id	sid	tid	token	lemma	pos
ap-1259	1	1	ap-5-10.dvi	ap-5-10.dvi	PROPN
ap-1259	1	2	acta	acta	PROPN
ap-1259	1	3	polytechnica	polytechnica	PROPN
ap-1259	1	4	vol	vol	NOUN
ap-1259	1	5	.	.	PROPN
ap-1259	2	1	50	50	NUM
ap-1259	2	2	no	no	NOUN
ap-1259	2	3	.	.	PUNCT
ap-1259	3	1	5/2010	5/2010	NUM
ap-1259	3	2	on	on	ADP
ap-1259	3	3	uq	uq	PROPN
ap-1259	3	4	(	(	PUNCT
ap-1259	3	5	sl2)-actions	sl2)-action	NOUN
ap-1259	3	6	on	on	ADP
ap-1259	3	7	the	the	DET
ap-1259	3	8	quantum	quantum	ADJ
ap-1259	3	9	plane	plane	NOUN
ap-1259	3	10	s.	s.	PROPN
ap-1259	3	11	duplij	duplij	PROPN
ap-1259	3	12	,	,	PUNCT
ap-1259	3	13	s.	s.	PROPN
ap-1259	3	14	sinel’shchikov	sinel’shchikov	PROPN
ap-1259	3	15	abstract	abstract	ADJ
ap-1259	3	16	to	to	PART
ap-1259	3	17	give	give	VERB
ap-1259	3	18	the	the	DET
ap-1259	3	19	complete	complete	ADJ
ap-1259	3	20	list	list	NOUN
ap-1259	3	21	of	of	ADP
ap-1259	3	22	uq	uq	PROPN
ap-1259	3	23	(	(	PUNCT
ap-1259	3	24	sl2)-actions	sl2)-action	NOUN
ap-1259	3	25	of	of	ADP
ap-1259	3	26	the	the	DET
ap-1259	3	27	quantum	quantum	ADJ
ap-1259	3	28	plane	plane	NOUN
ap-1259	3	29	,	,	PUNCT
ap-1259	3	30	we	we	PRON
ap-1259	3	31	first	first	ADV
ap-1259	3	32	obtain	obtain	VERB
ap-1259	3	33	the	the	DET
ap-1259	3	34	structure	structure	NOUN
ap-1259	3	35	of	of	ADP
ap-1259	3	36	quantum	quantum	ADJ
ap-1259	3	37	plane	plane	NOUN
ap-1259	3	38	automorphisms	automorphism	NOUN
ap-1259	3	39	.	.	PUNCT
ap-1259	4	1	then	then	ADV
ap-1259	4	2	we	we	PRON
ap-1259	4	3	introduce	introduce	VERB
ap-1259	4	4	some	some	DET
ap-1259	4	5	special	special	ADJ
ap-1259	4	6	symbolic	symbolic	ADJ
ap-1259	4	7	matrices	matrix	NOUN
ap-1259	4	8	to	to	PART
ap-1259	4	9	classify	classify	VERB
ap-1259	4	10	the	the	DET
ap-1259	4	11	series	series	NOUN
ap-1259	4	12	of	of	ADP
ap-1259	4	13	actions	action	NOUN
ap-1259	4	14	using	use	VERB
ap-1259	4	15	the	the	DET
ap-1259	4	16	weights	weight	NOUN
ap-1259	4	17	.	.	PUNCT
ap-1259	5	1	there	there	PRON
ap-1259	5	2	are	be	VERB
ap-1259	5	3	uncountably	uncountably	ADV
ap-1259	5	4	many	many	ADJ
ap-1259	5	5	isomorphism	isomorphism	NOUN
ap-1259	5	6	classes	class	NOUN
ap-1259	5	7	of	of	ADP
ap-1259	5	8	the	the	DET
ap-1259	5	9	symmetries	symmetry	NOUN
ap-1259	5	10	.	.	PUNCT
ap-1259	6	1	we	we	PRON
ap-1259	6	2	give	give	VERB
ap-1259	6	3	the	the	DET
ap-1259	6	4	classical	classical	ADJ
ap-1259	6	5	limit	limit	NOUN
ap-1259	6	6	of	of	ADP
ap-1259	6	7	the	the	DET
ap-1259	6	8	above	above	ADJ
ap-1259	6	9	actions	action	NOUN
ap-1259	6	10	.	.	PUNCT
ap-1259	7	1	keywords	keyword	NOUN
ap-1259	7	2	:	:	PUNCT
ap-1259	7	3	quantum	quantum	ADJ
ap-1259	7	4	universal	universal	NOUN
ap-1259	7	5	enveloping	enveloping	NOUN
ap-1259	7	6	algebra	algebra	NOUN
ap-1259	7	7	,	,	PUNCT
ap-1259	7	8	hopf	hopf	ADJ
ap-1259	7	9	algebra	algebra	NOUN
ap-1259	7	10	,	,	PUNCT
ap-1259	7	11	verma	verma	PROPN
ap-1259	7	12	module	module	NOUN
ap-1259	7	13	,	,	PUNCT
ap-1259	7	14	representation	representation	NOUN
ap-1259	7	15	,	,	PUNCT
ap-1259	7	16	composition	composition	NOUN
ap-1259	7	17	series	series	NOUN
ap-1259	7	18	,	,	PUNCT
ap-1259	7	19	projection	projection	NOUN
ap-1259	7	20	,	,	PUNCT
ap-1259	7	21	weight	weight	NOUN
ap-1259	7	22	.	.	PUNCT
ap-1259	8	1	we	we	PRON
ap-1259	8	2	present	present	VERB
ap-1259	8	3	and	and	CCONJ
ap-1259	8	4	classify	classify	VERB
ap-1259	8	5	uq	uq	NOUN
ap-1259	8	6	(	(	PUNCT
ap-1259	8	7	sl2)-actions	sl2)-action	NOUN
ap-1259	8	8	on	on	ADP
ap-1259	8	9	the	the	DET
ap-1259	8	10	quantum	quantum	ADJ
ap-1259	8	11	plane	plane	NOUN
ap-1259	8	12	[	[	X
ap-1259	8	13	1	1	NUM
ap-1259	8	14	]	]	PUNCT
ap-1259	8	15	.	.	PUNCT
ap-1259	9	1	the	the	DET
ap-1259	9	2	general	general	ADJ
ap-1259	9	3	form	form	NOUN
ap-1259	9	4	of	of	ADP
ap-1259	9	5	an	an	DET
ap-1259	9	6	automorphism	automorphism	NOUN
ap-1259	9	7	of	of	ADP
ap-1259	9	8	the	the	DET
ap-1259	9	9	quantum	quantum	ADJ
ap-1259	9	10	plane	plane	NOUN
ap-1259	9	11	[	[	X
ap-1259	9	12	5	5	NUM
ap-1259	9	13	]	]	PUNCT
ap-1259	9	14	allows	allow	VERB
ap-1259	9	15	us	we	PRON
ap-1259	9	16	to	to	PART
ap-1259	9	17	use	use	VERB
ap-1259	9	18	the	the	DET
ap-1259	9	19	notion	notion	NOUN
ap-1259	9	20	of	of	ADP
ap-1259	9	21	weight	weight	NOUN
ap-1259	9	22	.	.	PUNCT
ap-1259	10	1	to	to	PART
ap-1259	10	2	classify	classify	VERB
ap-1259	10	3	the	the	DET
ap-1259	10	4	actions	action	NOUN
ap-1259	10	5	we	we	PRON
ap-1259	10	6	introduce	introduce	VERB
ap-1259	10	7	a	a	DET
ap-1259	10	8	pair	pair	NOUN
ap-1259	10	9	of	of	ADP
ap-1259	10	10	symbolic	symbolic	ADJ
ap-1259	10	11	matrices	matrix	NOUN
ap-1259	10	12	,	,	PUNCT
ap-1259	10	13	which	which	PRON
ap-1259	10	14	label	label	VERB
ap-1259	10	15	the	the	DET
ap-1259	10	16	presence	presence	NOUN
ap-1259	10	17	of	of	ADP
ap-1259	10	18	nonzero	nonzero	PROPN
ap-1259	10	19	weight	weight	NOUN
ap-1259	10	20	vectors	vector	NOUN
ap-1259	10	21	.	.	PUNCT
ap-1259	11	1	finally	finally	ADV
ap-1259	11	2	,	,	PUNCT
ap-1259	11	3	we	we	PRON
ap-1259	11	4	present	present	VERB
ap-1259	11	5	the	the	DET
ap-1259	11	6	classical	classical	ADJ
ap-1259	11	7	limit	limit	NOUN
ap-1259	11	8	of	of	ADP
ap-1259	11	9	the	the	DET
ap-1259	11	10	obtained	obtain	VERB
ap-1259	11	11	actions	action	NOUN
ap-1259	11	12	.	.	PUNCT
ap-1259	12	1	the	the	DET
ap-1259	12	2	definitions	definition	NOUN
ap-1259	12	3	of	of	ADP
ap-1259	12	4	a	a	DET
ap-1259	12	5	hopf	hopf	ADJ
ap-1259	12	6	algebrah	algebrah	NOUN
ap-1259	12	7	andh	andh	NOUN
ap-1259	12	8	-	-	PUNCT
ap-1259	12	9	action	action	NOUN
ap-1259	12	10	,	,	PUNCT
ap-1259	12	11	the	the	DET
ap-1259	12	12	quantum	quantum	ADJ
ap-1259	12	13	universal	universal	NOUN
ap-1259	12	14	enveloping	envelop	VERB
ap-1259	12	15	algebra	algebra	NOUN
ap-1259	12	16	uq	uq	NOUN
ap-1259	12	17	(	(	PUNCT
ap-1259	12	18	sl2	sl2	PROPN
ap-1259	12	19	)	)	PUNCT
ap-1259	12	20	(	(	PUNCT
ap-1259	12	21	determined	determine	VERB
ap-1259	12	22	by	by	ADP
ap-1259	12	23	its	its	PRON
ap-1259	12	24	generators	generator	NOUN
ap-1259	12	25	k	k	PROPN
ap-1259	12	26	,	,	PUNCT
ap-1259	12	27	k−1	k−1	PROPN
ap-1259	12	28	,	,	PUNCT
ap-1259	12	29	e	e	PROPN
ap-1259	12	30	,	,	PUNCT
ap-1259	12	31	f	f	NOUN
ap-1259	12	32	)	)	PUNCT
ap-1259	12	33	,	,	PUNCT
ap-1259	12	34	and	and	CCONJ
ap-1259	12	35	other	other	ADJ
ap-1259	12	36	notations	notation	NOUN
ap-1259	12	37	can	can	AUX
ap-1259	12	38	be	be	AUX
ap-1259	12	39	found	find	VERB
ap-1259	12	40	in	in	ADP
ap-1259	12	41	[	[	X
ap-1259	12	42	3	3	NUM
ap-1259	12	43	]	]	PUNCT
ap-1259	12	44	.	.	PUNCT
ap-1259	13	1	the	the	DET
ap-1259	13	2	quantum	quantum	ADJ
ap-1259	13	3	plane	plane	NOUN
ap-1259	13	4	is	be	AUX
ap-1259	13	5	a	a	DET
ap-1259	13	6	unital	unital	ADJ
ap-1259	13	7	algebra	algebra	NOUN
ap-1259	13	8	cq[x	cq[x	PROPN
ap-1259	13	9	,	,	PUNCT
ap-1259	13	10	y	y	PROPN
ap-1259	13	11	]	]	PUNCT
ap-1259	13	12	generated	generate	VERB
ap-1259	13	13	by	by	ADP
ap-1259	13	14	x	x	PROPN
ap-1259	13	15	,	,	PUNCT
ap-1259	13	16	y	y	PROPN
ap-1259	13	17	and	and	CCONJ
ap-1259	13	18	the	the	DET
ap-1259	13	19	relation	relation	NOUN
ap-1259	13	20	yx	yx	PROPN
ap-1259	13	21	=	=	SYM
ap-1259	13	22	qxy	qxy	PROPN
ap-1259	13	23	,	,	PUNCT
ap-1259	13	24	and	and	CCONJ
ap-1259	13	25	we	we	PRON
ap-1259	13	26	assume	assume	VERB
ap-1259	13	27	that	that	SCONJ
ap-1259	13	28	0	0	PUNCT
ap-1259	13	29	<	<	X
ap-1259	13	30	q	q	X
ap-1259	13	31	<	<	X
ap-1259	13	32	1	1	NUM
ap-1259	13	33	.	.	PUNCT
ap-1259	14	1	the	the	DET
ap-1259	14	2	notation	notation	PROPN
ap-1259	14	3	cq[x	cq[x	PROPN
ap-1259	14	4	,	,	PUNCT
ap-1259	14	5	y]i	y]i	ADJ
ap-1259	14	6	for	for	ADP
ap-1259	14	7	the	the	DET
ap-1259	14	8	i	i	PROPN
ap-1259	14	9	-	-	PUNCT
ap-1259	14	10	th	th	X
ap-1259	14	11	homogeneous	homogeneous	ADJ
ap-1259	14	12	component	component	NOUN
ap-1259	14	13	of	of	ADP
ap-1259	14	14	cq[x	cq[x	PROPN
ap-1259	14	15	,	,	PUNCT
ap-1259	14	16	y	y	PROPN
ap-1259	14	17	]	]	X
ap-1259	14	18	,	,	PUNCT
ap-1259	14	19	being	be	AUX
ap-1259	14	20	the	the	DET
ap-1259	14	21	linear	linear	ADJ
ap-1259	14	22	span	span	NOUN
ap-1259	14	23	of	of	ADP
ap-1259	14	24	the	the	DET
ap-1259	14	25	monomials	monomial	NOUN
ap-1259	14	26	xmyn	xmyn	PROPN
ap-1259	14	27	with	with	ADP
ap-1259	14	28	m	m	PROPN
ap-1259	14	29	+	+	NOUN
ap-1259	14	30	n	n	PROPN
ap-1259	14	31	=	=	SYM
ap-1259	14	32	i	i	PROPN
ap-1259	14	33	,	,	PUNCT
ap-1259	14	34	is	be	AUX
ap-1259	14	35	used	use	VERB
ap-1259	14	36	.	.	PUNCT
ap-1259	15	1	denote	denote	VERB
ap-1259	15	2	by	by	ADP
ap-1259	15	3	(	(	PUNCT
ap-1259	15	4	p)i	p)i	X
ap-1259	15	5	the	the	DET
ap-1259	15	6	i	i	PROPN
ap-1259	15	7	-	-	PUNCT
ap-1259	15	8	th	th	X
ap-1259	15	9	homogeneous	homogeneous	ADJ
ap-1259	15	10	component	component	NOUN
ap-1259	15	11	of	of	ADP
ap-1259	15	12	a	a	DET
ap-1259	15	13	polynomial	polynomial	ADJ
ap-1259	15	14	p	p	PROPN
ap-1259	15	15	∈	∈	PROPN
ap-1259	15	16	cq[x	cq[x	NOUN
ap-1259	15	17	,	,	PUNCT
ap-1259	15	18	y	y	PROPN
ap-1259	15	19	]	]	X
ap-1259	15	20	,	,	PUNCT
ap-1259	15	21	that	that	PRON
ap-1259	15	22	is	be	AUX
ap-1259	15	23	the	the	DET
ap-1259	15	24	projection	projection	NOUN
ap-1259	15	25	of	of	ADP
ap-1259	15	26	p	p	NOUN
ap-1259	15	27	onto	onto	ADP
ap-1259	15	28	cq[x	cq[x	PROPN
ap-1259	15	29	,	,	PUNCT
ap-1259	15	30	y]i	y]i	ADJ
ap-1259	15	31	parallel	parallel	ADJ
ap-1259	15	32	to	to	ADP
ap-1259	15	33	the	the	DET
ap-1259	15	34	direct	direct	ADJ
ap-1259	15	35	sum	sum	NOUN
ap-1259	15	36	of	of	ADP
ap-1259	15	37	all	all	DET
ap-1259	15	38	other	other	ADJ
ap-1259	15	39	homogeneous	homogeneous	ADJ
ap-1259	15	40	components	component	NOUN
ap-1259	15	41	of	of	ADP
ap-1259	15	42	cq[x	cq[x	PROPN
ap-1259	15	43	,	,	PUNCT
ap-1259	15	44	y	y	PROPN
ap-1259	15	45	]	]	PUNCT
ap-1259	15	46	.	.	PUNCT
ap-1259	16	1	denote	denote	VERB
ap-1259	16	2	by	by	ADP
ap-1259	16	3	c[x	c[x	NOUN
ap-1259	16	4	]	]	X
ap-1259	16	5	and	and	CCONJ
ap-1259	16	6	c[y	c[y	NOUN
ap-1259	16	7	]	]	X
ap-1259	16	8	the	the	DET
ap-1259	16	9	linear	linear	ADJ
ap-1259	16	10	spans	span	NOUN
ap-1259	16	11	of	of	ADP
ap-1259	16	12	{	{	PUNCT
ap-1259	16	13	xn|n	xn|n	X
ap-1259	16	14	≥	≥	NOUN
ap-1259	16	15	0	0	NUM
ap-1259	16	16	}	}	PUNCT
ap-1259	16	17	and	and	CCONJ
ap-1259	16	18	{	{	PUNCT
ap-1259	16	19	yn|n	yn|n	NOUN
ap-1259	16	20	≥	≥	NOUN
ap-1259	16	21	0	0	NUM
ap-1259	16	22	}	}	PUNCT
ap-1259	16	23	,	,	PUNCT
ap-1259	16	24	respectively	respectively	ADV
ap-1259	16	25	.	.	PUNCT
ap-1259	17	1	the	the	DET
ap-1259	17	2	direct	direct	ADJ
ap-1259	17	3	sum	sum	NOUN
ap-1259	17	4	decompositions	decomposition	NOUN
ap-1259	17	5	cq[x	cq[x	NOUN
ap-1259	17	6	,	,	PUNCT
ap-1259	17	7	y	y	NOUN
ap-1259	17	8	]	]	X
ap-1259	17	9	=	=	PUNCT
ap-1259	17	10	c[x	c[x	NOUN
ap-1259	17	11	]	]	X
ap-1259	17	12	⊕	⊕	PROPN
ap-1259	17	13	ycq[x	ycq[x	PROPN
ap-1259	17	14	,	,	PUNCT
ap-1259	17	15	y	y	NOUN
ap-1259	17	16	]	]	X
ap-1259	17	17	=	=	SYM
ap-1259	17	18	c[y]⊕	c[y]⊕	ADJ
ap-1259	17	19	xcq[x	xcq[x	PROPN
ap-1259	17	20	,	,	PUNCT
ap-1259	17	21	y	y	X
ap-1259	17	22	]	]	PUNCT
ap-1259	17	23	is	be	AUX
ap-1259	17	24	obvious	obvious	ADJ
ap-1259	17	25	.	.	PUNCT
ap-1259	18	1	let	let	VERB
ap-1259	18	2	(	(	PUNCT
ap-1259	18	3	p	p	NOUN
ap-1259	18	4	)	)	PUNCT
ap-1259	18	5	x	x	X
ap-1259	18	6	be	be	AUX
ap-1259	18	7	a	a	DET
ap-1259	18	8	projection	projection	NOUN
ap-1259	18	9	of	of	ADP
ap-1259	18	10	a	a	DET
ap-1259	18	11	polynomial	polynomial	ADJ
ap-1259	18	12	p	p	PROPN
ap-1259	18	13	∈	∈	PROPN
ap-1259	18	14	cq[x	cq[x	NOUN
ap-1259	18	15	,	,	PUNCT
ap-1259	18	16	y	y	PROPN
ap-1259	18	17	]	]	X
ap-1259	18	18	to	to	PART
ap-1259	18	19	c[x	c[x	VERB
ap-1259	18	20	]	]	PUNCT
ap-1259	18	21	parallel	parallel	NOUN
ap-1259	18	22	to	to	ADP
