-7596	333	3	physics	physics	NOUN
ap-7596	333	4	424:168378	424:168378	PROPN
ap-7596	333	5	,	,	PUNCT
ap-7596	333	6	2021	2021	NUM
ap-7596	333	7	.	.	PUNCT
ap-7596	334	1	https://doi.org/10.1016/j.aop.2020.168378	https://doi.org/10.1016/j.aop.2020.168378	X
ap-7596	334	2	.	.	PUNCT
ap-7596	335	1	[	[	X
ap-7596	335	2	11	11	NUM
ap-7596	335	3	]	]	PUNCT
ap-7596	335	4	j.	j.	PROPN
ap-7596	335	5	dixmier	dixmier	PROPN
ap-7596	335	6	.	.	PUNCT
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ap-7596	336	2	enveloppantes	enveloppante	NOUN
ap-7596	336	3	.	.	PUNCT
ap-7596	337	1	hermann	hermann	PROPN
ap-7596	337	2	,	,	PUNCT
ap-7596	337	3	paris	paris	PROPN
ap-7596	337	4	,	,	PUNCT
ap-7596	337	5	1974	1974	NUM
ap-7596	337	6	.	.	PUNCT
ap-7596	338	1	[	[	X
ap-7596	338	2	12	12	NUM
ap-7596	338	3	]	]	PUNCT
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ap-7596	338	5	a.	a.	NOUN
ap-7596	338	6	shifman	shifman	PROPN
ap-7596	338	7	,	,	PUNCT
ap-7596	338	8	a.	a.	NOUN
ap-7596	338	9	v.	v.	PROPN
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ap-7596	338	11	.	.	PUNCT
ap-7596	339	1	quantal	quantal	ADJ
ap-7596	339	2	problems	problem	NOUN
ap-7596	339	3	with	with	ADP
ap-7596	339	4	partial	partial	ADJ
ap-7596	339	5	algebraization	algebraization	NOUN
ap-7596	339	6	of	of	ADP
ap-7596	339	7	the	the	DET
ap-7596	339	8	spectrum	spectrum	NOUN
ap-7596	339	9	.	.	PUNCT
ap-7596	340	1	communications	communication	NOUN
ap-7596	340	2	in	in	ADP
ap-7596	340	3	mathematical	mathematical	ADJ
ap-7596	340	4	physics	physics	NOUN
ap-7596	340	5	126:347–365	126:347–365	NUM
ap-7596	340	6	,	,	PUNCT
ap-7596	340	7	1989	1989	NUM
ap-7596	340	8	.	.	PUNCT
ap-7596	341	1	https://doi.org/10.1007/bf02125129	https://doi.org/10.1007/bf02125129	X
ap-7596	341	2	.	.	PUNCT
ap-7596	342	1	[	[	X
ap-7596	342	2	13	13	NUM
ap-7596	342	3	]	]	PUNCT
ap-7596	342	4	a.	a.	NOUN
ap-7596	342	5	v.	v.	PROPN
ap-7596	342	6	turbiner	turbiner	PROPN
ap-7596	342	7	,	,	PUNCT
ap-7596	342	8	a.	a.	NOUN
ap-7596	342	9	g.	g.	PROPN
ap-7596	342	10	ushveridze	ushveridze	PROPN
ap-7596	342	11	.	.	PUNCT
ap-7596	343	1	spectral	spectral	ADJ
ap-7596	343	2	singularities	singularity	NOUN
ap-7596	343	3	and	and	CCONJ
ap-7596	343	4	quasi	quasi	ADJ
ap-7596	343	5	-	-	ADJ
ap-7596	343	6	exactly	exactly	ADV
ap-7596	343	7	solvable	solvable	ADJ
ap-7596	343	8	quantal	quantal	ADJ
ap-7596	343	9	problem	problem	NOUN
ap-7596	343	10	.	.	PUNCT
ap-7596	344	1	physics	physics	NOUN
ap-7596	344	2	letters	letter	NOUN
ap-7596	344	3	a	a	DET
ap-7596	344	4	126(3):181–183	126(3):181–183	NUM
ap-7596	344	5	,	,	PUNCT
ap-7596	344	6	1987	1987	NUM
ap-7596	344	7	.	.	PUNCT
ap-7596	345	1	https://doi.org/10.1016/0375-9601(87)90456-7	https://doi.org/10.1016/0375-9601(87)90456-7	NOUN
ap-7596	345	2	.	.	PUNCT
ap-7596	346	1	[	[	X
ap-7596	346	2	14	14	NUM
ap-7596	346	3	]	]	X
ap-7596	346	4	m.	m.	NOUN
ap-7596	346	5	a.	a.	NOUN
ap-7596	346	6	rodríguez	rodríguez	PROPN
ap-7596	346	7	,	,	PUNCT