ap-1259	18	23	ycq[x	ycq[x	PROPN
ap-1259	18	24	,	,	PUNCT
ap-1259	18	25	y	y	NOUN
ap-1259	18	26	]	]	PUNCT
ap-1259	18	27	.	.	PUNCT
ap-1259	19	1	proposition	proposition	NOUN
ap-1259	19	2	1	1	NUM
ap-1259	19	3	let	let	VERB
ap-1259	19	4	ψ	ψ	PART
ap-1259	19	5	be	be	AUX
ap-1259	19	6	an	an	DET
ap-1259	19	7	automorphism	automorphism	NOUN
ap-1259	19	8	of	of	ADP
ap-1259	19	9	cq[x	cq[x	PROPN
ap-1259	19	10	,	,	PUNCT
ap-1259	19	11	y	y	PROPN
ap-1259	19	12	]	]	X
ap-1259	19	13	,	,	PUNCT
ap-1259	19	14	then	then	ADV
ap-1259	19	15	there	there	PRON
ap-1259	19	16	exist	exist	VERB
ap-1259	19	17	nonzero	nonzero	PROPN
ap-1259	19	18	constants	constant	NOUN
ap-1259	19	19	α	α	PRON
ap-1259	19	20	,	,	PUNCT
ap-1259	19	21	β	β	NOUN
ap-1259	19	22	such	such	ADJ
ap-1259	19	23	that	that	SCONJ
ap-1259	19	24	[	[	X
ap-1259	19	25	5	5	NUM
ap-1259	19	26	]	]	SYM
ap-1259	19	27	ψ	ψ	PROPN
ap-1259	19	28	:x	:x	PROPN
ap-1259	19	29	�	�	PROPN
ap-1259	19	30	→	→	SYM
ap-1259	19	31	αx	αx	PROPN
ap-1259	19	32	,	,	PUNCT
ap-1259	19	33	y	y	PROPN
ap-1259	19	34	�	�	PROPN
ap-1259	19	35	→	→	SYM
ap-1259	19	36	βy	βy	PROPN
ap-1259	19	37	.	.	PUNCT
ap-1259	20	1	(	(	PUNCT
ap-1259	20	2	1	1	X
ap-1259	20	3	)	)	PUNCT
ap-1259	20	4	for	for	ADP
ap-1259	20	5	any	any	DET
ap-1259	20	6	uq	uq	NOUN
ap-1259	20	7	(	(	PUNCT
ap-1259	20	8	sl2)-action	sl2)-action	PROPN
ap-1259	20	9	on	on	ADP
ap-1259	20	10	cq[x	cq[x	PROPN
ap-1259	20	11	,	,	PUNCT
ap-1259	20	12	y	y	PROPN
ap-1259	20	13	]	]	X
ap-1259	20	14	,	,	PUNCT
ap-1259	20	15	we	we	PRON
ap-1259	20	16	associate	associate	VERB
ap-1259	20	17	a	a	DET
ap-1259	20	18	2×	2×	NUM
ap-1259	20	19	3	3	NUM
ap-1259	20	20	matrix	matrix	NOUN
ap-1259	20	21	,	,	PUNCT
ap-1259	20	22	to	to	PART
ap-1259	20	23	be	be	AUX
ap-1259	20	24	referred	refer	VERB
ap-1259	20	25	to	to	ADP
ap-1259	20	26	as	as	ADP
ap-1259	20	27	a	a	DET
ap-1259	20	28	full	full	ADJ
ap-1259	20	29	action	action	NOUN
ap-1259	20	30	matrix	matrix	NOUN
ap-1259	20	31	m	m	VERB
ap-1259	21	1	def	def	PROPN
ap-1259	21	2	=	=	SYM
ap-1259	21	3	∥∥∥∥∥∥∥∥	∥∥∥∥∥∥∥∥	PROPN
ap-1259	21	4	k	k	X
ap-1259	21	5	(	(	PUNCT
ap-1259	21	6	x	x	X
ap-1259	21	7	)	)	PUNCT
ap-1259	21	8	k	k	PROPN
ap-1259	21	9	(	(	PUNCT
ap-1259	21	10	y	y	NOUN
ap-1259	21	11	)	)	PUNCT
ap-1259	21	12	e	e	NOUN
ap-1259	21	13	(	(	PUNCT
ap-1259	21	14	x	x	NOUN
ap-1259	21	15	)	)	PUNCT
ap-1259	21	16	e	e	NOUN
ap-1259	21	17	(	(	PUNCT
ap-1259	21	18	y	y	PROPN
ap-1259	21	19	)	)	PUNCT
ap-1259	21	20	f	f	NOUN
ap-1259	21	21	(	(	PUNCT
ap-1259	21	22	x	x	X
ap-1259	21	23	)	)	PUNCT
ap-1259	21	24	f	f	PROPN
ap-1259	21	25	(	(	PUNCT
ap-1259	21	26	y	y	PROPN
ap-1259	21	27	)	)	PUNCT
ap-1259	21	28	∥∥∥∥∥∥∥∥	∥∥∥∥∥∥∥∥	NUM
ap-1259	21	29	.	.	PUNCT
ap-1259	22	1	(	(	PUNCT
ap-1259	22	2	2	2	X
ap-1259	22	3	)	)	PUNCT
ap-1259	22	4	an	an	DET
ap-1259	22	5	extension	extension	NOUN
ap-1259	22	6	of	of	ADP
ap-1259	22	7	uq	uq	PROPN
ap-1259	22	8	(	(	PUNCT
ap-1259	22	9	sl2)-action	sl2)-action	PROPN
ap-1259	22	10	from	from	ADP
ap-1259	22	11	the	the	DET
ap-1259	22	12	generators	generator	NOUN
ap-1259	22	13	to	to	PART
ap-1259	22	14	cq[x	cq[x	VERB
ap-1259	22	15	,	,	PUNCT
ap-1259	22	16	y	y	PROPN
ap-1259	22	17	]	]	PUNCT
ap-1259	22	18	is	be	AUX
ap-1259	22	19	given	give	VERB
ap-1259	22	20	by	by	ADP
ap-1259	22	21	(	(	PUNCT
ap-1259	22	22	ab)u	ab)u	ADP
ap-1259	22	23	def	def	ADJ
ap-1259	22	24	=	=	SYM
ap-1259	22	25	a	a	DET
ap-1259	22	26	(	(	PUNCT
ap-1259	22	27	bu	bu	PROPN
ap-1259	22	28	)	)	PUNCT
ap-1259	22	29	,	,	PUNCT
ap-1259	22	30	a	a	DET
ap-1259	22	31	(	(	PUNCT
ap-1259	22	32	uv	uv	NOUN
ap-1259	22	33	)	)	PUNCT
ap-1259	22	34	def	def	NOUN
ap-1259	22	35	=	=	SYM
ap-1259	22	36	σi	σi	NOUN
ap-1259	22	37	(	(	PUNCT
ap-1259	22	38	a′	a′	PROPN
ap-1259	22	39	iu	iu	ADP
ap-1259	22	40	)	)	PUNCT
ap-1259	22	41	·	·	PUNCT
ap-1259	22	42	(	(	PUNCT
ap-1259	22	43	a′′	a′′	NOUN
ap-1259	22	44	i	i	PROPN
ap-1259	22	45	v	v	PROPN
ap-1259	22	46	)	)	PUNCT
ap-1259	22	47	,	,	PUNCT
ap-1259	22	48	a	a	PRON
ap-1259	22	49	,	,	PUNCT
ap-1259	22	50	b	b	PROPN
ap-1259	22	51	∈	∈	PROPN
ap-1259	22	52	uq	uq	NOUN
ap-1259	22	53	(	(	PUNCT
ap-1259	22	54	sl2	sl2	PROPN
ap-1259	22	55	)	)	PUNCT
ap-1259	22	56	,	,	PUNCT
ap-1259	22	57	u	u	NOUN
ap-1259	22	58	,	,	PUNCT
ap-1259	22	59	v	v	PROPN
ap-1259	22	60	∈	∈	PROPN
ap-1259	22	61	cq[x	cq[x	NOUN
ap-1259	22	62	,	,	PUNCT
ap-1259	22	63	y	y	X
ap-1259	22	64	]	]	PUNCT
ap-1259	22	65	together	together	ADV
ap-1259	22	66	with	with	ADP
ap-1259	22	67	the	the	DET
ap-1259	22	68	natural	natural	ADJ
ap-1259	22	69	compatibility	compatibility	NOUN
ap-1259	22	70	conditions	condition	NOUN
ap-1259	22	71	[	[	X
ap-1259	22	72	3	3	NUM
ap-1259	22	73	]	]	PUNCT
ap-1259	22	74	.	.	PUNCT
ap-1259	23	1	we	we	PRON
ap-1259	23	2	have	have	VERB
ap-1259	23	3	from	from	ADP
ap-1259	23	4	(	(	PUNCT
ap-1259	23	5	1	1	NUM
ap-1259	23	6	)	)	PUNCT
ap-1259	23	7	that	that	SCONJ
ap-1259	23	8	the	the	DET
ap-1259	23	9	action	action	NOUN
ap-1259	23	10	of	of	ADP
ap-1259	23	11	k	k	PROPN
ap-1259	23	12	is	be	AUX
ap-1259	23	13	determined	determine	VERB
ap-1259	23	14	by	by	ADP
ap-1259	23	15	its	its	PRON
ap-1259	23	16	action	action	NOUN
ap-1259	23	17	ψ	ψ	X
ap-1259	23	18	on	on	ADP
ap-1259	23	19	x	x	PUNCT
ap-1259	23	20	and	and	CCONJ
ap-1259	23	21	y	y	PROPN
ap-1259	23	22	given	give	VERB
ap-1259	23	23	by	by	ADP
ap-1259	23	24	a	a	DET
ap-1259	23	25	1	1	NUM
ap-1259	23	26	×	×	NOUN
ap-1259	23	27	2	2	NUM
ap-1259	23	28	matrix	matrix	NOUN
ap-1259	23	29	mk	mk	NOUN
ap-1259	23	30	mk	mk	PROPN
ap-1259	23	31	def	def	PROPN
ap-1259	23	32	=	=	PUNCT
ap-1259	23	33	‖k	‖k	PROPN
ap-1259	23	34	(	(	PUNCT
ap-1259	23	35	x	x	X
ap-1259	23	36	)	)	PUNCT
ap-1259	23	37	,	,	PUNCT
ap-1259	23	38	k	k	PROPN
ap-1259	23	39	(	(	PUNCT
ap-1259	23	40	y)‖	y)‖	NOUN
ap-1259	23	41	=	=	SYM
ap-1259	23	42	‖αx	‖αx	PROPN
ap-1259	23	43	,	,	PUNCT
ap-1259	23	44	βy‖	βy‖	PROPN
ap-1259	23	45	,	,	PUNCT
ap-1259	23	46	(	(	PUNCT
ap-1259	23	47	3	3	X
ap-1259	23	48	)	)	PUNCT
ap-1259	23	49	where	where	SCONJ
ap-1259	23	50	α	α	X
ap-1259	23	51	,	,	PUNCT
ap-1259	23	52	β	β	PROPN
ap-1259	23	53	∈	∈	PROPN
ap-1259	23	54	c\	c\	PROPN
ap-1259	23	55	{	{	PUNCT
ap-1259	23	56	0	0	NUM
ap-1259	23	57	}	}	PUNCT
ap-1259	23	58	.	.	PUNCT
ap-1259	24	1	this	this	PRON
ap-1259	24	2	allows	allow	VERB
ap-1259	24	3	us	we	PRON
ap-1259	24	4	to	to	PART
ap-1259	24	5	introduce	introduce	VERB
ap-1259	24	6	the	the	DET
ap-1259	24	7	weight	weight	NOUN
ap-1259	24	8	of	of	ADP
ap-1259	24	9	xnym	xnym	PROPN
ap-1259	24	10	∈	∈	PROPN
ap-1259	24	11	cq[x	cq[x	PROPN
ap-1259	24	12	,	,	PUNCT
ap-1259	24	13	y	y	PROPN
ap-1259	24	14	]	]	PUNCT
ap-1259	24	15	as	as	ADP
ap-1259	24	16	wt	wt	PROPN
ap-1259	24	17	(	(	PUNCT
ap-1259	24	18	xnym	xnym	PROPN
ap-1259	24	19	)	)	PUNCT
ap-1259	24	20	=	=	NOUN
ap-1259	24	21	αnβm	αnβm	NOUN
ap-1259	24	22	.	.	PUNCT
ap-1259	25	1	another	another	DET
ap-1259	25	2	submatrix	submatrix	NOUN
ap-1259	25	3	of	of	ADP
ap-1259	25	4	m	m	PROPN
ap-1259	25	5	is	be	AUX
ap-1259	25	6	mef	mef	NOUN
ap-1259	25	7	def	def	PROPN
ap-1259	25	8	=	=	SYM
ap-1259	25	9	∥∥∥∥∥	∥∥∥∥∥	PROPN
ap-1259	25	10	e	e	X
ap-1259	25	11	(	(	PUNCT
ap-1259	25	12	x	x	NOUN
ap-1259	25	13	)	)	PUNCT
ap-1259	25	14	e	e	NOUN
ap-1259	25	15	(	(	PUNCT
ap-1259	25	16	y	y	PROPN
ap-1259	25	17	)	)	PUNCT
ap-1259	25	18	f	f	NOUN
ap-1259	25	19	(	(	PUNCT
ap-1259	25	20	x	x	X
ap-1259	25	21	)	)	PUNCT
ap-1259	25	22	f	f	PROPN
ap-1259	25	23	(	(	PUNCT
ap-1259	25	24	y	y	PROPN
ap-1259	25	25	)	)	PUNCT
ap-1259	25	26	∥∥∥∥∥	∥∥∥∥∥	NUM
ap-1259	25	27	.	.	PUNCT
ap-1259	26	1	(	(	PUNCT
ap-1259	26	2	4	4	X
ap-1259	26	3	)	)	PUNCT
ap-1259	26	4	we	we	PRON
ap-1259	26	5	call	call	VERB
ap-1259	26	6	mk	mk	NOUN
ap-1259	26	7	and	and	CCONJ
ap-1259	26	8	mef	mef	NOUN
ap-1259	26	9	an	an	DET
ap-1259	26	10	action	action	NOUN
ap-1259	26	11	k	k	NOUN
ap-1259	26	12	-	-	NOUN
ap-1259	26	13	matrix	matrix	NOUN
ap-1259	26	14	and	and	CCONJ
ap-1259	26	15	an	an	DET
ap-1259	26	16	action	action	NOUN
ap-1259	26	17	ef	ef	NOUN
ap-1259	26	18	-matrix	-matrix	NOUN
ap-1259	26	19	,	,	PUNCT
ap-1259	26	20	respectively	respectively	ADV
ap-1259	26	21	.	.	PUNCT
ap-1259	27	1	each	each	DET
ap-1259	27	2	entry	entry	NOUN
ap-1259	27	3	of	of	ADP
ap-1259	27	4	m	m	PROPN
ap-1259	27	5	is	be	AUX
ap-1259	27	6	a	a	DET
ap-1259	27	7	weight	weight	NOUN
ap-1259	27	8	vector	vector	NOUN
ap-1259	27	9	(	(	PUNCT
ap-1259	27	10	by	by	ADP
ap-1259	27	11	(	(	PUNCT
ap-1259	27	12	3	3	NUM
ap-1259	27	13	)	)	PUNCT
ap-1259	27	14	and	and	CCONJ
ap-1259	27	15	(	(	PUNCT
ap-1259	27	16	1	1	NUM
ap-1259	27	17	)	)	PUNCT
ap-1259	27	18	)	)	PUNCT
ap-1259	27	19	,	,	PUNCT
ap-1259	27	20	and	and	CCONJ
ap-1259	27	21	all	all	DET
ap-1259	27	22	the	the	DET
ap-1259	27	23	nonzero	nonzero	NOUN
ap-1259	27	24	monomials	monomial	NOUN
ap-1259	27	25	which	which	PRON
ap-1259	27	26	constitute	constitute	VERB
ap-1259	27	27	a	a	DET
ap-1259	27	28	specific	specific	ADJ
ap-1259	27	29	entry	entry	NOUN
ap-1259	27	30	have	have	VERB
ap-1259	27	31	the	the	DET
ap-1259	27	32	same	same	ADJ
ap-1259	27	33	weight	weight	NOUN
ap-1259	27	34	.	.	PUNCT
ap-1259	28	1	we	we	PRON
ap-1259	28	2	use	use	VERB
ap-1259	28	3	the	the	DET
ap-1259	28	4	notation	notation	NOUN
ap-1259	28	5	wt	wt	PROPN
ap-1259	28	6	(	(	PUNCT
ap-1259	28	7	m	m	NOUN
ap-1259	28	8	)	)	PUNCT
ap-1259	28	9	def	def	ADJ
ap-1259	28	10	=	=	SYM
ap-1259	28	11	⎛⎜⎜⎝	⎛⎜⎜⎝	NOUN
ap-1259	28	12	wt	wt	PROPN
ap-1259	28	13	(	(	PUNCT
ap-1259	28	14	k	k	X
ap-1259	28	15	(	(	PUNCT
ap-1259	28	16	x	x	NOUN
ap-1259	28	17	)	)	PUNCT
ap-1259	28	18	)	)	PUNCT
ap-1259	29	1	wt	wt	INTJ
ap-1259	29	2	(	(	PUNCT
ap-1259	29	3	k	k	X
ap-1259	29	4	(	(	PUNCT
ap-1259	29	5	y	y	NOUN
ap-1259	29	6	)	)	PUNCT
ap-1259	29	7	)	)	PUNCT
ap-1259	29	8	wt	wt	X
ap-1259	29	9	(	(	PUNCT
ap-1259	29	10	e	e	X
ap-1259	29	11	(	(	PUNCT
ap-1259	29	12	x	x	NOUN
ap-1259	29	13	)	)	PUNCT
ap-1259	29	14	)	)	PUNCT
ap-1259	30	1	wt	wt	X
ap-1259	30	2	(	(	PUNCT
ap-1259	30	3	e	e	X
ap-1259	30	4	(	(	PUNCT
ap-1259	30	5	y	y	NOUN
ap-1259	30	6	)	)	PUNCT
ap-1259	30	7	)	)	PUNCT
ap-1259	30	8	wt	wt	INTJ
ap-1259	31	1	(	(	PUNCT
ap-1259	31	2	f	f	X
ap-1259	31	3	(	(	PUNCT
ap-1259	31	4	x	x	NOUN
ap-1259	31	5	)	)	PUNCT
ap-1259	31	6	)	)	PUNCT
ap-1259	31	7	wt	wt	INTJ
ap-1259	31	8	(	(	PUNCT
ap-1259	31	9	f	f	PROPN
ap-1259	31	10	(	(	PUNCT
ap-1259	31	11	y	y	NOUN
ap-1259	31	12	)	)	PUNCT
ap-1259	31	13	)	)	PUNCT
ap-1259	31	14	⎞⎟⎟⎠	⎞⎟⎟⎠	NOUN
ap-1259	32	1	(	(	PUNCT
ap-1259	32	2	5	5	NUM
ap-1259	32	3	)	)	PUNCT
ap-1259	32	4	�	�	PROPN
ap-1259	32	5	�	�	PROPN
ap-1259	32	6	⎛⎜⎜⎝	⎛⎜⎜⎝	NOUN
ap-1259	32	7	wt	wt	PROPN
ap-1259	32	8	(	(	PUNCT
ap-1259	32	9	x	x	NOUN
ap-1259	32	10	)	)	PUNCT
ap-1259	32	11	wt	wt	PROPN
ap-1259	32	12	(	(	PUNCT
ap-1259	32	13	y	y	NOUN
ap-1259	32	14	)	)	PUNCT
ap-1259	32	15	q2wt	q2wt	PUNCT
ap-1259	33	1	(	(	PUNCT
ap-1259	33	2	x	x	X
ap-1259	33	3	)	)	PUNCT
ap-1259	33	4	q2wt	q2wt	PUNCT
ap-1259	33	5	(	(	PUNCT
ap-1259	33	6	y	y	NOUN
ap-1259	33	7	)	)	PUNCT
ap-1259	33	8	q−2wt	q−2wt	NOUN
ap-1259	33	9	(	(	PUNCT
ap-1259	33	10	x	x	NOUN
ap-1259	33	11	)	)	PUNCT
ap-1259	33	12	q−2wt	q−2wt	NOUN
ap-1259	33	13	(	(	PUNCT
ap-1259	33	14	y	y	NOUN
ap-1259	33	15	)	)	PUNCT
ap-1259	33	16	⎞⎟⎟⎠=	⎞⎟⎟⎠=	NOUN
ap-1259	33	17	⎛⎜⎜⎝	⎛⎜⎜⎝	NOUN
ap-1259	33	18	α	α	PROPN
ap-1259	33	19	β	β	X
ap-1259	33	20	q2α	q2α	PROPN
ap-1259	34	1	q2β	q2β	NUM
ap-1259	34	2	q−2α	q−2α	PROPN
ap-1259	34	3	q−2β	q−2β	PROPN
ap-1259	34	4	⎞⎟⎟⎠	⎞⎟⎟⎠	NOUN
ap-1259	34	5	,	,	PUNCT
ap-1259	34	6	where	where	SCONJ
ap-1259	34	7	the	the	DET
ap-1259	34	8	matrix	matrix	NOUN
ap-1259	34	9	relation	relation	NOUN
ap-1259	34	10	�	�	PROPN
ap-1259	34	11	�	�	PROPN
ap-1259	34	12	is	be	AUX
ap-1259	34	13	treated	treat	VERB
ap-1259	34	14	as	as	ADP
ap-1259	34	15	a	a	DET
ap-1259	34	16	set	set	NOUN
ap-1259	34	17	of	of	ADP
ap-1259	34	18	elementwise	elementwise	ADJ
ap-1259	34	19	equalities	equality	NOUN
ap-1259	34	20	if	if	SCONJ
ap-1259	34	21	they	they	PRON
ap-1259	34	22	are	be	AUX
ap-1259	34	23	applicable	applicable	ADJ
ap-1259	34	24	,	,	PUNCT
ap-1259	34	25	that	that	ADV
ap-1259	34	26	is	is	ADV
ap-1259	34	27	,	,	PUNCT
ap-1259	34	28	when	when	SCONJ
ap-1259	34	29	the	the	DET
ap-1259	34	30	corresponding	corresponding	ADJ
ap-1259	34	31	entry	entry	NOUN
ap-1259	34	32	ofm	ofm	PROPN
ap-1259	34	33	is	be	AUX
ap-1259	34	34	nonzero	nonzero	NOUN
ap-1259	34	35	(	(	PUNCT
ap-1259	34	36	hence	hence	ADV
ap-1259	34	37	admits	admit	VERB
ap-1259	34	38	a	a	DET
ap-1259	34	39	well	well	ADV
ap-1259	34	40	-	-	PUNCT
ap-1259	34	41	defined	define	VERB
ap-1259	34	42	weight	weight	NOUN
ap-1259	34	43	)	)	PUNCT
ap-1259	34	44	.	.	PUNCT
ap-1259	35	1	denote	denote	VERB
ap-1259	35	2	by	by	ADP
ap-1259	35	3	(	(	PUNCT
ap-1259	35	4	m)i	m)i	X
ap-1259	35	5	the	the	DET
ap-1259	35	6	i	i	PROPN
ap-1259	35	7	-	-	PUNCT
ap-1259	35	8	th	th	X
ap-1259	35	9	homogeneous	homogeneous	ADJ
ap-1259	35	10	component	component	NOUN
ap-1259	35	11	ofm	ofm	PROPN
ap-1259	35	12	which	which	PRON
ap-1259	35	13	,	,	PUNCT
ap-1259	35	14	if	if	SCONJ
ap-1259	35	15	nonzero	nonzero	PROPN
ap-1259	35	16	,	,	PUNCT
ap-1259	35	17	admits	admit	VERB
ap-1259	35	18	a	a	DET
ap-1259	35	19	well	well	ADV
ap-1259	35	20	-	-	PUNCT
ap-1259	35	21	defined	define	VERB
ap-1259	35	22	weight	weight	NOUN
ap-1259	35	23	.	.	PUNCT
ap-1259	36	1	introduce	introduce	VERB
ap-1259	36	2	the	the	DET
ap-1259	36	3	constants	constant	NOUN
ap-1259	36	4	a0	a0	PROPN
ap-1259	36	5	,	,	PUNCT
ap-1259	36	6	b0	b0	PROPN
ap-1259	36	7	,	,	PUNCT
ap-1259	36	8	c0	c0	NOUN
ap-1259	36	9	,	,	PUNCT
ap-1259	36	10	d0	d0	PROPN
ap-1259	36	11	∈	∈	PROPN
ap-1259	36	12	c	c	NOUN
ap-1259	36	13	such	such	ADJ
ap-1259	36	14	that	that	SCONJ
ap-1259	36	15	the	the	DET
ap-1259	36	16	zero	zero	NUM
ap-1259	36	17	degree	degree	NOUN
ap-1259	36	18	component	component	NOUN
ap-1259	36	19	of	of	ADP
ap-1259	36	20	the	the	DET
ap-1259	36	21	full	full	ADJ
ap-1259	36	22	action	action	NOUN
ap-1259	36	23	matrix	matrix	NOUN
ap-1259	36	24	25	25	NUM
ap-1259	36	25	acta	acta	PROPN
ap-1259	36	26	polytechnica	polytechnica	PROPN
ap-1259	36	27	vol	vol	NOUN
ap-1259	36	28	.	.	PROPN
ap-1259	37	1	50	50	NUM
ap-1259	37	2	no	no	NOUN
ap-1259	37	3	.	.	PUNCT
ap-1259	38	1	5/2010	5/2010	PROPN
ap-1259	38	2	is	be	AUX
ap-1259	38	3	(	(	PUNCT
ap-1259	38	4	m)0	m)0	NOUN
ap-1259	38	5	=	=	NOUN
ap-1259	38	6	⎛⎜⎜⎝	⎛⎜⎜⎝	NOUN
ap-1259	38	7	0	0	NUM
ap-1259	38	8	0	0	NUM
ap-1259	38	9	a0	a0	PROPN
ap-1259	38	10	b0	b0	PROPN
ap-1259	38	11	c0	c0	PROPN
ap-1259	38	12	d0	d0	PROPN
ap-1259	38	13	⎞⎟⎟⎠	⎞⎟⎟⎠	PROPN
ap-1259	38	14	0	0	NUM
ap-1259	38	15	.	.	PUNCT
ap-1259	39	1	(	(	PUNCT
ap-1259	39	2	6	6	X
ap-1259	39	3	)	)	PUNCT
ap-1259	39	4	we	we	PRON
ap-1259	39	5	keep	keep	VERB
ap-1259	39	6	the	the	DET
ap-1259	39	7	subscript	subscript	NOUN
ap-1259	39	8	0	0	NUM
ap-1259	39	9	to	to	ADP
ap-1259	39	10	the	the	DET
ap-1259	39	11	matrix	matrix	NOUN
ap-1259	39	12	in	in	ADP
ap-1259	39	13	the	the	DET
ap-1259	39	14	r.h.s	r.h.s	NOUN
ap-1259	39	15	.	.	PUNCT
ap-1259	40	1	to	to	PART
ap-1259	40	2	emphasize	emphasize	VERB
ap-1259	40	3	the	the	DET
ap-1259	40	4	origin	origin	NOUN
ap-1259	40	5	of	of	ADP
ap-1259	40	6	this	this	DET
ap-1259	40	7	matrix	matrix	NOUN
ap-1259	40	8	as	as	ADP
ap-1259	40	9	the	the	DET
ap-1259	40	10	0	0	NUM
ap-1259	40	11	-	-	PUNCT
ap-1259	40	12	th	th	X
ap-1259	40	13	homogeneous	homogeneous	ADJ
ap-1259	40	14	component	component	NOUN
ap-1259	40	15	of	of	ADP
ap-1259	40	16	m	m	PROPN
ap-1259	40	17	.	.	PUNCT
ap-1259	41	1	weights	weight	NOUN
ap-1259	41	2	of	of	ADP
ap-1259	41	3	nonzero	nonzero	PROPN
ap-1259	41	4	projections	projection	NOUN
ap-1259	41	5	of	of	ADP
ap-1259	41	6	(	(	PUNCT
ap-1259	41	7	weight	weight	NOUN
ap-1259	41	8	)	)	PUNCT
ap-1259	41	9	entries	entry	NOUN
ap-1259	41	10	of	of	ADP
ap-1259	41	11	m	m	PRON
ap-1259	41	12	should	should	AUX
ap-1259	41	13	have	have	VERB
ap-1259	41	14	the	the	DET
ap-1259	41	15	same	same	ADJ
ap-1259	41	16	weight	weight	NOUN
ap-1259	41	17	,	,	PUNCT
ap-1259	41	18	then	then	ADV
ap-1259	41	19	wt	wt	INTJ
ap-1259	41	20	(	(	PUNCT
ap-1259	41	21	(	(	PUNCT
ap-1259	41	22	m)0	m)0	PROPN
ap-1259	41	23	)	)	PUNCT
ap-1259	41	24	�	�	PROPN
ap-1259	41	25	�	�	PROPN
ap-1259	41	26	⎛⎜⎜⎝	⎛⎜⎜⎝	NOUN
ap-1259	41	27	0	0	NUM
ap-1259	41	28	0	0	NUM
ap-1259	41	29	q2α	q2α	PROPN
ap-1259	41	30	q2β	q2β	VERB
ap-1259	42	1	q−2α	q−2α	PROPN
ap-1259	42	2	q−2β	q−2β	PROPN
ap-1259	42	3	⎞⎟⎟⎠	⎞⎟⎟⎠	PROPN
ap-1259	42	4	0	0	NUM
ap-1259	42	5	.	.	PUNCT
ap-1259	43	1	(	(	PUNCT
ap-1259	43	2	7	7	X
ap-1259	43	3	)	)	PUNCT
ap-1259	43	4	all	all	DET
ap-1259	43	5	the	the	DET
ap-1259	43	6	entries	entry	NOUN
ap-1259	43	7	of	of	ADP
ap-1259	43	8	(	(	PUNCT
ap-1259	43	9	m)0	m)0	NOUN
ap-1259	43	10	are	be	AUX
ap-1259	43	11	constants	constant	NOUN
ap-1259	43	12	(	(	PUNCT
ap-1259	43	13	6	6	NUM
ap-1259	43	14	)	)	PUNCT
ap-1259	43	15	,	,	PUNCT
ap-1259	43	16	and	and	CCONJ
ap-1259	43	17	so	so	ADV
ap-1259	43	18	wt	wt	INTJ
ap-1259	43	19	(	(	PUNCT
ap-1259	43	20	(	(	PUNCT
ap-1259	43	21	m)0	m)0	PROPN
ap-1259	43	22	)	)	PUNCT
ap-1259	43	23	�	�	PROPN
ap-1259	43	24	�	�	PROPN
ap-1259	43	25	⎛⎜⎜⎝	⎛⎜⎜⎝	NOUN
ap-1259	43	26	0	0	NUM
ap-1259	43	27	0	0	NUM
ap-1259	43	28	1	1	NUM
ap-1259	43	29	1	1	NUM
ap-1259	43	30	1	1	NUM
ap-1259	43	31	1	1	NUM
ap-1259	43	32	⎞⎟⎟⎠	⎞⎟⎟⎠	NOUN
ap-1259	43	33	0	0	NUM
ap-1259	43	34	.	.	PUNCT
ap-1259	44	1	(	(	PUNCT
ap-1259	44	2	8)	8)	NUM
ap-1259	44	3	let	let	VERB
ap-1259	44	4	us	we	PRON
ap-1259	44	5	use	use	VERB
ap-1259	44	6	(	(	PUNCT
ap-1259	44	7	mef	mef	NOUN
ap-1259	44	8	)	)	PUNCT
ap-1259	44	9	i	i	PRON
ap-1259	44	10	to	to	PART
ap-1259	44	11	construct	construct	VERB
ap-1259	44	12	a	a	DET
ap-1259	44	13	symbolic	symbolic	ADJ
ap-1259	44	14	matrix	matrix	NOUN
ap-1259	44	15	(	(	PUNCT
ap-1259	44	16	�	�	PROPN
ap-1259	44	17	mef	mef	PROPN
ap-1259	44	18	)	)	PUNCT
ap-1259	44	19	i	i	PRON
ap-1259	44	20	whose	whose	DET
ap-1259	44	21	entries	entry	NOUN
ap-1259	44	22	are	be	AUX
ap-1259	44	23	symbols	symbol	NOUN
ap-1259	44	24	0	0	NUM
ap-1259	44	25	or	or	CCONJ
ap-1259	44	26	�	�	PROPN
ap-1259	44	27	in	in	ADP
ap-1259	44	28	such	such	DET
ap-1259	44	29	a	a	DET
ap-1259	44	30	way	way	NOUN
ap-1259	44	31	:	:	PUNCT
ap-1259	44	32	a	a	DET
ap-1259	44	33	nonzero	nonzero	ADJ
ap-1259	44	34	entry	entry	NOUN
ap-1259	44	35	of	of	ADP
ap-1259	44	36	(	(	PUNCT
ap-1259	44	37	mef	mef	NOUN
ap-1259	44	38	)	)	PUNCT
ap-1259	44	39	i	i	PRON
ap-1259	44	40	is	be	AUX
ap-1259	44	41	replaced	replace	VERB
ap-1259	44	42	by	by	ADP
ap-1259	44	43	�	�	PROPN
ap-1259	44	44	,	,	PUNCT
ap-1259	44	45	while	while	SCONJ
ap-1259	44	46	a	a	DET
ap-1259	44	47	zero	zero	NUM
ap-1259	44	48	entry	entry	NOUN
ap-1259	44	49	is	be	AUX
ap-1259	44	50	replaced	replace	VERB
ap-1259	44	51	by	by	ADP
ap-1259	44	52	the	the	DET
ap-1259	44	53	symbol	symbol	NOUN
ap-1259	44	54	0	0	NUM
ap-1259	44	55	.	.	PUNCT
ap-1259	45	1	for	for	ADP
ap-1259	45	2	0	0	NUM
ap-1259	45	3	-	-	PUNCT
ap-1259	45	4	th	th	VERB
ap-1259	45	5	components	component	NOUN
ap-1259	45	6	the	the	DET
ap-1259	45	7	specific	specific	ADJ
ap-1259	45	8	relations	relation	NOUN
ap-1259	45	9	involved	involve	VERB
ap-1259	45	10	in	in	ADP
ap-1259	45	11	(	(	PUNCT
ap-1259	45	12	7	7	X
ap-1259	45	13	)	)	PUNCT
ap-1259	45	14	imply	imply	VERB
ap-1259	45	15	that	that	SCONJ
ap-1259	45	16	each	each	DET
ap-1259	45	17	column	column	NOUN
ap-1259	45	18	of	of	ADP
ap-1259	45	19	(	(	PUNCT
ap-1259	45	20	�	�	PROPN
ap-1259	45	21	mef	mef	PROPN
ap-1259	45	22	)	)	PUNCT
ap-1259	45	23	0	0	NUM
ap-1259	45	24	should	should	AUX
ap-1259	45	25	contain	contain	VERB
ap-1259	45	26	at	at	ADV
ap-1259	45	27	least	least	ADV
ap-1259	45	28	one	one	NUM
ap-1259	45	29	0	0	NUM
ap-1259	45	30	,	,	PUNCT
ap-1259	45	31	therefore	therefore	ADV
ap-1259	45	32	we	we	PRON
ap-1259	45	33	have	have	VERB
ap-1259	45	34	9	9	NUM
ap-1259	45	35	possibilities	possibility	NOUN
ap-1259	45	36	.	.	PUNCT
ap-1259	46	1	apply	apply	VERB
ap-1259	46	2	e	e	PROPN
ap-1259	46	3	and	and	CCONJ
ap-1259	46	4	f	f	PROPN
ap-1259	46	5	to	to	PART
ap-1259	46	6	yx	yx	NOUN
ap-1259	46	7	=	=	PUNCT
ap-1259	46	8	qxy	qxy	PROPN
ap-1259	46	9	using	use	VERB
ap-1259	46	10	(	(	PUNCT
ap-1259	46	11	3	3	NUM
ap-1259	46	12	)	)	PUNCT
ap-1259	46	13	to	to	PART
ap-1259	46	14	get	get	VERB
ap-1259	46	15	ye	ye	PRON
ap-1259	46	16	(	(	PUNCT
ap-1259	46	17	x)−	x)−	PROPN
ap-1259	46	18	qβe	qβe	PROPN
ap-1259	46	19	(	(	PUNCT
ap-1259	46	20	x	x	NOUN
ap-1259	46	21	)	)	PUNCT
ap-1259	46	22	y	y	PROPN
ap-1259	46	23	=	=	SYM
ap-1259	46	24	qxe	qxe	NOUN
ap-1259	46	25	(	(	PUNCT
ap-1259	46	26	y)−	y)−	PROPN
ap-1259	46	27	αe	αe	PROPN
ap-1259	46	28	(	(	PUNCT
ap-1259	46	29	y)x	y)x	NOUN
ap-1259	46	30	,	,	PUNCT
ap-1259	46	31	(	(	PUNCT
ap-1259	46	32	9	9	X
ap-1259	46	33	)	)	PUNCT
ap-1259	46	34	f	f	NOUN
ap-1259	46	35	(	(	PUNCT
ap-1259	46	36	x	x	X
ap-1259	46	37	)	)	PUNCT
ap-1259	46	38	y	y	PROPN
ap-1259	46	39	−	−	PROPN
ap-1259	46	40	q−1β−1yf	q−1β−1yf	NOUN
ap-1259	46	41	(	(	PUNCT
ap-1259	46	42	x	x	NOUN
ap-1259	46	43	)	)	PUNCT
ap-1259	46	44	=	=	SYM
ap-1259	46	45	(	(	PUNCT
ap-1259	46	46	10	10	NUM
ap-1259	46	47	)	)	PUNCT
ap-1259	46	48	q−1f	q−1f	X
ap-1259	46	49	(	(	PUNCT
ap-1259	46	50	y)x	y)x	NOUN
ap-1259	46	51	−	−	PROPN
ap-1259	46	52	α−1xf	α−1xf	PROPN
ap-1259	46	53	(	(	PUNCT
ap-1259	46	54	y	y	NOUN
ap-1259	46	55	)	)	PUNCT
ap-1259	46	56	.	.	PUNCT
ap-1259	47	1	we	we	PRON
ap-1259	47	2	project	project	VERB
ap-1259	47	3	(	(	PUNCT
ap-1259	47	4	9)-(10	9)-(10	NOUN
ap-1259	47	5	)	)	PUNCT
ap-1259	47	6	to	to	PART
ap-1259	47	7	cq[x	cq[x	PROPN
ap-1259	47	8	,	,	PUNCT
ap-1259	47	9	y]1	y]1	ADV
ap-1259	47	10	and	and	CCONJ
ap-1259	47	11	obtain	obtain	VERB
ap-1259	47	12	a0	a0	NOUN
ap-1259	47	13	(	(	PUNCT
ap-1259	47	14	1−	1−	NUM
ap-1259	47	15	qβ	qβ	NOUN
ap-1259	47	16	)	)	PUNCT
ap-1259	47	17	y	y	PROPN
ap-1259	47	18	=	=	SYM
ap-1259	47	19	b0	b0	PROPN
ap-1259	47	20	(	(	PUNCT
ap-1259	47	21	q	q	NOUN
ap-1259	47	22	−	−	PROPN
ap-1259	47	23	α	α	NUM
ap-1259	47	24	)	)	PUNCT
ap-1259	47	25	x	x	NOUN
ap-1259	47	26	,	,	PUNCT
ap-1259	47	27	d0	d0	NOUN
ap-1259	47	28	(	(	PUNCT
ap-1259	47	29	1−	1−	NUM
ap-1259	47	30	qα−1)x	qα−1)x	PUNCT
ap-1259	48	1	=	=	SYM
ap-1259	48	2	c0	c0	X
ap-1259	48	3	(	(	PUNCT
ap-1259	48	4	q	q	NOUN
ap-1259	48	5	−	−	NUM
ap-1259	48	6	β−1	β−1	NUM
ap-1259	48	7	)	)	PUNCT
ap-1259	48	8	y	y	PROPN
ap-1259	48	9	,	,	PUNCT
ap-1259	48	10	which	which	PRON
ap-1259	48	11	gives	give	VERB
ap-1259	48	12	a0	a0	PROPN
ap-1259	48	13	(	(	PUNCT
ap-1259	48	14	1−	1−	NUM
ap-1259	48	15	qβ	qβ	NOUN
ap-1259	48	16	)	)	PUNCT
ap-1259	48	17	=	=	SYM
ap-1259	48	18	b0	b0	NOUN
ap-1259	48	19	(	(	PUNCT
ap-1259	48	20	q	q	NOUN
ap-1259	48	21	−	−	PROPN
ap-1259	48	22	α	α	NOUN
ap-1259	48	23	)	)	PUNCT
ap-1259	48	24	=	=	PUNCT
ap-1259	48	25	(	(	PUNCT
ap-1259	48	26	11	11	NUM
ap-1259	48	27	)	)	PUNCT
ap-1259	48	28	d0	d0	NOUN
ap-1259	48	29	(	(	PUNCT
ap-1259	48	30	1−	1−	NUM
ap-1259	48	31	qα−1	qα−1	NOUN
ap-1259	48	32	)	)	PUNCT
ap-1259	49	1	=	=	SYM
ap-1259	49	2	c0	c0	X
ap-1259	49	3	(	(	PUNCT
ap-1259	49	4	q	q	NOUN
ap-1259	49	5	−	−	NUM
ap-1259	49	6	β−1	β−1	NUM
ap-1259	49	7	)	)	PUNCT
ap-1259	49	8	=	=	SYM
ap-1259	49	9	0	0	X
ap-1259	49	10	.	.	PUNCT
ap-1259	49	11	due	due	ADP
ap-1259	49	12	to	to	ADP
ap-1259	49	13	(	(	PUNCT
ap-1259	49	14	11	11	NUM
ap-1259	49	15	)	)	PUNCT
ap-1259	49	16	,	,	PUNCT
ap-1259	49	17	weight	weight	NOUN
ap-1259	49	18	constants	constant	VERB