ap-7596	346	8	p.	p.	PROPN
ap-7596	346	9	winternitz	winternitz	PROPN
ap-7596	346	10	.	.	PUNCT
ap-7596	347	1	quantum	quantum	ADJ
ap-7596	347	2	superintegrability	superintegrability	NOUN
ap-7596	347	3	and	and	CCONJ
ap-7596	347	4	exact	exact	ADJ
ap-7596	347	5	solvability	solvability	NOUN
ap-7596	347	6	in	in	ADP
ap-7596	347	7	n	n	ADP
ap-7596	347	8	dimensions	dimension	NOUN
ap-7596	347	9	.	.	PUNCT
ap-7596	348	1	journal	journal	PROPN
ap-7596	348	2	of	of	ADP
ap-7596	348	3	mathematical	mathematical	ADJ
ap-7596	348	4	physics	physics	PROPN
ap-7596	348	5	43:1309–1322	43:1309–1322	PROPN
ap-7596	348	6	,	,	PUNCT
ap-7596	348	7	2002	2002	NUM
ap-7596	348	8	.	.	PUNCT
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ap-7596	349	2	.	.	PUNCT
ap-7596	350	1	[	[	X
ap-7596	350	2	15	15	NUM
ap-7596	350	3	]	]	X
ap-7596	350	4	a.	a.	NOUN
ap-7596	350	5	sergyeyev	sergyeyev	PROPN
ap-7596	350	6	.	.	PUNCT
ap-7596	351	1	exact	exact	ADJ
ap-7596	351	2	solvability	solvability	NOUN
ap-7596	351	3	of	of	ADP
ap-7596	351	4	superintegrable	superintegrable	ADJ
ap-7596	351	5	benenti	benenti	PROPN
ap-7596	351	6	systems	system	NOUN
ap-7596	351	7	.	.	PUNCT
ap-7596	352	1	journal	journal	PROPN
ap-7596	352	2	of	of	ADP
ap-7596	352	3	mathematical	mathematical	ADJ
ap-7596	352	4	physics	physics	NOUN
ap-7596	352	5	48(5):052114	48(5):052114	NUM
ap-7596	352	6	,	,	PUNCT
ap-7596	352	7	2007	2007	NUM
ap-7596	352	8	.	.	PUNCT
ap-7596	353	1	https://doi.org/10.1063/1.2738829	https://doi.org/10.1063/1.2738829	X
ap-7596	353	2	.	.	PUNCT
ap-7596	354	1	[	[	X
ap-7596	354	2	16	16	X
ap-7596	354	3	]	]	X
ap-7596	354	4	v.	v.	ADP
ap-7596	354	5	ovsienko	ovsienko	PROPN
ap-7596	354	6	,	,	PUNCT
ap-7596	354	7	a.	a.	NOUN
ap-7596	354	8	v.	v.	PROPN
ap-7596	354	9	turbiner	turbiner	NOUN
ap-7596	354	10	.	.	PUNCT
ap-7596	355	1	plongements	plongement	NOUN
ap-7596	355	2	d’une	d’une	VERB
ap-7596	355	3	algèbre	algèbre	ADV
ap-7596	355	4	de	de	X
ap-7596	355	5	lie	lie	NOUN
ap-7596	355	6	dans	dan	NOUN
ap-7596	355	7	son	son	VERB
ap-7596	355	8	algèbre	algèbre	PROPN
ap-7596	355	9	enveloppante	enveloppante	PROPN
ap-7596	355	10	.	.	PUNCT
ap-7596	356	1	comptes	compte	VERB
ap-7596	356	2	rendus	rendus	PROPN
ap-7596	356	3	de	de	PROPN
ap-7596	356	4	l’académie	l’académie	PROPN
ap-7596	356	5	des	des	PROPN
ap-7596	356	6	sciences	sciences	PROPN
ap-7596	356	7	paris	paris	PROPN
ap-7596	356	8	314:13–16	314:13–16	NUM
ap-7596	356	9	,	,	PUNCT
ap-7596	356	10	1992	1992	NUM
ap-7596	356	11	.	.	PUNCT
ap-7596	357	1	[	[	X
ap-7596	357	2	17	17	NUM
ap-7596	357	3	]	]	PUNCT
ap-7596	357	4	a.	a.	NOUN
ap-7596	357	5	verona	verona	PROPN
ap-7596	357	6	.	.	PUNCT
ap-7596	358	1	introducere	introducere	PROPN
ap-7596	358	2	in	in	ADP
ap-7596	358	3	coomologia	coomologia	NOUN
ap-7596	358	4	algebrelor	algebrelor	NOUN
ap-7596	358	5	lie	lie	NOUN
ap-7596	358	6	.	.	PUNCT
ap-7596	359	1	editura	editura	PROPN
ap-7596	359	2	academiei	academiei	PROPN
ap-7596	359	3	rep	rep	PROPN