ap-1259	49	19	α	α	PROPN
ap-1259	49	20	and	and	CCONJ
ap-1259	49	21	β	β	X
ap-1259	49	22	are	be	AUX
ap-1259	49	23	1	1	NUM
ap-1259	49	24	)	)	PUNCT
ap-1259	49	25	a0	a0	NOUN
ap-1259	49	26	=	=	SYM
ap-1259	49	27	0	0	PUNCT
ap-1259	50	1	=	=	NOUN
ap-1259	50	2	⇒	⇒	NOUN
ap-1259	50	3	β	β	X
ap-1259	50	4	=	=	SYM
ap-1259	50	5	q−1	q−1	PROPN
ap-1259	50	6	,	,	PUNCT
ap-1259	50	7	(	(	PUNCT
ap-1259	50	8	12	12	NUM
ap-1259	50	9	)	)	PUNCT
ap-1259	50	10	2	2	NUM
ap-1259	50	11	)	)	PUNCT
ap-1259	50	12	b0	b0	NOUN
ap-1259	50	13	=	=	SYM
ap-1259	50	14	0	0	PUNCT
ap-1259	51	1	=	=	NOUN
ap-1259	51	2	⇒	⇒	VERB
ap-1259	51	3	α	α	X
ap-1259	51	4	=	=	SYM
ap-1259	51	5	q	q	ADJ
ap-1259	51	6	,	,	PUNCT
ap-1259	51	7	(	(	PUNCT
ap-1259	51	8	13	13	NUM
ap-1259	51	9	)	)	PUNCT
ap-1259	51	10	3	3	NUM
ap-1259	51	11	)	)	PUNCT
ap-1259	51	12	c0	c0	NOUN
ap-1259	51	13	=	=	SYM
ap-1259	51	14	0	0	PUNCT
ap-1259	52	1	=	=	NOUN
ap-1259	52	2	⇒	⇒	NOUN
ap-1259	52	3	β	β	X
ap-1259	52	4	=	=	SYM
ap-1259	52	5	q−1	q−1	PROPN
ap-1259	52	6	,	,	PUNCT
ap-1259	52	7	(	(	PUNCT
ap-1259	52	8	14	14	NUM
ap-1259	52	9	)	)	PUNCT
ap-1259	52	10	4	4	NUM
ap-1259	52	11	)	)	PUNCT
ap-1259	52	12	d0	d0	NOUN
ap-1259	52	13	=	=	SYM
ap-1259	52	14	0	0	PUNCT
ap-1259	53	1	=	=	NOUN
ap-1259	53	2	⇒	⇒	X
ap-1259	53	3	α	α	X
ap-1259	53	4	=	=	SYM
ap-1259	53	5	q.	q.	PROPN
ap-1259	53	6	(	(	PUNCT
ap-1259	53	7	15	15	NUM
ap-1259	53	8	)	)	PUNCT
ap-1259	53	9	we	we	PRON
ap-1259	53	10	compare	compare	VERB
ap-1259	53	11	this	this	PRON
ap-1259	53	12	to	to	ADP
ap-1259	53	13	(	(	PUNCT
ap-1259	53	14	7)–(8	7)–(8	NUM
ap-1259	53	15	)	)	PUNCT
ap-1259	53	16	and	and	CCONJ
ap-1259	53	17	deduce	deduce	VERB
ap-1259	53	18	that	that	SCONJ
ap-1259	53	19	the	the	DET
ap-1259	53	20	symbolic	symbolic	ADJ
ap-1259	53	21	matrices	matrix	NOUN
ap-1259	53	22	containing	contain	VERB
ap-1259	53	23	two	two	NUM
ap-1259	53	24	�	�	PROPN
ap-1259	53	25	’s	’s	PART
ap-1259	53	26	should	should	AUX
ap-1259	53	27	be	be	AUX
ap-1259	53	28	excluded	exclude	VERB
ap-1259	53	29	.	.	PUNCT
ap-1259	54	1	using	use	VERB
ap-1259	54	2	(	(	PUNCT
ap-1259	54	3	7	7	NUM
ap-1259	54	4	)	)	PUNCT
ap-1259	54	5	and	and	CCONJ
ap-1259	54	6	(	(	PUNCT
ap-1259	54	7	12)–(15	12)–(15	NUM
ap-1259	54	8	)	)	PUNCT
ap-1259	54	9	we	we	PRON
ap-1259	54	10	conclude	conclude	VERB
ap-1259	54	11	that	that	SCONJ
ap-1259	54	12	the	the	DET
ap-1259	54	13	position	position	NOUN
ap-1259	54	14	of	of	ADP
ap-1259	54	15	�	�	PROPN
ap-1259	54	16	in	in	ADP
ap-1259	54	17	the	the	DET
ap-1259	54	18	remaining	remain	VERB
ap-1259	54	19	symbolic	symbolic	ADJ
ap-1259	54	20	matrices	matrix	NOUN
ap-1259	54	21	determines	determine	VERB
ap-1259	54	22	the	the	DET
ap-1259	54	23	associated	associated	ADJ
ap-1259	54	24	weight	weight	NOUN
ap-1259	54	25	constants	constant	NOUN
ap-1259	54	26	(	(	PUNCT
ap-1259	54	27	�	�	NOUN
ap-1259	54	28	0	0	NUM
ap-1259	54	29	0	0	NUM
ap-1259	54	30	0	0	NUM
ap-1259	54	31	)	)	PUNCT
ap-1259	54	32	0	0	PUNCT
ap-1259	55	1	=	=	NOUN
ap-1259	55	2	⇒	⇒	VERB
ap-1259	55	3	α	α	NOUN
ap-1259	55	4	=	=	SYM
ap-1259	55	5	q−2	q−2	PROPN
ap-1259	55	6	,	,	PUNCT
ap-1259	55	7	β	β	X
ap-1259	55	8	=	=	SYM
ap-1259	55	9	q−1	q−1	PROPN
ap-1259	55	10	,	,	PUNCT
ap-1259	55	11	(	(	PUNCT
ap-1259	55	12	16	16	NUM
ap-1259	55	13	)	)	PUNCT
ap-1259	55	14	(	(	PUNCT
ap-1259	55	15	0	0	NUM
ap-1259	55	16	�	�	PROPN
ap-1259	55	17	0	0	NUM
ap-1259	55	18	0	0	NUM
ap-1259	55	19	)	)	PUNCT
ap-1259	55	20	0	0	PUNCT
ap-1259	56	1	=	=	NOUN
ap-1259	56	2	⇒	⇒	VERB
ap-1259	56	3	α	α	X
ap-1259	56	4	=	=	SYM
ap-1259	56	5	q	q	NOUN
ap-1259	56	6	,	,	PUNCT
ap-1259	56	7	β	β	X
ap-1259	56	8	=	=	SYM
ap-1259	56	9	q−2	q−2	PROPN
ap-1259	56	10	,	,	PUNCT
ap-1259	56	11	(	(	PUNCT
ap-1259	56	12	17	17	NUM
ap-1259	56	13	)	)	PUNCT
ap-1259	56	14	(	(	PUNCT
ap-1259	56	15	0	0	NUM
ap-1259	56	16	0	0	NUM
ap-1259	56	17	�	�	PROPN
ap-1259	56	18	0	0	NUM
ap-1259	56	19	)	)	PUNCT
ap-1259	56	20	0	0	PUNCT
ap-1259	57	1	=	=	NOUN
ap-1259	57	2	⇒	⇒	VERB
ap-1259	57	3	α	α	X
ap-1259	57	4	=	=	SYM
ap-1259	57	5	q2	q2	NOUN
ap-1259	57	6	,	,	PUNCT
ap-1259	57	7	β	β	X
ap-1259	57	8	=	=	SYM
ap-1259	57	9	q−1	q−1	PROPN
ap-1259	57	10	,	,	PUNCT
ap-1259	57	11	(	(	PUNCT
ap-1259	57	12	18	18	NUM
ap-1259	57	13	)	)	PUNCT
ap-1259	57	14	(	(	PUNCT
ap-1259	57	15	0	0	NUM
ap-1259	57	16	0	0	NUM
ap-1259	57	17	0	0	NUM
ap-1259	57	18	�	�	PROPN
ap-1259	57	19	)	)	PUNCT
ap-1259	57	20	0	0	PUNCT
ap-1259	58	1	=	=	NOUN
ap-1259	58	2	⇒	⇒	VERB
ap-1259	58	3	α	α	X
ap-1259	58	4	=	=	SYM
ap-1259	58	5	q	q	NOUN
ap-1259	58	6	,	,	PUNCT
ap-1259	58	7	β	β	NOUN
ap-1259	58	8	=	=	SYM
ap-1259	58	9	q2	q2	PROPN
ap-1259	58	10	,	,	PUNCT
ap-1259	58	11	(	(	PUNCT
ap-1259	58	12	19	19	NUM
ap-1259	58	13	)	)	PUNCT
ap-1259	58	14	and	and	CCONJ
ap-1259	58	15	the	the	DET
ap-1259	58	16	matrix	matrix	NOUN
ap-1259	58	17	(	(	PUNCT
ap-1259	58	18	0	0	NUM
ap-1259	58	19	0	0	NUM
ap-1259	58	20	0	0	NUM
ap-1259	58	21	0	0	NUM
ap-1259	58	22	)	)	PUNCT
ap-1259	58	23	0	0	NUM
ap-1259	58	24	does	do	AUX
ap-1259	58	25	not	not	PART
ap-1259	58	26	determine	determine	VERB
ap-1259	58	27	any	any	DET
ap-1259	58	28	weight	weight	NOUN
ap-1259	58	29	constants	constant	NOUN
ap-1259	58	30	.	.	PUNCT
ap-1259	59	1	in	in	ADP
ap-1259	59	2	the	the	DET
ap-1259	59	3	1	1	NUM
ap-1259	59	4	-	-	PUNCT
ap-1259	59	5	st	st	NOUN
ap-1259	59	6	homogeneous	homogeneous	ADJ
ap-1259	59	7	component	component	NOUN
ap-1259	59	8	we	we	PRON
ap-1259	59	9	have	have	VERB
ap-1259	59	10	wt	wt	PROPN
ap-1259	59	11	(	(	PUNCT
ap-1259	59	12	e	e	X
ap-1259	59	13	(	(	PUNCT
ap-1259	59	14	x	x	NOUN
ap-1259	59	15	)	)	PUNCT
ap-1259	59	16	)	)	PUNCT
ap-1259	60	1	=	=	SYM
ap-1259	60	2	q2wt	q2wt	PUNCT
ap-1259	60	3	(	(	PUNCT
ap-1259	60	4	x	x	X
ap-1259	60	5	)	)	PUNCT
ap-1259	60	6	=	=	SYM
ap-1259	60	7	wt	wt	X
ap-1259	60	8	(	(	PUNCT
ap-1259	60	9	x	x	NOUN
ap-1259	60	10	)	)	PUNCT
ap-1259	60	11	(	(	PUNCT
ap-1259	60	12	because	because	SCONJ
ap-1259	60	13	0	0	NUM
ap-1259	60	14	<	<	X
ap-1259	60	15	q	q	X
ap-1259	60	16	<	<	X
ap-1259	60	17	1	1	NUM
ap-1259	60	18	)	)	PUNCT
ap-1259	60	19	,	,	PUNCT
ap-1259	60	20	which	which	PRON
ap-1259	60	21	implies	imply	VERB
ap-1259	60	22	(	(	PUNCT
ap-1259	60	23	e	e	X
ap-1259	60	24	(	(	PUNCT
ap-1259	60	25	x))1	x))1	NOUN
ap-1259	60	26	=	=	SYM
ap-1259	60	27	a1y	a1y	NOUN
ap-1259	60	28	,	,	PUNCT
ap-1259	60	29	and	and	CCONJ
ap-1259	60	30	similarly	similarly	ADV
ap-1259	60	31	we	we	PRON
ap-1259	60	32	obtain	obtain	VERB
ap-1259	60	33	(	(	PUNCT
ap-1259	60	34	mef	mef	NOUN
ap-1259	60	35	)	)	PUNCT
ap-1259	60	36	1	1	NUM
ap-1259	60	37	=	=	SYM
ap-1259	60	38	(	(	PUNCT
ap-1259	60	39	a1y	a1y	NOUN
ap-1259	60	40	b1x	b1x	PROPN
ap-1259	60	41	c1y	c1y	NOUN
ap-1259	60	42	d1x	d1x	PRON
ap-1259	60	43	)	)	PUNCT
ap-1259	60	44	1	1	NUM
ap-1259	60	45	,	,	PUNCT
ap-1259	60	46	(	(	PUNCT
ap-1259	60	47	20	20	NUM
ap-1259	60	48	)	)	PUNCT
ap-1259	60	49	where	where	SCONJ
ap-1259	60	50	a1	a1	NOUN
ap-1259	60	51	,	,	PUNCT
ap-1259	60	52	b1	b1	NOUN
ap-1259	60	53	,	,	PUNCT
ap-1259	60	54	c1	c1	NOUN
ap-1259	60	55	,	,	PUNCT
ap-1259	60	56	d1	d1	PROPN
ap-1259	60	57	∈	∈	PROPN
ap-1259	60	58	c.	c.	NOUN
ap-1259	61	1	so	so	SCONJ
ap-1259	61	2	we	we	PRON
ap-1259	61	3	introduce	introduce	VERB
ap-1259	61	4	a	a	DET
ap-1259	61	5	symbolic	symbolic	ADJ
ap-1259	61	6	matrix	matrix	NOUN
ap-1259	61	7	(	(	PUNCT
ap-1259	61	8	�	�	PROPN
ap-1259	61	9	mef	mef	PROPN
ap-1259	61	10	)	)	PUNCT
ap-1259	61	11	1	1	NUM
ap-1259	61	12	as	as	ADP
ap-1259	61	13	above	above	ADV
ap-1259	61	14	.	.	PUNCT
ap-1259	62	1	the	the	DET
ap-1259	62	2	relations	relation	NOUN
ap-1259	62	3	between	between	ADP
ap-1259	62	4	weights	weight	NOUN
ap-1259	62	5	similar	similar	ADJ
ap-1259	62	6	to	to	ADP
ap-1259	62	7	(	(	PUNCT
ap-1259	62	8	7	7	X
ap-1259	62	9	)	)	PUNCT
ap-1259	62	10	give	give	VERB
ap-1259	62	11	wt	wt	PROPN
ap-1259	62	12	(	(	PUNCT
ap-1259	62	13	(	(	PUNCT
ap-1259	62	14	mef	mef	NOUN
ap-1259	62	15	)	)	PUNCT
ap-1259	62	16	1	1	NUM
ap-1259	62	17	)	)	PUNCT
ap-1259	62	18	�	�	PROPN
ap-1259	62	19	�	�	PROPN
ap-1259	62	20	(	(	PUNCT
ap-1259	62	21	q2α	q2α	PROPN
ap-1259	62	22	q2β	q2β	VERB
ap-1259	62	23	q−2α	q−2α	PROPN
ap-1259	62	24	q−2β	q−2β	PROPN
ap-1259	62	25	)	)	PUNCT
ap-1259	62	26	1	1	NUM
ap-1259	62	27	�	�	PROPN
ap-1259	62	28	�	�	PROPN
ap-1259	62	29	(	(	PUNCT
ap-1259	62	30	21	21	NUM
ap-1259	62	31	)	)	PUNCT
ap-1259	62	32	(	(	PUNCT
ap-1259	62	33	β	β	X
ap-1259	62	34	α	α	X
ap-1259	62	35	β	β	X
ap-1259	62	36	α	α	NOUN
ap-1259	62	37	)	)	PUNCT
ap-1259	62	38	1	1	NUM
ap-1259	62	39	.	.	PUNCT
ap-1259	63	1	as	as	ADP
ap-1259	63	2	a	a	DET
ap-1259	63	3	consequence	consequence	NOUN
ap-1259	63	4	we	we	PRON
ap-1259	63	5	have	have	VERB
ap-1259	63	6	that	that	SCONJ
ap-1259	63	7	every	every	DET
ap-1259	63	8	row	row	NOUN
ap-1259	63	9	and	and	CCONJ
ap-1259	63	10	every	every	DET
ap-1259	63	11	column	column	NOUN
ap-1259	63	12	of	of	ADP
ap-1259	63	13	(	(	PUNCT
ap-1259	63	14	�	�	PROPN
ap-1259	63	15	m	m	NOUN
ap-1259	63	16	ef	ef	NOUN
ap-1259	63	17	)	)	PUNCT
ap-1259	63	18	1	1	NUM
ap-1259	63	19	should	should	AUX
ap-1259	63	20	contain	contain	VERB
ap-1259	63	21	at	at	ADV
ap-1259	63	22	least	least	ADV
ap-1259	63	23	one	one	NUM
ap-1259	63	24	0	0	NUM
ap-1259	63	25	.	.	PUNCT
ap-1259	64	1	we	we	PRON
ap-1259	64	2	project	project	VERB
ap-1259	64	3	(	(	PUNCT
ap-1259	64	4	9)-(10	9)-(10	NOUN
ap-1259	64	5	)	)	PUNCT
ap-1259	64	6	to	to	PART
ap-1259	64	7	cq[x	cq[x	VERB
ap-1259	64	8	,	,	PUNCT
ap-1259	64	9	y]2	y]2	X
ap-1259	64	10	and	and	CCONJ
ap-1259	64	11	get	get	VERB
ap-1259	64	12	a1	a1	NOUN
ap-1259	64	13	(	(	PUNCT
ap-1259	64	14	1−	1−	NUM
ap-1259	64	15	qβ	qβ	NOUN
ap-1259	64	16	)	)	PUNCT
ap-1259	65	1	y2	y2	PROPN
ap-1259	66	1	=	=	SYM
ap-1259	67	1	b1	b1	PROPN
ap-1259	68	1	(	(	PUNCT
ap-1259	69	1	q	q	NOUN
ap-1259	69	2	−	−	PROPN
ap-1259	69	3	α	α	NOUN
ap-1259	69	4	)	)	PUNCT
ap-1259	69	5	x2	x2	PROPN
ap-1259	69	6	,	,	PUNCT
ap-1259	69	7	(	(	PUNCT
ap-1259	69	8	22	22	X
ap-1259	69	9	)	)	PUNCT
ap-1259	69	10	d1	d1	NOUN
ap-1259	69	11	(	(	PUNCT
ap-1259	69	12	1−	1−	NUM
ap-1259	69	13	qα−1)x2	qα−1)x2	PROPN
ap-1259	69	14	=	=	PROPN
ap-1259	69	15	c1	c1	PROPN
ap-1259	69	16	(	(	PUNCT
ap-1259	69	17	q	q	PROPN
ap-1259	69	18	−	−	NUM
ap-1259	69	19	β−1	β−1	SYM
ap-1259	69	20	)	)	PUNCT
ap-1259	69	21	y2	y2	NOUN
ap-1259	69	22	,	,	PUNCT
ap-1259	69	23	(	(	PUNCT
ap-1259	69	24	23	23	X
ap-1259	69	25	)	)	PUNCT
ap-1259	69	26	whence	whence	NOUN
ap-1259	69	27	a1	a1	NOUN
ap-1259	69	28	(	(	PUNCT
ap-1259	69	29	1−	1−	NUM
ap-1259	69	30	qβ	qβ	NOUN
ap-1259	69	31	)	)	PUNCT
ap-1259	69	32	=	=	SYM
ap-1259	69	33	b1	b1	NOUN
ap-1259	69	34	(	(	PUNCT
ap-1259	69	35	q	q	NOUN
ap-1259	69	36	−	−	PROPN
ap-1259	70	1	α	α	NOUN
ap-1259	71	1	)	)	PUNCT
ap-1259	72	1	=	=	SYM
ap-1259	72	2	d1	d1	PROPN
ap-1259	72	3	(	(	PUNCT
ap-1259	72	4	1−	1−	NUM
ap-1259	72	5	qα−1	qα−1	NOUN
ap-1259	72	6	)	)	PUNCT
ap-1259	72	7	=	=	SYM
ap-1259	72	8	c1	c1	PROPN
ap-1259	72	9	(	(	PUNCT
ap-1259	72	10	q	q	PROPN
ap-1259	72	11	−	−	NUM
ap-1259	72	12	β−1	β−1	NUM
ap-1259	72	13	)	)	PUNCT
ap-1259	72	14	=	=	SYM
ap-1259	72	15	0	0	X
ap-1259	72	16	.	.	PUNCT
ap-1259	73	1	so	so	ADV
ap-1259	73	2	we	we	PRON
ap-1259	73	3	obtain	obtain	VERB
ap-1259	73	4	1	1	NUM
ap-1259	73	5	)	)	PUNCT
ap-1259	73	6	a1	a1	NOUN
ap-1259	73	7	=	=	SYM
ap-1259	73	8	0	0	PUNCT
ap-1259	74	1	=	=	NOUN
ap-1259	74	2	⇒	⇒	NOUN
ap-1259	74	3	β	β	X
ap-1259	74	4	=	=	SYM
ap-1259	74	5	q−1	q−1	PROPN
ap-1259	74	6	,	,	PUNCT
ap-1259	74	7	(	(	PUNCT
ap-1259	74	8	24	24	NUM
ap-1259	74	9	)	)	SYM
ap-1259	74	10	2	2	NUM
ap-1259	74	11	)	)	PUNCT
ap-1259	74	12	b1	b1	NOUN
ap-1259	74	13	=	=	SYM
ap-1259	74	14	0	0	PUNCT
ap-1259	75	1	=	=	NOUN
ap-1259	75	2	⇒	⇒	VERB
ap-1259	75	3	α	α	X
ap-1259	75	4	=	=	SYM
ap-1259	75	5	q	q	ADJ
ap-1259	75	6	,	,	PUNCT
ap-1259	75	7	(	(	PUNCT
ap-1259	75	8	25	25	NUM
ap-1259	75	9	)	)	PUNCT
ap-1259	75	10	3	3	NUM
ap-1259	75	11	)	)	PUNCT
ap-1259	75	12	c1	c1	NOUN
ap-1259	75	13	=	=	NOUN
ap-1259	75	14	0	0	PUNCT
ap-1259	76	1	=	=	NOUN
ap-1259	76	2	⇒	⇒	NOUN
ap-1259	76	3	β	β	X
ap-1259	76	4	=	=	SYM
ap-1259	76	5	q−1	q−1	PROPN
ap-1259	76	6	,	,	PUNCT
ap-1259	76	7	(	(	PUNCT
ap-1259	76	8	26	26	NUM
ap-1259	76	9	)	)	PUNCT
ap-1259	76	10	4	4	NUM
ap-1259	76	11	)	)	PUNCT
ap-1259	76	12	d1	d1	NOUN
ap-1259	76	13	=	=	SYM
ap-1259	76	14	0	0	PUNCT
ap-1259	77	1	=	=	NOUN
ap-1259	77	2	⇒	⇒	X
ap-1259	77	3	α	α	X
ap-1259	77	4	=	=	SYM
ap-1259	77	5	q.	q.	PROPN
ap-1259	77	6	(	(	PUNCT
ap-1259	77	7	27	27	NUM
ap-1259	77	8	)	)	PUNCT
ap-1259	77	9	the	the	DET
ap-1259	77	10	symbolic	symbolic	ADJ
ap-1259	77	11	matrix	matrix	NOUN
ap-1259	77	12	(	(	PUNCT
ap-1259	77	13	�	�	PROPN
ap-1259	77	14	0	0	NUM
ap-1259	77	15	0	0	NUM
ap-1259	77	16	�	�	PROPN
ap-1259	77	17	)	)	PUNCT
ap-1259	77	18	1	1	NUM
ap-1259	77	19	can	can	AUX
ap-1259	77	20	be	be	AUX
ap-1259	77	21	discarded	discard	VERB
ap-1259	77	22	from	from	ADP
ap-1259	77	23	the	the	DET
ap-1259	77	24	list	list	NOUN
ap-1259	77	25	of	of	ADP
ap-1259	77	26	symbolic	symbolic	ADJ
ap-1259	77	27	matrices	matrix	NOUN
ap-1259	77	28	with	with	ADP
ap-1259	77	29	at	at	ADV
ap-1259	77	30	least	least	ADV
ap-1259	77	31	one	one	NUM
ap-1259	77	32	0	0	NUM
ap-1259	77	33	at	at	ADP
ap-1259	77	34	every	every	DET
ap-1259	77	35	row	row	NOUN
ap-1259	77	36	or	or	CCONJ
ap-1259	77	37	column	column	NOUN
ap-1259	77	38	,	,	PUNCT
ap-1259	77	39	because	because	SCONJ
ap-1259	77	40	of	of	ADP
ap-1259	77	41	(	(	PUNCT
ap-1259	77	42	21	21	NUM
ap-1259	77	43	)	)	PUNCT
ap-1259	77	44	,	,	PUNCT
ap-1259	77	45	26	26	NUM
ap-1259	77	46	acta	acta	PROPN
ap-1259	77	47	polytechnica	polytechnica	PROPN
ap-1259	77	48	vol	vol	NOUN
ap-1259	77	49	.	.	PROPN
ap-1259	78	1	50	50	NUM
ap-1259	78	2	no	no	NOUN
ap-1259	78	3	.	.	PUNCT
ap-1259	79	1	5/2010	5/2010	NUM
ap-1259	79	2	(	(	PUNCT
ap-1259	79	3	24)–(27	24)–(27	NUM
ap-1259	79	4	)	)	PUNCT
ap-1259	79	5	.	.	PUNCT
ap-1259	80	1	for	for	ADP
ap-1259	80	2	other	other	ADJ
ap-1259	80	3	symbolic	symbolic	ADJ
ap-1259	80	4	matrices	matrix	NOUN
ap-1259	80	5	with	with	ADP
ap-1259	80	6	the	the	DET
ap-1259	80	7	above	above	ADJ
ap-1259	80	8	property	property	NOUN
ap-1259	80	9	we	we	PRON
ap-1259	80	10	have	have	AUX
ap-1259	80	11	(	(	PUNCT
ap-1259	80	12	�	�	X
ap-1259	80	13	0	0	NUM
ap-1259	80	14	0	0	NUM
ap-1259	80	15	0	0	NUM
ap-1259	80	16	)	)	PUNCT
ap-1259	80	17	1	1	NUM
ap-1259	80	18	=	=	NOUN
ap-1259	80	19	⇒	⇒	VERB
ap-1259	80	20	α	α	X
ap-1259	80	21	=	=	SYM
ap-1259	80	22	q−3	q−3	PROPN
ap-1259	80	23	,	,	PUNCT
ap-1259	80	24	β	β	X
ap-1259	80	25	=	=	SYM
ap-1259	80	26	q−1	q−1	PROPN
ap-1259	80	27	,	,	PUNCT
ap-1259	80	28	(	(	PUNCT
ap-1259	80	29	28	28	NUM
ap-1259	80	30	)	)	PUNCT
ap-1259	80	31	(	(	PUNCT
ap-1259	80	32	0	0	NUM
ap-1259	80	33	�	�	PROPN
ap-1259	80	34	0	0	NUM
ap-1259	80	35	0	0	NUM
ap-1259	80	36	)	)	PUNCT
ap-1259	80	37	1	1	NUM
ap-1259	81	1	=	=	NOUN
ap-1259	81	2	⇒	⇒	VERB
ap-1259	81	3	α	α	NOUN
ap-1259	81	4	=	=	SYM
ap-1259	81	5	q	q	NOUN
ap-1259	81	6	,	,	PUNCT
ap-1259	81	7	β	β	X
ap-1259	81	8	=	=	SYM
ap-1259	81	9	q−1	q−1	PROPN
ap-1259	81	10	,	,	PUNCT
ap-1259	81	11	(	(	PUNCT
ap-1259	81	12	29	29	NUM
ap-1259	81	13	)	)	PUNCT
ap-1259	81	14	(	(	PUNCT
ap-1259	81	15	0	0	NUM
ap-1259	81	16	0	0	NUM
ap-1259	81	17	�	�	PROPN
ap-1259	81	18	0	0	NUM
ap-1259	81	19	)	)	PUNCT
ap-1259	81	20	1	1	NUM
ap-1259	81	21	=	=	NOUN
ap-1259	81	22	⇒	⇒	VERB
ap-1259	81	23	α	α	NOUN
ap-1259	81	24	=	=	SYM
ap-1259	81	25	q	q	NOUN
ap-1259	81	26	,	,	PUNCT
ap-1259	81	27	β	β	X
ap-1259	81	28	=	=	SYM
ap-1259	81	29	q−1	q−1	PROPN
ap-1259	81	30	,	,	PUNCT
ap-1259	81	31	(	(	PUNCT
ap-1259	81	32	30	30	NUM
ap-1259	81	33	)	)	PUNCT
ap-1259	81	34	(	(	PUNCT
ap-1259	81	35	0	0	NUM
ap-1259	81	36	0	0	NUM
ap-1259	81	37	0	0	NUM
ap-1259	81	38	�	�	PROPN
ap-1259	81	39	)	)	PUNCT
ap-1259	81	40	1	1	NUM
ap-1259	82	1	=	=	NOUN
ap-1259	82	2	⇒	⇒	VERB
ap-1259	82	3	α	α	NOUN
ap-1259	82	4	=	=	SYM
ap-1259	82	5	q	q	NOUN
ap-1259	82	6	,	,	PUNCT
ap-1259	82	7	β	β	NOUN
ap-1259	82	8	=	=	SYM
ap-1259	82	9	q3	q3	PROPN
ap-1259	82	10	,	,	PUNCT
ap-1259	82	11	(	(	PUNCT
ap-1259	82	12	31	31	NUM
ap-1259	82	13	)	)	PUNCT
ap-1259	82	14	(	(	PUNCT
ap-1259	82	15	0	0	NUM
ap-1259	82	16	�	�	PROPN
ap-1259	82	17	�	�	PROPN
ap-1259	82	18	0	0	NUM
ap-1259	82	19	)	)	PUNCT
ap-1259	82	20	1	1	NUM
ap-1259	82	21	=	=	NOUN
ap-1259	82	22	⇒	⇒	VERB
ap-1259	82	23	α	α	NOUN
ap-1259	82	24	=	=	SYM
ap-1259	82	25	q	q	NOUN
ap-1259	82	26	,	,	PUNCT
ap-1259	82	27	β	β	X
ap-1259	82	28	=	=	SYM
ap-1259	82	29	q−1	q−1	PROPN
ap-1259	82	30	,	,	PUNCT
ap-1259	82	31	(	(	PUNCT
ap-1259	82	32	32	32	NUM
ap-1259	82	33	)	)	PUNCT
ap-1259	82	34	and	and	CCONJ
ap-1259	82	35	the	the	DET
ap-1259	82	36	matrix	matrix	NOUN
ap-1259	82	37	(	(	PUNCT
ap-1259	82	38	0	0	NUM
ap-1259	82	39	0	0	NUM
ap-1259	82	40	0	0	NUM
ap-1259	82	41	0	0	NUM
ap-1259	82	42	)	)	PUNCT
ap-1259	82	43	1	1	NUM
ap-1259	82	44	does	do	AUX
ap-1259	82	45	not	not	PART
ap-1259	82	46	determine	determine	VERB
ap-1259	82	47	the	the	DET
ap-1259	82	48	weight	weight	NOUN
ap-1259	82	49	constants	constant	NOUN
ap-1259	82	50	.	.	PUNCT
ap-1259	83	1	let	let	VERB
ap-1259	83	2	us	we	PRON
ap-1259	83	3	introduce	introduce	VERB
ap-1259	83	4	a	a	DET
ap-1259	83	5	table	table	NOUN
ap-1259	83	6	of	of	ADP
ap-1259	83	7	families	family	NOUN
ap-1259	83	8	of	of	ADP
ap-1259	83	9	uq	uq	PROPN
ap-1259	83	10	(	(	PUNCT
ap-1259	83	11	sl2)actions	sl2)actions	PROPN
ap-1259	83	12	,	,	PUNCT
ap-1259	83	13	each	each	DET
ap-1259	83	14	family	family	NOUN
ap-1259	83	15	is	be	AUX
ap-1259	83	16	labeled	label	VERB
ap-1259	83	17	by	by	ADP
ap-1259	83	18	two	two	NUM
ap-1259	83	19	symbolic	symbolic	ADJ
ap-1259	83	20	matrices	matrix	NOUN
ap-1259	83	21	(	(	PUNCT
ap-1259	83	22	�	�	PROPN
ap-1259	83	23	mef	mef	PROPN
ap-1259	83	24	)	)	PUNCT
ap-1259	83	25	0	0	NUM
ap-1259	83	26	,	,	PUNCT
ap-1259	83	27	(	(	PUNCT
ap-1259	83	28	�	�	PROPN
ap-1259	83	29	mef	mef	PROPN
ap-1259	83	30	)	)	PUNCT
ap-1259	83	31	1	1	NUM
ap-1259	83	32	,	,	PUNCT
ap-1259	83	33	and	and	CCONJ
ap-1259	83	34	we	we	PRON
ap-1259	83	35	call	call	VERB
ap-1259	83	36	it	it	PRON
ap-1259	83	37	a	a	DET
ap-1259	83	38	[	[	X
ap-1259	83	39	(	(	PUNCT
ap-1259	83	40	�	�	PROPN
ap-1259	83	41	m	m	NOUN
ap-1259	83	42	ef	ef	PROPN
ap-1259	83	43	)	)	PUNCT
ap-1259	83	44	0	0	NUM
ap-1259	83	45	;	;	PUNCT
ap-1259	83	46	(	(	PUNCT
ap-1259	83	47	�	�	PROPN
ap-1259	83	48	mef	mef	PROPN
ap-1259	83	49	)	)	PUNCT
ap-1259	83	50	1	1	NUM
ap-1259	83	51	]	]	SYM
ap-1259	83	52	-series	-serie	NOUN
ap-1259	83	53	.	.	PUNCT
ap-1259	84	1	note	note	VERB
ap-1259	84	2	that	that	SCONJ
ap-1259	84	3	the	the	DET
ap-1259	84	4	series	series	NOUN
ap-1259	84	5	labeled	label	VERB
ap-1259	84	6	with	with	ADP
ap-1259	84	7	pairs	pair	NOUN
ap-1259	84	8	of	of	ADP
ap-1259	84	9	nonzero	nonzero	ADJ
ap-1259	84	10	symbolic	symbolic	ADJ
ap-1259	84	11	matrices	matrix	NOUN
ap-1259	84	12	at	at	ADP
ap-1259	84	13	both	both	DET
ap-1259	84	14	positions	position	NOUN
ap-1259	84	15	are	be	AUX
ap-1259	84	16	empty	empty	ADJ
ap-1259	84	17	,	,	PUNCT
ap-1259	84	18	because	because	SCONJ
ap-1259	84	19	each	each	DET
ap-1259	84	20	such	such	ADJ
ap-1259	84	21	matrix	matrix	NOUN
ap-1259	84	22	determines	determine	VERB
ap-1259	84	23	a	a	DET
ap-1259	84	24	pair	pair	NOUN
ap-1259	84	25	of	of	ADP
ap-1259	84	26	specific	specific	ADJ
ap-1259	84	27	weight	weight	NOUN
ap-1259	84	28	constants	constant	NOUN
ap-1259	84	29	α	α	NOUN
ap-1259	84	30	and	and	CCONJ
ap-1259	84	31	β	β	X
ap-1259	84	32	(	(	PUNCT
ap-1259	84	33	16)–(19	16)–(19	NUM
ap-1259	84	34	)	)	PUNCT
ap-1259	84	35	which	which	PRON
ap-1259	84	36	fails	fail	VERB
ap-1259	84	37	to	to	PART
ap-1259	84	38	coincide	coincide	VERB
ap-1259	84	39	to	to	ADP
ap-1259	84	40	any	any	DET
ap-1259	84	41	pair	pair	NOUN
ap-1259	84	42	of	of	ADP
ap-1259	84	43	such	such	ADJ
ap-1259	84	44	constants	constant	NOUN
ap-1259	84	45	associated	associate	VERB
ap-1259	84	46	to	to	ADP
ap-1259	84	47	the	the	DET
ap-1259	84	48	set	set	NOUN
ap-1259	84	49	of	of	ADP
ap-1259	84	50	nonzero	nonzero	PROPN
ap-1259	84	51	symbolic	symbolic	ADJ
ap-1259	84	52	matrices	matrix	NOUN
ap-1259	84	53	at	at	ADP
ap-1259	84	54	the	the	DET
ap-1259	84	55	second	second	ADJ
ap-1259	84	56	position	position	NOUN
ap-1259	84	57	(	(	PUNCT
ap-1259	84	58	28)–(32	28)–(32	NOUN
ap-1259	84	59	)	)	PUNCT
ap-1259	84	60	.	.	PUNCT
ap-1259	85	1	also	also	ADV
ap-1259	85	2	the	the	DET
ap-1259	85	3	series	series	NOUN
ap-1259	85	4	with	with	ADP
ap-1259	85	5	zero	zero	NUM
ap-1259	85	6	symbolic	symbolic	ADJ
ap-1259	85	7	matrix	matrix	NOUN
ap-1259	85	8	at	at	ADP
ap-1259	85	9	the	the	DET
ap-1259	85	10	first	first	ADJ
ap-1259	85	11	position	position	NOUN
ap-1259	85	12	and	and	CCONJ
ap-1259	85	13	symbolic	symbolic	ADJ
ap-1259	85	14	matrices	matrix	NOUN
ap-1259	85	15	containing	contain	VERB
ap-1259	85	16	only	only	ADV
ap-1259	85	17	one	one	NUM
ap-1259	85	18	�	�	NOUN
ap-1259	85	19	at	at	ADP
ap-1259	85	20	the	the	DET
ap-1259	85	21	second	second	ADJ
ap-1259	85	22	position	position	NOUN
ap-1259	85	23	are	be	AUX
ap-1259	85	24	empty	empty	ADJ
ap-1259	85	25	.	.	PUNCT
ap-1259	86	1	in	in	ADP
ap-1259	86	2	this	this	DET
ap-1259	86	3	way	way	NOUN
ap-1259	86	4	we	we	PRON
ap-1259	86	5	get	get	VERB
ap-1259	86	6	24	24	NUM
ap-1259	86	7	“	"	PUNCT
ap-1259	86	8	empty	empty	ADJ
ap-1259	86	9	”	"	PUNCT
ap-1259	86	10	[	[	X
ap-1259	86	11	(	(	PUNCT
ap-1259	86	12	�	�	PROPN
ap-1259	86	13	mef	mef	PROPN
ap-1259	86	14	)	)	PUNCT
ap-1259	86	15	0	0	NUM
ap-1259	87	1	;	;	PUNCT
ap-1259	87	2	(	(	PUNCT
ap-1259	87	3	�	�	PROPN
ap-1259	87	4	m	m	NOUN
ap-1259	87	5	ef	ef	NOUN
ap-1259	87	6	)	)	PUNCT
ap-1259	87	7	1	1	NUM
ap-1259	87	8	]	]	PUNCT
ap-1259	87	9	series	series	NOUN
ap-1259	87	10	.	.	PUNCT
ap-1259	88	1	let	let	VERB
ap-1259	88	2	us	we	PRON
ap-1259	88	3	turn	turn	VERB
ap-1259	88	4	to	to	ADP
ap-1259	88	5	“	"	PUNCT
ap-1259	88	6	non	non	ADJ
ap-1259	88	7	-	-	ADJ
ap-1259	88	8	empty	empty	ADJ
ap-1259	88	9	”	"	PUNCT
ap-1259	88	10	series	series	NOUN
ap-1259	88	11	and	and	CCONJ
ap-1259	88	12	begin	begin	VERB
ap-1259	88	13	with	with	ADP
ap-1259	88	14	the	the	DET
ap-1259	88	15	case	case	NOUN
ap-1259	88	16	in	in	ADP
ap-1259	88	17	which	which	PRON
ap-1259	88	18	the	the	DET
ap-1259	88	19	action	action	NOUN
ap-1259	88	20	ef	ef	PROPN
ap-1259	88	21	-matrix	-matrix	PROPN
ap-1259	88	22	is	be	AUX
ap-1259	88	23	zero	zero	NUM
ap-1259	88	24	.	.	PUNCT
ap-1259	89	1	theorem	theorem	VERB
ap-1259	89	2	2	2	NUM
ap-1259	90	1	the	the	DET
ap-1259	90	2	[	[	X
ap-1259	90	3	(	(	PUNCT
ap-1259	90	4	0	0	NUM
ap-1259	90	5	0	0	NUM
ap-1259	90	6	0	0	NUM
ap-1259	90	7	0	0	NUM
ap-1259	90	8	)	)	PUNCT
ap-1259	90	9	0	0	NUM
ap-1259	90	10	;	;	PUNCT
ap-1259	90	11	(	(	PUNCT
ap-1259	90	12	0	0	NUM
ap-1259	90	13	0	0	NUM
ap-1259	90	14	0	0	NUM
ap-1259	90	15	0	0	NUM
ap-1259	90	16	)	)	PUNCT
ap-1259	90	17	1	1	NUM
ap-1259	90	18	]	]	PUNCT
ap-1259	90	19	-series	-serie	NOUN
ap-1259	90	20	consists	consist	VERB
ap-1259	90	21	of	of	ADP
ap-1259	90	22	four	four	NUM
ap-1259	90	23	uq	uq	NOUN
ap-1259	90	24	(	(	PUNCT
ap-1259	90	25	sl2)-module	sl2)-module	PROPN
ap-1259	90	26	algebra	algebra	NOUN
ap-1259	90	27	structures	structure	NOUN
ap-1259	90	28	on	on	ADP
ap-1259	90	29	the	the	DET
ap-1259	90	30	quantum	quantum	ADJ
ap-1259	90	31	plane	plane	NOUN
ap-1259	90	32	given	give	VERB
ap-1259	90	33	by	by	ADP
ap-1259	90	34	k	k	PROPN
ap-1259	90	35	(	(	PUNCT