ap-7596	359	4	.	.	PROPN
ap-7596	359	5	soc	soc	PROPN
ap-7596	359	6	.	.	PUNCT
ap-7596	360	1	românia	românia	PROPN
ap-7596	360	2	,	,	PUNCT
ap-7596	360	3	bucuresti	bucuresti	PROPN
ap-7596	360	4	,	,	PUNCT
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ap-7596	360	6	.	.	PUNCT
ap-7596	361	1	[	[	X
ap-7596	361	2	18	18	NUM
ap-7596	361	3	]	]	X
ap-7596	361	4	r.	r.	PROPN
ap-7596	361	5	t.	t.	PROPN
ap-7596	361	6	sharp	sharp	PROPN
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ap-7596	361	9	s.	s.	PROPN
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ap-7596	361	11	.	.	PUNCT
ap-7596	362	1	internal	internal	ADJ
ap-7596	362	2	-	-	PUNCT
ap-7596	362	3	labeling	labeling	NOUN
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ap-7596	362	5	.	.	PUNCT
ap-7596	363	1	journal	journal	PROPN
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ap-7596	363	4	physics	physics	PROPN
ap-7596	363	5	10(11):2033–2038	10(11):2033–2038	PROPN
ap-7596	363	6	,	,	PUNCT
ap-7596	363	7	1969	1969	NUM
ap-7596	363	8	.	.	PUNCT
ap-7596	364	1	https://doi.org/10.1063/1.1664799	https://doi.org/10.1063/1.1664799	PROPN
ap-7596	364	2	.	.	PUNCT
ap-7596	365	1	21	21	NUM
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ap-7596	367	8	-	-	PUNCT
ap-7596	367	9	stursberg	stursberg	PROPN
ap-7596	367	10	acta	acta	PROPN
ap-7596	367	11	polytechnica	polytechnica	PROPN
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ap-7596	368	8	lassner	lassner	PROPN
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ap-7596	369	1	an	an	DET
ap-7596	369	2	extension	extension	NOUN
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ap-7596	369	4	buchberger	buchberger	NOUN
ap-7596	369	5	’s	’s	PART
ap-7596	369	6	algorithm	algorithm	NOUN
ap-7596	369	7	and	and	CCONJ
ap-7596	369	8	calculations	calculation	NOUN
ap-7596	369	9	in	in	ADP
ap-7596	369	10	enveloping	envelop	VERB
ap-7596	369	11	fields	field	NOUN
ap-7596	369	12	of	of	ADP
ap-7596	369	13	lie	lie	NOUN
ap-7596	369	14	algebras	algebras	PROPN
ap-7596	369	15	.	.	PUNCT
ap-7596	370	1	journal	journal	PROPN
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ap-7596	370	3	symbolic	symbolic	ADJ
ap-7596	370	4	computation	computation	NOUN
ap-7596	370	5	6(2	6(2	NUM
ap-7596	370	6	-	-	SYM
ap-7596	370	7	3):361–370	3):361–370	NUM
ap-7596	370	8	,	,	PUNCT
ap-7596	370	9	1988	1988	NUM
ap-7596	370	10	.	.	PUNCT
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ap-7596	372	5	g.	g.	PROPN
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ap-7596	372	7	,	,	PUNCT
ap-7596	372	8	j.	j.	PROPN
ap-7596	372	9	patera	patera	PROPN
ap-7596	372	10	.	.	PUNCT
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ap-7596	373	2	of	of	ADP
ap-7596	373	3	dimensions	dimension	NOUN
ap-7596	373	4	,	,	PUNCT
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ap-7596	373	6	and	and	CCONJ
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ap-7596	373	8	rules	rule	NOUN
ap-7596	373	9	for	for	ADP