ap-1259	90	36	x	x	NOUN
ap-1259	90	37	)	)	PUNCT
ap-1259	90	38	=	=	SYM
ap-1259	90	39	±x	±x	PROPN
ap-1259	90	40	,	,	PUNCT
ap-1259	90	41	k	k	PROPN
ap-1259	90	42	(	(	PUNCT
ap-1259	90	43	y	y	NOUN
ap-1259	90	44	)	)	PUNCT
ap-1259	90	45	=	=	SYM
ap-1259	90	46	±y	±y	PROPN
ap-1259	90	47	,	,	PUNCT
ap-1259	90	48	(	(	PUNCT
ap-1259	90	49	33	33	NUM
ap-1259	90	50	)	)	PUNCT
ap-1259	90	51	e	e	NOUN
ap-1259	90	52	(	(	PUNCT
ap-1259	90	53	x	x	NOUN
ap-1259	90	54	)	)	PUNCT
ap-1259	90	55	=	=	SYM
ap-1259	90	56	e	e	X
ap-1259	90	57	(	(	PUNCT
ap-1259	90	58	y	y	NOUN
ap-1259	90	59	)	)	PUNCT
ap-1259	90	60	=	=	SYM
ap-1259	91	1	f	f	X
ap-1259	91	2	(	(	PUNCT
ap-1259	91	3	x	x	X
ap-1259	91	4	)	)	PUNCT
ap-1259	91	5	=	=	SYM
ap-1259	91	6	f	f	PROPN
ap-1259	91	7	(	(	PUNCT
ap-1259	91	8	y	y	NOUN
ap-1259	91	9	)	)	PUNCT
ap-1259	91	10	=	=	SYM
ap-1259	91	11	0	0	NUM
ap-1259	91	12	,	,	PUNCT
ap-1259	91	13	(	(	PUNCT
ap-1259	91	14	34	34	NUM
ap-1259	91	15	)	)	PUNCT
ap-1259	91	16	which	which	PRON
ap-1259	91	17	are	be	AUX
ap-1259	91	18	pairwise	pairwise	PROPN
ap-1259	91	19	non	non	ADJ
ap-1259	91	20	-	-	ADJ
ap-1259	91	21	isomorphic	isomorphic	ADJ
ap-1259	91	22	.	.	PUNCT
ap-1259	92	1	the	the	DET
ap-1259	92	2	next	next	ADJ
ap-1259	92	3	theorem	theorem	NOUN
ap-1259	92	4	describes	describe	VERB
ap-1259	92	5	the	the	DET
ap-1259	92	6	well	well	ADV
ap-1259	92	7	-	-	PUNCT
ap-1259	92	8	known	know	VERB
ap-1259	92	9	symmetry	symmetry	NOUN
ap-1259	92	10	[	[	X
ap-1259	92	11	6	6	NUM
ap-1259	92	12	,	,	PUNCT
ap-1259	92	13	7	7	NUM
ap-1259	92	14	]	]	PUNCT
ap-1259	92	15	.	.	PUNCT
ap-1259	93	1	theorem	theorem	VERB
ap-1259	93	2	3	3	NUM
ap-1259	94	1	the	the	DET
ap-1259	94	2	[	[	X
ap-1259	94	3	(	(	PUNCT
ap-1259	94	4	0	0	NUM
ap-1259	94	5	0	0	NUM
ap-1259	94	6	0	0	NUM
ap-1259	94	7	0	0	NUM
ap-1259	94	8	)	)	PUNCT
ap-1259	94	9	0	0	NUM
ap-1259	95	1	;	;	PUNCT
ap-1259	95	2	(	(	PUNCT
ap-1259	95	3	0	0	NUM
ap-1259	95	4	�	�	PROPN
ap-1259	95	5	�	�	PROPN
ap-1259	95	6	0	0	NUM
ap-1259	95	7	)	)	PUNCT
ap-1259	95	8	1	1	NUM
ap-1259	95	9	]	]	PUNCT
ap-1259	95	10	-series	-serie	NOUN
ap-1259	95	11	consists	consist	VERB
ap-1259	95	12	of	of	ADP
ap-1259	95	13	a	a	DET
ap-1259	95	14	one	one	NUM
ap-1259	95	15	-	-	PUNCT
ap-1259	95	16	parameter	parameter	NOUN
ap-1259	95	17	(	(	PUNCT
ap-1259	95	18	τ	τ	PROPN
ap-1259	95	19	∈	∈	PROPN
ap-1259	95	20	c	c	NOUN
ap-1259	95	21	\	\	X
ap-1259	95	22	{	{	PUNCT
ap-1259	95	23	0	0	NUM
ap-1259	95	24	}	}	PUNCT
ap-1259	95	25	)	)	PUNCT
ap-1259	95	26	family	family	NOUN
ap-1259	95	27	of	of	ADP
ap-1259	95	28	uq	uq	PROPN
ap-1259	95	29	(	(	PUNCT
ap-1259	95	30	sl2)-module	sl2)-module	PROPN
ap-1259	95	31	algebra	algebra	NOUN
ap-1259	95	32	structures	structure	NOUN
ap-1259	95	33	on	on	ADP
ap-1259	95	34	the	the	DET
ap-1259	95	35	quantum	quantum	ADJ
ap-1259	95	36	plane	plane	NOUN
ap-1259	95	37	k	k	PROPN
ap-1259	95	38	(	(	PUNCT
ap-1259	95	39	x	x	X
ap-1259	95	40	)	)	PUNCT
ap-1259	96	1	=	=	SYM
ap-1259	96	2	qx	qx	INTJ
ap-1259	96	3	,	,	PUNCT
ap-1259	96	4	k	k	PROPN
ap-1259	96	5	(	(	PUNCT
ap-1259	96	6	y	y	NOUN
ap-1259	96	7	)	)	PUNCT
ap-1259	96	8	=	=	SYM
ap-1259	97	1	q−1y	q−1y	NOUN
ap-1259	97	2	,	,	PUNCT
ap-1259	97	3	(	(	PUNCT
ap-1259	97	4	35	35	NUM
ap-1259	97	5	)	)	PUNCT
ap-1259	97	6	e	e	NOUN
ap-1259	97	7	(	(	PUNCT
ap-1259	97	8	x	x	X
ap-1259	97	9	)	)	PUNCT
ap-1259	97	10	=	=	SYM
ap-1259	97	11	0	0	NUM
ap-1259	97	12	,	,	PUNCT
ap-1259	97	13	e	e	X
ap-1259	97	14	(	(	PUNCT
ap-1259	97	15	y	y	NOUN
ap-1259	97	16	)	)	PUNCT
ap-1259	97	17	=	=	SYM
ap-1259	97	18	τx	τx	PROPN
ap-1259	97	19	,	,	PUNCT
ap-1259	97	20	(	(	PUNCT
ap-1259	97	21	36	36	NUM
ap-1259	97	22	)	)	PUNCT
ap-1259	97	23	f	f	NOUN
ap-1259	97	24	(	(	PUNCT
ap-1259	97	25	x	x	X
ap-1259	97	26	)	)	PUNCT
ap-1259	97	27	=	=	SYM
ap-1259	97	28	τ−1y	τ−1y	PROPN
ap-1259	97	29	,	,	PUNCT
ap-1259	97	30	f	f	PROPN
ap-1259	97	31	(	(	PUNCT
ap-1259	97	32	y	y	NOUN
ap-1259	97	33	)	)	PUNCT
ap-1259	97	34	=	=	SYM
ap-1259	98	1	0	0	X
ap-1259	98	2	.	.	PUNCT
ap-1259	99	1	(	(	PUNCT
ap-1259	99	2	37	37	NUM
ap-1259	99	3	)	)	PUNCT
ap-1259	99	4	all	all	DET
ap-1259	99	5	these	these	DET
ap-1259	99	6	structures	structure	NOUN
ap-1259	99	7	are	be	AUX
ap-1259	99	8	isomorphic	isomorphic	ADJ
ap-1259	99	9	,	,	PUNCT
ap-1259	99	10	in	in	ADP
ap-1259	99	11	particular	particular	ADJ
ap-1259	99	12	to	to	ADP
ap-1259	99	13	the	the	DET
ap-1259	99	14	action	action	NOUN
ap-1259	99	15	as	as	ADP
ap-1259	99	16	above	above	ADV
ap-1259	99	17	with	with	ADP
ap-1259	99	18	τ	τ	PROPN
ap-1259	99	19	=	=	SYM
ap-1259	99	20	1	1	X
ap-1259	99	21	.	.	PUNCT
ap-1259	100	1	the	the	DET
ap-1259	100	2	essential	essential	ADJ
ap-1259	100	3	claim	claim	NOUN
ap-1259	100	4	here	here	ADV
ap-1259	100	5	which	which	PRON
ap-1259	100	6	is	be	AUX
ap-1259	100	7	not	not	PART
ap-1259	100	8	covered	cover	VERB
ap-1259	100	9	by	by	ADP
ap-1259	100	10	[	[	X
ap-1259	100	11	6	6	NUM
ap-1259	100	12	,	,	PUNCT
ap-1259	100	13	7	7	NUM
ap-1259	100	14	]	]	PUNCT
ap-1259	100	15	,	,	PUNCT
ap-1259	100	16	is	be	AUX
ap-1259	100	17	that	that	SCONJ
ap-1259	100	18	no	no	ADV
ap-1259	100	19	higher	high	ADJ
ap-1259	100	20	(	(	PUNCT
ap-1259	100	21	>	>	X
ap-1259	100	22	1	1	NUM
ap-1259	100	23	)	)	PUNCT
ap-1259	100	24	degree	degree	NOUN
ap-1259	100	25	terms	term	NOUN
ap-1259	100	26	could	could	AUX
ap-1259	100	27	appear	appear	VERB
ap-1259	100	28	in	in	ADP
ap-1259	100	29	the	the	DET
ap-1259	100	30	expressions	expression	NOUN
ap-1259	100	31	for	for	ADP
ap-1259	100	32	e(x	e(x	NUM
ap-1259	100	33	)	)	PUNCT
ap-1259	100	34	,	,	PUNCT
ap-1259	100	35	e(y	e(y	PROPN
ap-1259	100	36	)	)	PUNCT
ap-1259	100	37	,	,	PUNCT
ap-1259	100	38	f(x	f(x	PROPN
ap-1259	100	39	)	)	PUNCT
ap-1259	100	40	,	,	PUNCT
ap-1259	100	41	f(y	f(y	NOUN
ap-1259	100	42	)	)	PUNCT
ap-1259	100	43	in	in	ADP
ap-1259	100	44	(	(	PUNCT
ap-1259	100	45	36	36	NUM
ap-1259	100	46	)	)	PUNCT
ap-1259	100	47	and	and	CCONJ
ap-1259	100	48	(	(	PUNCT
ap-1259	100	49	37	37	NUM
ap-1259	100	50	)	)	PUNCT
ap-1259	100	51	.	.	PUNCT
ap-1259	101	1	this	this	PRON
ap-1259	101	2	can	can	AUX
ap-1259	101	3	be	be	AUX
ap-1259	101	4	proved	prove	VERB
ap-1259	101	5	by	by	ADP
ap-1259	101	6	a	a	DET
ap-1259	101	7	routine	routine	ADJ
ap-1259	101	8	computation	computation	NOUN
ap-1259	101	9	which	which	PRON
ap-1259	101	10	relies	rely	VERB
ap-1259	101	11	upon	upon	SCONJ
ap-1259	101	12	our	our	PRON
ap-1259	101	13	assumption	assumption	NOUN
ap-1259	101	14	0	0	PUNCT
ap-1259	101	15	<	<	X
ap-1259	101	16	q	q	X
ap-1259	101	17	<	<	X
ap-1259	101	18	1	1	NUM
ap-1259	101	19	.	.	PUNCT
ap-1259	101	20	consider	consider	VERB
ap-1259	101	21	the	the	DET
ap-1259	101	22	symmetries	symmetry	NOUN
ap-1259	101	23	whose	whose	DET
ap-1259	101	24	symbolic	symbolic	ADJ
ap-1259	101	25	matrix	matrix	NOUN
ap-1259	101	26	(	(	PUNCT
ap-1259	101	27	�	�	PROPN
ap-1259	101	28	m	m	NOUN
ap-1259	101	29	ef	ef	NOUN
ap-1259	101	30	)	)	PUNCT
ap-1259	101	31	0	0	PUNCT
ap-1259	102	1	contains	contain	VERB
ap-1259	102	2	one	one	NUM
ap-1259	102	3	�	�	PROPN
ap-1259	102	4	.	.	PUNCT
ap-1259	103	1	theorem	theorem	VERB
ap-1259	103	2	4	4	NUM
ap-1259	103	3	the	the	DET
ap-1259	103	4	[	[	X
ap-1259	103	5	(	(	PUNCT
ap-1259	103	6	0	0	NUM
ap-1259	103	7	�	�	PROPN
ap-1259	103	8	0	0	NUM
ap-1259	103	9	0	0	NUM
ap-1259	103	10	)	)	PUNCT
ap-1259	103	11	0	0	NUM
ap-1259	103	12	;	;	PUNCT
ap-1259	103	13	(	(	PUNCT
ap-1259	103	14	0	0	NUM
ap-1259	103	15	0	0	NUM
ap-1259	103	16	0	0	NUM
ap-1259	103	17	0	0	NUM
ap-1259	103	18	)	)	PUNCT
ap-1259	103	19	1	1	NUM
ap-1259	103	20	]	]	PUNCT
ap-1259	103	21	-series	-serie	NOUN
ap-1259	103	22	consists	consist	VERB
ap-1259	103	23	of	of	ADP
ap-1259	103	24	a	a	DET
ap-1259	103	25	one	one	NUM
ap-1259	103	26	-	-	PUNCT
ap-1259	103	27	parameter	parameter	NOUN
ap-1259	103	28	(	(	PUNCT
ap-1259	103	29	b0	b0	NOUN
ap-1259	103	30	∈	∈	PROPN
ap-1259	103	31	c	c	NOUN
ap-1259	103	32	\	\	X
ap-1259	103	33	{	{	PUNCT
ap-1259	103	34	0	0	NUM
ap-1259	103	35	}	}	PUNCT
ap-1259	103	36	)	)	PUNCT
ap-1259	103	37	family	family	NOUN
ap-1259	103	38	of	of	ADP
ap-1259	103	39	uq	uq	PROPN
ap-1259	103	40	(	(	PUNCT
ap-1259	103	41	sl2)-module	sl2)-module	PROPN
ap-1259	103	42	algebra	algebra	NOUN
ap-1259	103	43	structures	structure	NOUN
ap-1259	103	44	on	on	ADP
ap-1259	103	45	the	the	DET
ap-1259	103	46	quantum	quantum	ADJ
ap-1259	103	47	plane	plane	NOUN
ap-1259	103	48	k	k	PROPN
ap-1259	103	49	(	(	PUNCT
ap-1259	103	50	x	x	X
ap-1259	103	51	)	)	PUNCT
ap-1259	103	52	=	=	SYM
ap-1259	104	1	qx	qx	INTJ
ap-1259	104	2	,	,	PUNCT
ap-1259	104	3	k	k	PROPN
ap-1259	104	4	(	(	PUNCT
ap-1259	104	5	y	y	NOUN
ap-1259	104	6	)	)	PUNCT
ap-1259	104	7	=	=	SYM
ap-1259	105	1	q−2y	q−2y	NOUN
ap-1259	105	2	,	,	PUNCT
ap-1259	105	3	(	(	PUNCT
ap-1259	105	4	38	38	NUM
ap-1259	105	5	)	)	PUNCT
ap-1259	105	6	e	e	NOUN
ap-1259	105	7	(	(	PUNCT
ap-1259	105	8	x	x	X
ap-1259	105	9	)	)	PUNCT
ap-1259	105	10	=	=	SYM
ap-1259	105	11	0	0	NUM
ap-1259	105	12	,	,	PUNCT
ap-1259	105	13	e	e	X
ap-1259	105	14	(	(	PUNCT
ap-1259	105	15	y	y	NOUN
ap-1259	105	16	)	)	PUNCT
ap-1259	105	17	=	=	SYM
ap-1259	105	18	b0	b0	NOUN
ap-1259	105	19	,	,	PUNCT
ap-1259	105	20	(	(	PUNCT
ap-1259	105	21	39	39	NUM
ap-1259	105	22	)	)	PUNCT
ap-1259	105	23	f	f	NOUN
ap-1259	105	24	(	(	PUNCT
ap-1259	105	25	x	x	X
ap-1259	105	26	)	)	PUNCT
ap-1259	105	27	=	=	VERB
ap-1259	105	28	b−10	b−10	VERB
ap-1259	106	1	xy	xy	PROPN
ap-1259	106	2	,	,	PUNCT
ap-1259	106	3	f	f	PROPN
ap-1259	106	4	(	(	PUNCT
ap-1259	106	5	y	y	NOUN
ap-1259	106	6	)	)	PUNCT
ap-1259	106	7	=	=	SYM
ap-1259	106	8	−qb−10	−qb−10	PROPN
ap-1259	106	9	y2	y2	PROPN
ap-1259	106	10	.	.	PUNCT
ap-1259	107	1	(	(	PUNCT
ap-1259	107	2	40	40	NUM
ap-1259	107	3	)	)	PUNCT
ap-1259	107	4	all	all	DET
ap-1259	107	5	these	these	DET
ap-1259	107	6	structures	structure	NOUN
ap-1259	107	7	are	be	AUX
ap-1259	107	8	isomorphic	isomorphic	ADJ
ap-1259	107	9	,	,	PUNCT
ap-1259	107	10	in	in	ADP
ap-1259	107	11	particular	particular	ADJ
ap-1259	107	12	to	to	ADP
ap-1259	107	13	the	the	DET
ap-1259	107	14	action	action	NOUN
ap-1259	107	15	as	as	ADP
ap-1259	107	16	above	above	ADV
ap-1259	107	17	with	with	ADP
ap-1259	107	18	b0	b0	NOUN
ap-1259	107	19	=	=	SYM
ap-1259	107	20	1	1	X
ap-1259	107	21	.	.	PUNCT
ap-1259	107	22	theorem	theorem	VERB
ap-1259	107	23	5	5	NUM
ap-1259	107	24	the	the	DET
ap-1259	107	25	[	[	X
ap-1259	107	26	(	(	PUNCT
ap-1259	107	27	0	0	NUM
ap-1259	107	28	0	0	NUM
ap-1259	107	29	�	�	PROPN
ap-1259	107	30	0	0	NUM
ap-1259	107	31	)	)	PUNCT
ap-1259	107	32	0	0	NUM
ap-1259	107	33	;	;	PUNCT
ap-1259	107	34	(	(	PUNCT
ap-1259	107	35	0	0	NUM
ap-1259	107	36	0	0	NUM
ap-1259	107	37	0	0	NUM
ap-1259	107	38	0	0	NUM
ap-1259	107	39	)	)	PUNCT
ap-1259	107	40	1	1	NUM
ap-1259	107	41	]	]	PUNCT
ap-1259	107	42	-series	-serie	NOUN
ap-1259	107	43	consists	consist	VERB
ap-1259	107	44	of	of	ADP
ap-1259	107	45	a	a	DET
ap-1259	107	46	one	one	NUM
ap-1259	107	47	-	-	PUNCT
ap-1259	107	48	parameter	parameter	NOUN
ap-1259	107	49	(	(	PUNCT
ap-1259	107	50	c0	c0	PROPN
ap-1259	107	51	∈	∈	PROPN
ap-1259	107	52	c	c	PROPN
ap-1259	107	53	\	\	X
ap-1259	107	54	{	{	PUNCT
ap-1259	107	55	0	0	NUM
ap-1259	107	56	}	}	PUNCT
ap-1259	107	57	)	)	PUNCT
ap-1259	107	58	family	family	NOUN
ap-1259	107	59	of	of	ADP
ap-1259	107	60	uq	uq	PROPN
ap-1259	107	61	(	(	PUNCT
ap-1259	107	62	sl2)-module	sl2)-module	PROPN
ap-1259	107	63	algebra	algebra	NOUN
ap-1259	107	64	structures	structure	NOUN
ap-1259	107	65	on	on	ADP
ap-1259	107	66	the	the	DET
ap-1259	107	67	quantum	quantum	ADJ
ap-1259	107	68	plane	plane	NOUN
ap-1259	107	69	k	k	PROPN
ap-1259	107	70	(	(	PUNCT
ap-1259	107	71	x	x	X
ap-1259	107	72	)	)	PUNCT
ap-1259	107	73	=	=	SYM
ap-1259	107	74	q2x	q2x	NOUN
ap-1259	107	75	,	,	PUNCT
ap-1259	107	76	k	k	PROPN
ap-1259	107	77	(	(	PUNCT
ap-1259	107	78	y	y	NOUN
ap-1259	107	79	)	)	PUNCT
ap-1259	107	80	=	=	SYM
ap-1259	108	1	q−1y	q−1y	NOUN
ap-1259	108	2	,	,	PUNCT
ap-1259	108	3	(	(	PUNCT
ap-1259	108	4	41	41	NUM
ap-1259	108	5	)	)	PUNCT
ap-1259	108	6	e	e	NOUN
ap-1259	108	7	(	(	PUNCT
ap-1259	108	8	x	x	X
ap-1259	108	9	)	)	PUNCT
ap-1259	108	10	=	=	SYM
ap-1259	108	11	−qc−10	−qc−10	NUM
ap-1259	108	12	x2	x2	NOUN
ap-1259	108	13	,	,	PUNCT
ap-1259	108	14	e	e	X
ap-1259	108	15	(	(	PUNCT
ap-1259	108	16	y	y	NOUN
ap-1259	108	17	)	)	PUNCT
ap-1259	108	18	=	=	PRON
ap-1259	108	19	c−10	c−10	PROPN
ap-1259	108	20	xy	xy	ADJ
ap-1259	108	21	,	,	PUNCT
ap-1259	108	22	(	(	PUNCT
ap-1259	108	23	42	42	NUM
ap-1259	108	24	)	)	PUNCT
ap-1259	108	25	f	f	NOUN
ap-1259	108	26	(	(	PUNCT
ap-1259	108	27	x	x	NOUN
ap-1259	108	28	)	)	PUNCT
ap-1259	108	29	=	=	SYM
ap-1259	108	30	c0	c0	PROPN
ap-1259	108	31	,	,	PUNCT
ap-1259	108	32	f	f	PROPN
ap-1259	108	33	(	(	PUNCT
ap-1259	108	34	y	y	NOUN
ap-1259	108	35	)	)	PUNCT
ap-1259	108	36	=	=	SYM
ap-1259	108	37	0	0	X
ap-1259	108	38	.	.	PUNCT
ap-1259	109	1	(	(	PUNCT
ap-1259	109	2	43	43	NUM
ap-1259	109	3	)	)	PUNCT
ap-1259	109	4	all	all	DET
ap-1259	109	5	these	these	DET
ap-1259	109	6	structures	structure	NOUN
ap-1259	109	7	are	be	AUX
ap-1259	109	8	isomorphic	isomorphic	ADJ
ap-1259	109	9	,	,	PUNCT
ap-1259	109	10	in	in	ADP
ap-1259	109	11	particular	particular	ADJ
ap-1259	109	12	to	to	ADP
ap-1259	109	13	the	the	DET
ap-1259	109	14	action	action	NOUN
ap-1259	109	15	as	as	ADP
ap-1259	109	16	above	above	ADV
ap-1259	109	17	with	with	ADP
ap-1259	109	18	c0	c0	NOUN
ap-1259	109	19	=	=	SYM
ap-1259	109	20	1	1	X
ap-1259	109	21	.	.	PUNCT
ap-1259	109	22	theorem	theorem	VERB
ap-1259	109	23	6	6	NUM
ap-1259	109	24	the	the	DET
ap-1259	109	25	[	[	X
ap-1259	109	26	(	(	PUNCT
ap-1259	109	27	�	�	PROPN
ap-1259	109	28	0	0	NUM
ap-1259	109	29	0	0	NUM
ap-1259	109	30	0	0	NUM
ap-1259	109	31	)	)	PUNCT
ap-1259	109	32	0	0	NUM
ap-1259	109	33	;	;	PUNCT
ap-1259	109	34	(	(	PUNCT
ap-1259	109	35	0	0	NUM
ap-1259	109	36	0	0	NUM
ap-1259	109	37	0	0	NUM
ap-1259	109	38	0	0	NUM
ap-1259	109	39	)	)	PUNCT
ap-1259	109	40	1	1	NUM
ap-1259	109	41	]	]	PUNCT
ap-1259	109	42	-series	-serie	NOUN
ap-1259	109	43	consists	consist	VERB
ap-1259	109	44	of	of	ADP
ap-1259	109	45	a	a	DET
ap-1259	109	46	three	three	NUM
ap-1259	109	47	-	-	PUNCT
ap-1259	109	48	parameter	parameter	NOUN
ap-1259	109	49	(	(	PUNCT
ap-1259	109	50	a0	a0	PROPN
ap-1259	109	51	∈	∈	PROPN
ap-1259	109	52	c	c	NOUN
ap-1259	109	53	\	\	X
ap-1259	109	54	{	{	PUNCT
ap-1259	109	55	0	0	NUM
ap-1259	109	56	}	}	PUNCT
ap-1259	109	57	,	,	PUNCT
ap-1259	109	58	s	s	X
ap-1259	109	59	,	,	PUNCT
ap-1259	109	60	t	t	PROPN
ap-1259	109	61	∈	∈	PROPN
ap-1259	109	62	c	c	X
ap-1259	109	63	)	)	PUNCT
ap-1259	109	64	family	family	NOUN
ap-1259	109	65	of	of	ADP
ap-1259	109	66	uq	uq	PROPN
ap-1259	109	67	(	(	PUNCT
ap-1259	109	68	sl2)-actions	sl2)-action	NOUN
ap-1259	109	69	on	on	ADP
ap-1259	109	70	the	the	DET
ap-1259	109	71	quantum	quantum	ADJ
ap-1259	109	72	plane	plane	NOUN
ap-1259	109	73	k	k	PROPN
ap-1259	109	74	(	(	PUNCT
ap-1259	109	75	x	x	X
ap-1259	109	76	)	)	PUNCT
ap-1259	109	77	=	=	SYM
ap-1259	109	78	q−2x	q−2x	NOUN
ap-1259	109	79	,	,	PUNCT
ap-1259	109	80	k	k	PROPN
ap-1259	109	81	(	(	PUNCT
ap-1259	109	82	y	y	NOUN
ap-1259	109	83	)	)	PUNCT
ap-1259	109	84	=	=	SYM
ap-1259	109	85	q−1y	q−1y	NOUN
ap-1259	109	86	,	,	PUNCT
ap-1259	109	87	(	(	PUNCT
ap-1259	109	88	44	44	NUM
ap-1259	109	89	)	)	PUNCT
ap-1259	109	90	e	e	NOUN
ap-1259	109	91	(	(	PUNCT
ap-1259	109	92	x	x	NOUN
ap-1259	109	93	)	)	PUNCT
ap-1259	109	94	=	=	SYM
ap-1259	109	95	a0	a0	PROPN
ap-1259	109	96	,	,	PUNCT
ap-1259	109	97	e	e	X
ap-1259	109	98	(	(	PUNCT
ap-1259	109	99	y	y	NOUN
ap-1259	109	100	)	)	PUNCT
ap-1259	109	101	=	=	SYM
ap-1259	109	102	0	0	NUM
ap-1259	109	103	,	,	PUNCT
ap-1259	109	104	(	(	PUNCT
ap-1259	109	105	45	45	NUM
ap-1259	109	106	)	)	PUNCT
ap-1259	109	107	f	f	NOUN
ap-1259	109	108	(	(	PUNCT
ap-1259	109	109	x	x	X
ap-1259	109	110	)	)	PUNCT
ap-1259	110	1	=	=	NOUN
ap-1259	110	2	−qa−1	−qa−1	NOUN
ap-1259	110	3	0	0	NUM
ap-1259	111	1	x2	x2	PROPN
ap-1259	111	2	+	+	PROPN
ap-1259	111	3	ty4	ty4	PROPN
ap-1259	111	4	,	,	PUNCT
ap-1259	111	5	f	f	PROPN
ap-1259	111	6	(	(	PUNCT
ap-1259	111	7	y	y	NOUN
ap-1259	111	8	)	)	PUNCT
ap-1259	111	9	=	=	VERB
ap-1259	112	1	−qa−1	−qa−1	NOUN
ap-1259	112	2	0	0	PUNCT
ap-1259	113	1	xy	xy	PROPN
ap-1259	113	2	+	+	X
ap-1259	113	3	sy3	sy3	NOUN
ap-1259	113	4	.	.	PUNCT
ap-1259	114	1	(	(	PUNCT
ap-1259	114	2	46	46	NUM
ap-1259	114	3	)	)	PUNCT
ap-1259	114	4	27	27	NUM
ap-1259	114	5	acta	acta	PROPN
ap-1259	114	6	polytechnica	polytechnica	PROPN
ap-1259	114	7	vol	vol	NOUN
ap-1259	114	8	.	.	PROPN
ap-1259	115	1	50	50	NUM
ap-1259	115	2	no	no	NOUN
ap-1259	115	3	.	.	PUNCT
ap-1259	116	1	5/2010	5/2010	NUM
ap-1259	116	2	the	the	DET
ap-1259	116	3	generic	generic	ADJ
ap-1259	116	4	domain	domain	NOUN
ap-1259	116	5	{	{	PUNCT
ap-1259	116	6	(	(	PUNCT
ap-1259	116	7	a0	a0	PROPN
ap-1259	116	8	,	,	PUNCT
ap-1259	116	9	s	s	PROPN
ap-1259	116	10	,	,	PUNCT
ap-1259	116	11	t	t	PROPN
ap-1259	116	12	)	)	PUNCT
ap-1259	116	13	|s	|s	PROPN
ap-1259	116	14	=	=	SYM
ap-1259	116	15	0	0	NUM
ap-1259	116	16	,	,	PUNCT
ap-1259	116	17	t	t	NOUN
ap-1259	116	18	=	=	SYM
ap-1259	116	19	0	0	NUM
ap-1259	116	20	}	}	PUNCT
ap-1259	116	21	with	with	ADP
ap-1259	116	22	respect	respect	NOUN
ap-1259	116	23	to	to	ADP
ap-1259	116	24	the	the	DET
ap-1259	116	25	parameters	parameter	NOUN
ap-1259	116	26	splits	split	VERB
ap-1259	116	27	into	into	ADP
ap-1259	116	28	uncountably	uncountably	ADV
ap-1259	116	29	many	many	ADJ
ap-1259	116	30	disjoint	disjoint	ADJ
ap-1259	116	31	subsets	subset	NOUN
ap-1259	116	32	{	{	PUNCT
ap-1259	116	33	(	(	PUNCT
ap-1259	116	34	a0	a0	PROPN
ap-1259	116	35	,	,	PUNCT
ap-1259	116	36	s	s	PROPN
ap-1259	116	37	,	,	PUNCT
ap-1259	116	38	t	t	PROPN
ap-1259	116	39	)	)	PUNCT
ap-1259	116	40	|s	|s	PROPN
ap-1259	117	1	=	=	SYM
ap-1259	117	2	0	0	NUM
ap-1259	117	3	,	,	PUNCT
ap-1259	117	4	t	t	NOUN
ap-1259	117	5	=	=	SYM
ap-1259	117	6	0	0	NUM
ap-1259	117	7	,	,	PUNCT
ap-1259	117	8	ϕ	ϕ	X
ap-1259	117	9	=	=	SYM
ap-1259	117	10	const	const	NOUN
ap-1259	117	11	}	}	PUNCT
ap-1259	117	12	,	,	PUNCT
ap-1259	117	13	where	where	SCONJ
ap-1259	117	14	ϕ	ϕ	NOUN
ap-1259	117	15	=	=	X
ap-1259	117	16	t	t	PROPN
ap-1259	117	17	a0s2	a0s2	INTJ
ap-1259	117	18	.	.	PUNCT
ap-1259	118	1	each	each	PRON
ap-1259	118	2	of	of	ADP
ap-1259	118	3	these	these	DET
ap-1259	118	4	subsets	subset	NOUN
ap-1259	118	5	corresponds	correspond	VERB
ap-1259	118	6	to	to	ADP
ap-1259	118	7	an	an	DET
ap-1259	118	8	isomorphism	isomorphism	NOUN
ap-1259	118	9	class	class	NOUN
ap-1259	118	10	of	of	ADP
ap-1259	118	11	uq	uq	PROPN
ap-1259	118	12	(	(	PUNCT
ap-1259	118	13	sl2)-module	sl2)-module	PROPN
ap-1259	118	14	algebra	algebra	NOUN
ap-1259	118	15	structures	structure	NOUN
ap-1259	118	16	.	.	PUNCT
ap-1259	119	1	additionally	additionally	ADV
ap-1259	119	2	there	there	PRON
ap-1259	119	3	exist	exist	VERB
ap-1259	119	4	three	three	NUM
ap-1259	119	5	more	more	ADJ
ap-1259	119	6	isomorphism	isomorphism	NOUN
ap-1259	119	7	classes	class	NOUN
ap-1259	119	8	which	which	PRON
ap-1259	119	9	correspond	correspond	VERB
ap-1259	119	10	to	to	ADP
ap-1259	119	11	the	the	DET
ap-1259	119	12	subsets	subset	NOUN
ap-1259	119	13	{	{	PUNCT
ap-1259	119	14	(	(	PUNCT
ap-1259	119	15	a0	a0	PROPN
ap-1259	119	16	,	,	PUNCT
ap-1259	119	17	s	s	PROPN
ap-1259	119	18	,	,	PUNCT
ap-1259	119	19	t	t	PROPN
ap-1259	119	20	)	)	PUNCT
ap-1259	119	21	|s	|s	PROPN
ap-1259	120	1	=	=	SYM
ap-1259	120	2	0	0	NUM
ap-1259	120	3	,	,	PUNCT
ap-1259	120	4	t	t	NOUN
ap-1259	120	5	=	=	SYM
ap-1259	120	6	0	0	NUM
ap-1259	120	7	}	}	PUNCT
ap-1259	120	8	,	,	PUNCT
ap-1259	120	9	{	{	PUNCT
ap-1259	120	10	(	(	PUNCT
ap-1259	120	11	a0	a0	PROPN
ap-1259	120	12	,	,	PUNCT
ap-1259	120	13	s	s	PROPN
ap-1259	120	14	,	,	PUNCT
ap-1259	120	15	t	t	PROPN
ap-1259	120	16	)	)	PUNCT
ap-1259	120	17	|s	|s	PROPN
ap-1259	120	18	=	=	SYM
ap-1259	120	19	0	0	NUM
ap-1259	120	20	,	,	PUNCT
ap-1259	120	21	t	t	NOUN
ap-1259	120	22	=	=	SYM
ap-1259	120	23	0	0	NUM
ap-1259	120	24	}	}	PUNCT
ap-1259	120	25	,	,	PUNCT
ap-1259	120	26	(	(	PUNCT
ap-1259	120	27	47	47	NUM
ap-1259	120	28	)	)	PUNCT
ap-1259	120	29	{	{	PUNCT
ap-1259	120	30	(	(	PUNCT
ap-1259	120	31	a0	a0	PROPN
ap-1259	120	32	,	,	PUNCT
ap-1259	120	33	s	s	PROPN
ap-1259	120	34	,	,	PUNCT
ap-1259	120	35	t	t	PROPN
ap-1259	120	36	)	)	PUNCT
ap-1259	120	37	|s	|s	PROPN
ap-1259	121	1	=	=	SYM
ap-1259	121	2	0	0	NUM
ap-1259	121	3	,	,	PUNCT
ap-1259	121	4	t	t	NOUN
ap-1259	121	5	=	=	SYM
ap-1259	121	6	0	0	NUM
ap-1259	121	7	}	}	PUNCT
ap-1259	121	8	.	.	PUNCT
ap-1259	122	1	the	the	DET
ap-1259	122	2	specific	specific	ADJ
ap-1259	122	3	form	form	NOUN
ap-1259	122	4	of	of	ADP
ap-1259	122	5	weights	weight	NOUN
ap-1259	122	6	for	for	ADP
ap-1259	122	7	x	x	SYM
ap-1259	122	8	and	and	CCONJ
ap-1259	122	9	y	y	PROPN
ap-1259	122	10	discards	discard	VERB
ap-1259	122	11	primordially	primordially	ADV
ap-1259	122	12	all	all	ADV
ap-1259	122	13	but	but	CCONJ
ap-1259	122	14	finitely	finitely	ADV
ap-1259	122	15	many	many	ADJ
ap-1259	122	16	terms	term	NOUN
ap-1259	122	17	(	(	PUNCT
ap-1259	122	18	monomials	monomial	NOUN
ap-1259	122	19	)	)	PUNCT
ap-1259	122	20	that	that	PRON
ap-1259	122	21	could	could	AUX
ap-1259	122	22	appear	appear	VERB
ap-1259	122	23	in	in	ADP
ap-1259	122	24	the	the	DET
ap-1259	122	25	expressions	expression	NOUN
ap-1259	122	26	for	for	ADP
ap-1259	122	27	e(x	e(x	NUM
ap-1259	122	28	)	)	PUNCT
ap-1259	122	29	,	,	PUNCT
ap-1259	122	30	e(y	e(y	PROPN
ap-1259	122	31	)	)	PUNCT
ap-1259	122	32	,	,	PUNCT
ap-1259	122	33	f(x	f(x	PROPN
ap-1259	122	34	)	)	PUNCT
ap-1259	122	35	,	,	PUNCT
ap-1259	122	36	f(y	f(y	NOUN
ap-1259	122	37	)	)	PUNCT
ap-1259	122	38	in	in	ADP
ap-1259	122	39	(	(	PUNCT
ap-1259	122	40	45	45	NUM
ap-1259	122	41	)	)	PUNCT
ap-1259	122	42	and	and	CCONJ
ap-1259	122	43	(	(	PUNCT
ap-1259	122	44	46	46	NUM
ap-1259	122	45	)	)	PUNCT
ap-1259	122	46	.	.	PUNCT
ap-1259	123	1	thus	thus	ADV
ap-1259	123	2	it	it	PRON
ap-1259	123	3	becomes	become	VERB
ap-1259	123	4	much	much	ADV
ap-1259	123	5	easier	easy	ADJ
ap-1259	123	6	to	to	PART
ap-1259	123	7	establish	establish	VERB
ap-1259	123	8	the	the	DET
ap-1259	123	9	latter	latter	ADJ
ap-1259	123	10	relations	relation	NOUN
ap-1259	123	11	than	than	SCONJ
ap-1259	123	12	to	to	PART
ap-1259	123	13	do	do	VERB
ap-1259	123	14	this	this	PRON
ap-1259	123	15	for	for	ADP
ap-1259	123	16	the	the	DET
ap-1259	123	17	corresponding	corresponding	ADJ
ap-1259	123	18	relations	relation	NOUN
ap-1259	123	19	in	in	ADP
ap-1259	123	20	the	the	DET
ap-1259	123	21	previous	previous	ADJ
ap-1259	123	22	theorems	theorem	NOUN
ap-1259	123	23	.	.	PUNCT
ap-1259	123	24	to	to	PART
ap-1259	123	25	prove	prove	VERB
ap-1259	123	26	the	the	DET
ap-1259	123	27	rest	rest	NOUN
ap-1259	123	28	of	of	ADP
ap-1259	123	29	the	the	DET
ap-1259	123	30	claims	claim	NOUN
ap-1259	123	31	,	,	PUNCT
ap-1259	123	32	one	one	NUM
ap-1259	123	33	needs	need	VERB
ap-1259	123	34	to	to	PART
ap-1259	123	35	guess	guess	VERB
ap-1259	123	36	the	the	DET
ap-1259	123	37	explicit	explicit	ADJ
ap-1259	123	38	form	form	NOUN
ap-1259	123	39	of	of	ADP
ap-1259	123	40	the	the	DET
ap-1259	123	41	required	require	VERB
ap-1259	123	42	isomorphisms	isomorphism	NOUN
ap-1259	123	43	.	.	PUNCT
ap-1259	124	1	theorem	theorem	VERB
ap-1259	124	2	7	7	NUM