ap-7596	373	10	representations	representation	NOUN
ap-7596	373	11	of	of	ADP
ap-7596	373	12	simple	simple	ADJ
ap-7596	373	13	lie	lie	NOUN
ap-7596	373	14	algebras	algebra	NOUN
ap-7596	373	15	.	.	PUNCT
ap-7596	374	1	marcel	marcel	PROPN
ap-7596	374	2	dekker	dekker	PROPN
ap-7596	374	3	,	,	PUNCT
ap-7596	374	4	new	new	PROPN
ap-7596	374	5	york	york	PROPN
ap-7596	374	6	,	,	PUNCT
ap-7596	374	7	1981	1981	NUM
ap-7596	374	8	.	.	PUNCT
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ap-7596	375	2	21	21	NUM
ap-7596	375	3	]	]	X
ap-7596	375	4	r.	r.	PROPN
ap-7596	375	5	campoamor	campoamor	PROPN
ap-7596	375	6	-	-	PUNCT
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ap-7596	375	8	.	.	PUNCT
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ap-7596	376	8	semidirect	semidirect	NOUN
ap-7596	376	9	products	product	NOUN
ap-7596	376	10	of	of	ADP
ap-7596	376	11	the	the	DET
ap-7596	376	12	exceptional	exceptional	ADJ
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ap-7596	376	21	.	.	PUNCT
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ap-7596	377	2	of	of	ADP
ap-7596	377	3	physics	physics	PROPN
ap-7596	377	4	a	a	PRON
ap-7596	377	5	:	:	PUNCT
ap-7596	377	6	mathematical	mathematical	ADJ
ap-7596	377	7	and	and	CCONJ
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ap-7596	377	9	37(40):9451–9466	37(40):9451–9466	NUM
ap-7596	377	10	,	,	PUNCT
ap-7596	377	11	2004	2004	NUM
ap-7596	377	12	.	.	PUNCT
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ap-7596	378	2	.	.	PUNCT
ap-7596	379	1	[	[	X
ap-7596	379	2	22	22	NUM
ap-7596	379	3	]	]	PUNCT
ap-7596	379	4	r.	r.	PROPN
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ap-7596	379	6	-	-	PUNCT
ap-7596	379	7	stursberg	stursberg	PROPN
ap-7596	379	8	,	,	PUNCT
ap-7596	379	9	i.	i.	PROPN
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ap-7596	380	3	pseudo	pseudo	NOUN
ap-7596	380	4	-	-	NOUN
ap-7596	380	5	galilean	galilean	PROPN
ap-7596	380	6	algebras	algebra	NOUN
ap-7596	380	7	and	and	CCONJ
ap-7596	380	8	their	their	PRON
ap-7596	380	9	casimir	casimir	NOUN
ap-7596	380	10	operators	operator	NOUN
ap-7596	380	11	.	.	PUNCT
ap-7596	381	1	journal	journal	PROPN
ap-7596	381	2	of	of	ADP
ap-7596	381	3	physics	physics	PROPN
ap-7596	381	4	a	a	PRON
ap-7596	381	5	:	:	PUNCT
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ap-7596	381	7	and	and	CCONJ
ap-7596	381	8	theoretical	theoretical	ADJ
ap-7596	381	9	52(47):475202	52(47):475202	PROPN
ap-7596	381	10	,	,	PUNCT
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ap-7596	381	12	.	.	PUNCT
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ap-7596	383	8	n.	n.	PROPN
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ap-7596	385	5	fields	field	NOUN
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ap-7596	385	7	the	the	DET
ap-7596	385	8	real	real	ADJ
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ap-7596	385	10	.	.	PUNCT
ap-7596	386	1	proceedings	proceeding	NOUN
ap-7596	386	2	of	of	ADP
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ap-7596	386	10	.	.	PUNCT
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ap-7596	387	2	.	.	PUNCT
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ap-7596	388	2	24	24	NUM
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ap-7596	388	5	a.	a.	PROPN
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ap-7596	388	9	d.	d.	PROPN
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ap-7596	389	12	superalgebra	superalgebra	NOUN
ap-7596	389	13	.	.	PUNCT
ap-7596	390	1	journal	journal	PROPN
ap-7596	390	2	of	of	ADP
ap-7596	390	3	physics	physics	PROPN
ap-7596	390	4	a	a	PRON
ap-7596	390	5	:	:	PUNCT
ap-7596	390	6	mathematical	mathematical	ADJ
ap-7596	390	7	and	and	CCONJ
ap-7596	390	8	theoretical	theoretical	ADJ
ap-7596	390	9	51(14):145203	51(14):145203	NUM
ap-7596	390	10	,	,	PUNCT
ap-7596	390	11	2018	2018	NUM
ap-7596	390	12	.	.	PUNCT
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ap-7596	392	2	25	25	NUM
ap-7596	392	3	]	]	PUNCT
ap-7596	392	4	p.	p.	NOUN
ap-7596	392	5	gaboriaud	gaboriaud	PROPN
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ap-7596	392	7	l.	l.	PROPN
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ap-7596	392	10	s.	s.	PROPN
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ap-7596	392	12	,	,	PUNCT
ap-7596	392	13	a.	a.	PROPN
ap-7596	392	14	zhedanov	zhedanov	PROPN
ap-7596	392	15	.	.	PUNCT
ap-7596	393	1	the	the	DET
ap-7596	393	2	generalized	generalized	ADJ
ap-7596	393	3	racah	racah	NOUN
ap-7596	393	4	algebra	algebra	NOUN
ap-7596	393	5	as	as	ADP
ap-7596	393	6	a	a	DET
ap-7596	393	7	commutant	commutant	NOUN
ap-7596	393	8	.	.	PUNCT
ap-7596	394	1	journal	journal	PROPN
ap-7596	394	2	of	of	ADP
ap-7596	394	3	physics	physics	PROPN
ap-7596	394	4	:	:	PUNCT
ap-7596	394	5	conference	conference	NOUN
ap-7596	394	6	series	series	NOUN
ap-7596	394	7	1194:012034	1194:012034	NUM
ap-7596	394	8	,	,	PUNCT
ap-7596	394	9	2019	2019	NUM
ap-7596	394	10	.	.	PUNCT
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ap-7596	395	2	.	.	PUNCT
ap-7596	396	1	22	22	NUM
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ap-7596	396	11	,	,	PUNCT
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ap-7596	396	13	1	1	NUM
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ap-7596	396	15	2	2	NUM
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ap-7596	396	19	3	3	NUM
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ap-7596	396	21	in	in	ADP
ap-7596	396	22	enveloping	envelop	VERB
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ap-7596	396	26	representations	representation	NOUN
ap-7596	396	27	4	4	NUM
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ap-7596	396	29	copies	copy	NOUN
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ap-7596	396	35	acknowledgements	acknowledgement	NOUN
ap-7596	396	36	references	reference	NOUN