ap-1259	124	3	the	the	DET
ap-1259	124	4	[	[	X
ap-1259	124	5	(	(	PUNCT
ap-1259	124	6	0	0	NUM
ap-1259	124	7	0	0	NUM
ap-1259	124	8	0	0	NUM
ap-1259	124	9	�	�	PROPN
ap-1259	124	10	)	)	PUNCT
ap-1259	124	11	0	0	NUM
ap-1259	125	1	;	;	PUNCT
ap-1259	125	2	(	(	PUNCT
ap-1259	125	3	0	0	NUM
ap-1259	125	4	0	0	NUM
ap-1259	125	5	0	0	NUM
ap-1259	125	6	0	0	NUM
ap-1259	125	7	)	)	PUNCT
ap-1259	125	8	1	1	NUM
ap-1259	126	1	]	]	PUNCT
ap-1259	126	2	-series	-serie	NOUN
ap-1259	126	3	consists	consist	VERB
ap-1259	126	4	of	of	ADP
ap-1259	126	5	a	a	DET
ap-1259	126	6	three	three	NUM
ap-1259	126	7	-	-	PUNCT
ap-1259	126	8	parameter	parameter	NOUN
ap-1259	126	9	(	(	PUNCT
ap-1259	126	10	d0	d0	PROPN
ap-1259	126	11	∈	∈	PROPN
ap-1259	126	12	c	c	NOUN
ap-1259	126	13	\	\	X
ap-1259	126	14	{	{	PUNCT
ap-1259	126	15	0	0	NUM
ap-1259	126	16	}	}	PUNCT
ap-1259	126	17	,	,	PUNCT
ap-1259	126	18	s	s	X
ap-1259	126	19	,	,	PUNCT
ap-1259	126	20	t	t	PROPN
ap-1259	126	21	∈	∈	PROPN
ap-1259	126	22	c	c	X
ap-1259	126	23	)	)	PUNCT
ap-1259	126	24	family	family	NOUN
ap-1259	126	25	of	of	ADP
ap-1259	126	26	uq	uq	PROPN
ap-1259	126	27	(	(	PUNCT
ap-1259	126	28	sl2)-actions	sl2)-action	NOUN
ap-1259	126	29	on	on	ADP
ap-1259	126	30	the	the	DET
ap-1259	126	31	quantum	quantum	ADJ
ap-1259	126	32	plane	plane	NOUN
ap-1259	126	33	k	k	PROPN
ap-1259	126	34	(	(	PUNCT
ap-1259	126	35	x	x	X
ap-1259	126	36	)	)	PUNCT
ap-1259	126	37	=	=	SYM
ap-1259	126	38	qx	qx	INTJ
ap-1259	126	39	,	,	PUNCT
ap-1259	126	40	k	k	PROPN
ap-1259	126	41	(	(	PUNCT
ap-1259	126	42	y	y	NOUN
ap-1259	126	43	)	)	PUNCT
ap-1259	126	44	=	=	SYM
ap-1259	127	1	q2y	q2y	PROPN
ap-1259	127	2	,	,	PUNCT
ap-1259	127	3	(	(	PUNCT
ap-1259	127	4	48	48	NUM
ap-1259	127	5	)	)	PUNCT
ap-1259	127	6	e	e	NOUN
ap-1259	127	7	(	(	PUNCT
ap-1259	127	8	x	x	X
ap-1259	127	9	)	)	PUNCT
ap-1259	127	10	=	=	NOUN
ap-1259	127	11	−qd−10	−qd−10	PROPN
ap-1259	127	12	xy	xy	PROPN
ap-1259	127	13	+	+	CCONJ
ap-1259	127	14	sx3	sx3	PROPN
ap-1259	127	15	,	,	PUNCT
ap-1259	127	16	e	e	PROPN
ap-1259	127	17	(	(	PUNCT
ap-1259	127	18	y	y	NOUN
ap-1259	127	19	)	)	PUNCT
ap-1259	127	20	=	=	SYM
ap-1259	127	21	−qd−10	−qd−10	PROPN
ap-1259	128	1	y2	y2	PROPN
ap-1259	128	2	+	+	CCONJ
ap-1259	128	3	tx4	tx4	PROPN
ap-1259	128	4	,	,	PUNCT
ap-1259	128	5	(	(	PUNCT
ap-1259	128	6	49	49	NUM
ap-1259	128	7	)	)	PUNCT
ap-1259	128	8	f	f	NOUN
ap-1259	128	9	(	(	PUNCT
ap-1259	128	10	x	x	X
ap-1259	128	11	)	)	PUNCT
ap-1259	128	12	=	=	SYM
ap-1259	128	13	0	0	NUM
ap-1259	128	14	,	,	PUNCT
ap-1259	128	15	f	f	PROPN
ap-1259	128	16	(	(	PUNCT
ap-1259	128	17	y	y	NOUN
ap-1259	128	18	)	)	PUNCT
ap-1259	128	19	=	=	SYM
ap-1259	128	20	d0	d0	NOUN
ap-1259	128	21	,	,	PUNCT
ap-1259	128	22	(	(	PUNCT
ap-1259	128	23	50	50	NUM
ap-1259	128	24	)	)	PUNCT
ap-1259	128	25	here	here	ADV
ap-1259	128	26	we	we	PRON
ap-1259	128	27	have	have	VERB
ap-1259	128	28	the	the	DET
ap-1259	128	29	domain	domain	NOUN
ap-1259	128	30	{	{	PUNCT
ap-1259	128	31	(	(	PUNCT
ap-1259	128	32	d0	d0	NOUN
ap-1259	128	33	,	,	PUNCT
ap-1259	128	34	s	s	PROPN
ap-1259	128	35	,	,	PUNCT
ap-1259	128	36	t	t	PROPN
ap-1259	128	37	)	)	PUNCT
ap-1259	128	38	|s	|s	PROPN
ap-1259	129	1	=	=	SYM
ap-1259	129	2	0	0	NUM
ap-1259	129	3	,	,	PUNCT
ap-1259	129	4	t	t	NOUN
ap-1259	129	5	=	=	SYM
ap-1259	129	6	0	0	NUM
ap-1259	129	7	}	}	PUNCT
ap-1259	129	8	which	which	PRON
ap-1259	129	9	splits	split	VERB
ap-1259	129	10	into	into	ADP
ap-1259	129	11	the	the	DET
ap-1259	129	12	disjoint	disjoint	NOUN
ap-1259	129	13	subsets	subset	NOUN
ap-1259	129	14	{	{	PUNCT
ap-1259	129	15	(	(	PUNCT
ap-1259	129	16	d0	d0	NOUN
ap-1259	129	17	,	,	PUNCT
ap-1259	129	18	s	s	PROPN
ap-1259	129	19	,	,	PUNCT
ap-1259	129	20	t	t	PROPN
ap-1259	129	21	)	)	PUNCT
ap-1259	129	22	|s	|s	PROPN
ap-1259	130	1	=	=	SYM
ap-1259	130	2	0	0	NUM
ap-1259	130	3	,	,	PUNCT
ap-1259	130	4	t	t	NOUN
ap-1259	130	5	=	=	SYM
ap-1259	130	6	0	0	NUM
ap-1259	130	7	,	,	PUNCT
ap-1259	130	8	ϕ	ϕ	X
ap-1259	130	9	=	=	SYM
ap-1259	130	10	const	const	NOUN
ap-1259	130	11	}	}	PUNCT
ap-1259	130	12	with	with	ADP
ap-1259	130	13	ϕ	ϕ	PROPN
ap-1259	130	14	=	=	SYM
ap-1259	130	15	t	t	PROPN
ap-1259	130	16	d0s2	d0s2	VERB
ap-1259	130	17	.	.	PUNCT
ap-1259	131	1	this	this	DET
ap-1259	131	2	uncountable	uncountable	ADJ
ap-1259	131	3	family	family	NOUN
ap-1259	131	4	of	of	ADP
ap-1259	131	5	subsets	subset	NOUN
ap-1259	131	6	is	be	AUX
ap-1259	131	7	in	in	ADP
ap-1259	131	8	one	one	NUM
ap-1259	131	9	-	-	PUNCT
ap-1259	131	10	to	to	ADP
ap-1259	131	11	-	-	PUNCT
ap-1259	131	12	one	one	NUM
ap-1259	131	13	correspondence	correspondence	NOUN
ap-1259	131	14	to	to	ADP
ap-1259	131	15	isomorphism	isomorphism	NOUN
ap-1259	131	16	classes	class	NOUN
ap-1259	131	17	of	of	ADP
ap-1259	131	18	uq	uq	PROPN
ap-1259	131	19	(	(	PUNCT
ap-1259	131	20	sl2)-module	sl2)-module	PROPN
ap-1259	131	21	algebra	algebra	NOUN
ap-1259	131	22	structures	structure	NOUN
ap-1259	131	23	.	.	PUNCT
ap-1259	132	1	in	in	ADP
ap-1259	132	2	addition	addition	NOUN
ap-1259	132	3	,	,	PUNCT
ap-1259	132	4	one	one	PRON
ap-1259	132	5	also	also	ADV
ap-1259	132	6	has	have	VERB
ap-1259	132	7	three	three	NUM
ap-1259	132	8	more	more	ADJ
ap-1259	132	9	isomorphism	isomorphism	NOUN
ap-1259	132	10	classes	class	NOUN
ap-1259	132	11	which	which	PRON
ap-1259	132	12	are	be	AUX
ap-1259	132	13	labelled	label	VERB
ap-1259	132	14	by	by	ADP
ap-1259	132	15	the	the	DET
ap-1259	132	16	subsets	subset	NOUN
ap-1259	132	17	{	{	PUNCT
ap-1259	132	18	(	(	PUNCT
ap-1259	132	19	d0	d0	NOUN
ap-1259	132	20	,	,	PUNCT
ap-1259	132	21	s	s	PROPN
ap-1259	132	22	,	,	PUNCT
ap-1259	132	23	t	t	PROPN
ap-1259	132	24	)	)	PUNCT
ap-1259	132	25	|s	|s	PROPN
ap-1259	133	1	=	=	SYM
ap-1259	133	2	0	0	NUM
ap-1259	133	3	,	,	PUNCT
ap-1259	133	4	t	t	NOUN
ap-1259	133	5	=	=	SYM
ap-1259	133	6	0	0	NUM
ap-1259	133	7	}	}	PUNCT
ap-1259	133	8	,	,	PUNCT
ap-1259	133	9	{	{	PUNCT
ap-1259	133	10	(	(	PUNCT
ap-1259	133	11	d0	d0	NOUN
ap-1259	133	12	,	,	PUNCT
ap-1259	133	13	s	s	PROPN
ap-1259	133	14	,	,	PUNCT
ap-1259	133	15	t	t	PROPN
ap-1259	133	16	)	)	PUNCT
ap-1259	133	17	|s	|s	PROPN
ap-1259	133	18	=	=	SYM
ap-1259	133	19	0	0	NUM
ap-1259	133	20	,	,	PUNCT
ap-1259	133	21	t	t	NOUN
ap-1259	133	22	=	=	SYM
ap-1259	133	23	0	0	NUM
ap-1259	133	24	}	}	PUNCT
ap-1259	133	25	,	,	PUNCT
ap-1259	133	26	{	{	PUNCT
ap-1259	133	27	(	(	PUNCT
ap-1259	133	28	d0	d0	NOUN
ap-1259	133	29	,	,	PUNCT
ap-1259	133	30	s	s	PROPN
ap-1259	133	31	,	,	PUNCT
ap-1259	133	32	t	t	PROPN
ap-1259	133	33	)	)	PUNCT
ap-1259	133	34	|s	|s	PROPN
ap-1259	134	1	=	=	SYM
ap-1259	134	2	0	0	NUM
ap-1259	134	3	,	,	PUNCT
ap-1259	134	4	t	t	NOUN
ap-1259	134	5	=	=	SYM
ap-1259	134	6	0	0	NUM
ap-1259	134	7	}	}	PUNCT
ap-1259	134	8	.	.	PUNCT
ap-1259	135	1	remark	remark	PROPN
ap-1259	135	2	8	8	NUM
ap-1259	135	3	the	the	DET
ap-1259	135	4	uq	uq	PROPN
ap-1259	135	5	(	(	PUNCT
ap-1259	135	6	sl2)-symmetries	sl2)-symmetrie	NOUN
ap-1259	135	7	on	on	ADP
ap-1259	135	8	cq[x	cq[x	PROPN
ap-1259	135	9	,	,	PUNCT
ap-1259	135	10	y	y	PROPN
ap-1259	135	11	]	]	PUNCT
ap-1259	135	12	picked	pick	VERB
ap-1259	135	13	from	from	ADP
ap-1259	135	14	different	different	ADJ
ap-1259	135	15	series	series	NOUN
ap-1259	135	16	are	be	AUX
ap-1259	135	17	nonisomorphic	nonisomorphic	ADJ
ap-1259	135	18	,	,	PUNCT
ap-1259	135	19	and	and	CCONJ
ap-1259	136	1	the	the	DET
ap-1259	136	2	actions	action	NOUN
ap-1259	136	3	of	of	ADP
ap-1259	136	4	k	k	PROPN
ap-1259	136	5	in	in	ADP
ap-1259	136	6	different	different	ADJ
ap-1259	136	7	series	series	NOUN
ap-1259	136	8	are	be	AUX
ap-1259	136	9	different	different	ADJ
ap-1259	136	10	.	.	PUNCT
ap-1259	137	1	remark	remark	NOUN
ap-1259	137	2	9	9	NUM
ap-1259	138	1	there	there	PRON
ap-1259	138	2	are	be	VERB
ap-1259	138	3	no	no	DET
ap-1259	138	4	uq	uq	NOUN
ap-1259	138	5	(	(	PUNCT
ap-1259	138	6	sl2)-symmetries	sl2)-symmetrie	NOUN
ap-1259	138	7	on	on	ADP
ap-1259	138	8	cq[x	cq[x	PROPN
ap-1259	138	9	,	,	PUNCT
ap-1259	138	10	y	y	PROPN
ap-1259	138	11	]	]	X
ap-1259	138	12	other	other	ADJ
ap-1259	138	13	than	than	ADP
ap-1259	138	14	those	those	PRON
ap-1259	138	15	presented	present	VERB
ap-1259	138	16	in	in	ADP
ap-1259	138	17	the	the	DET
ap-1259	138	18	above	above	ADJ
ap-1259	138	19	theorems	theorem	NOUN
ap-1259	138	20	,	,	PUNCT
ap-1259	138	21	because	because	SCONJ
ap-1259	138	22	the	the	DET
ap-1259	138	23	assumptions	assumption	NOUN
ap-1259	138	24	exhaust	exhaust	VERB
ap-1259	138	25	all	all	DET
ap-1259	138	26	admissible	admissible	ADJ
ap-1259	138	27	forms	form	NOUN
ap-1259	138	28	for	for	ADP
ap-1259	138	29	the	the	DET
ap-1259	138	30	components	component	NOUN
ap-1259	138	31	(	(	PUNCT
ap-1259	138	32	mef	mef	NOUN
ap-1259	138	33	)	)	PUNCT
ap-1259	138	34	0	0	NUM
ap-1259	138	35	,	,	PUNCT
ap-1259	138	36	(	(	PUNCT
ap-1259	138	37	mef	mef	NOUN
ap-1259	138	38	)	)	PUNCT
ap-1259	138	39	1	1	NUM
ap-1259	138	40	of	of	ADP
ap-1259	138	41	the	the	DET
ap-1259	138	42	action	action	NOUN
ap-1259	138	43	ef	ef	PROPN
ap-1259	138	44	-matrix	-matrix	PROPN
ap-1259	138	45	.	.	PUNCT
ap-1259	139	1	the	the	DET
ap-1259	139	2	associated	associated	ADJ
ap-1259	139	3	classical	classical	ADJ
ap-1259	139	4	limit	limit	NOUN
ap-1259	139	5	actions	action	NOUN
ap-1259	139	6	of	of	ADP
ap-1259	139	7	the	the	DET
ap-1259	139	8	lie	lie	NOUN
ap-1259	139	9	algebra	algebra	NOUN
ap-1259	139	10	sl2	sl2	PROPN
ap-1259	139	11	(	(	PUNCT
ap-1259	139	12	here	here	ADV
ap-1259	139	13	it	it	PRON
ap-1259	139	14	is	be	AUX
ap-1259	139	15	the	the	DET
ap-1259	139	16	lie	lie	NOUN
ap-1259	139	17	algebra	algebra	NOUN
ap-1259	139	18	generated	generate	VERB
ap-1259	139	19	by	by	ADP
ap-1259	139	20	e	e	PROPN
ap-1259	139	21	,	,	PUNCT
ap-1259	139	22	f	f	PROPN
ap-1259	139	23	,	,	PUNCT
ap-1259	139	24	h	h	NOUN
ap-1259	139	25	subject	subject	ADJ
ap-1259	139	26	to	to	ADP
ap-1259	139	27	the	the	DET
ap-1259	139	28	relations	relation	NOUN
ap-1259	139	29	[	[	X
ap-1259	139	30	h	h	X
ap-1259	139	31	,	,	PUNCT
ap-1259	139	32	e	e	X
ap-1259	139	33	]	]	X
ap-1259	139	34	=	=	SYM
ap-1259	139	35	2e	2e	NOUN
ap-1259	139	36	,	,	PUNCT
ap-1259	139	37	[	[	X
ap-1259	139	38	h	h	X
ap-1259	139	39	,	,	PUNCT
ap-1259	139	40	f	f	X
ap-1259	139	41	]	]	PUNCT
ap-1259	139	42	=	=	PUNCT
ap-1259	140	1	−2f	−2f	PROPN
ap-1259	140	2	,	,	PUNCT
ap-1259	140	3	[	[	X
ap-1259	140	4	e	e	X
ap-1259	140	5	,	,	PUNCT
ap-1259	140	6	f	f	X
ap-1259	140	7	]	]	X
ap-1259	140	8	=	=	SYM
ap-1259	140	9	h	h	NOUN
ap-1259	140	10	)	)	PUNCT
ap-1259	140	11	on	on	ADP
ap-1259	140	12	c[x	c[x	PROPN
ap-1259	140	13	,	,	PUNCT
ap-1259	140	14	y	y	NOUN
ap-1259	140	15	]	]	PUNCT
ap-1259	140	16	by	by	ADP
ap-1259	140	17	differentiations	differentiation	NOUN
ap-1259	140	18	is	be	AUX
ap-1259	140	19	derived	derive	VERB
ap-1259	140	20	from	from	ADP
ap-1259	140	21	the	the	DET
ap-1259	140	22	quantum	quantum	ADJ
ap-1259	140	23	action	action	NOUN
ap-1259	140	24	via	via	ADP
ap-1259	140	25	substituting	substitute	VERB
ap-1259	140	26	k	k	PROPN
ap-1259	140	27	=	=	SYM
ap-1259	140	28	qh	qh	PROPN
ap-1259	140	29	with	with	ADP
ap-1259	140	30	subsequent	subsequent	ADJ
ap-1259	140	31	formal	formal	ADJ
ap-1259	140	32	passage	passage	NOUN
ap-1259	140	33	to	to	ADP
ap-1259	140	34	the	the	DET
ap-1259	140	35	limit	limit	NOUN
ap-1259	140	36	as	as	ADP
ap-1259	140	37	q	q	NOUN
ap-1259	140	38	→	→	SYM
ap-1259	140	39	1	1	X
ap-1259	140	40	.	.	X
ap-1259	141	1	we	we	PRON
ap-1259	141	2	present	present	VERB
ap-1259	141	3	all	all	DET
ap-1259	141	4	quantum	quantum	ADJ
ap-1259	141	5	and	and	CCONJ
ap-1259	141	6	classical	classical	ADJ
ap-1259	141	7	actions	action	NOUN
ap-1259	141	8	in	in	ADP
ap-1259	141	9	table	table	NOUN
ap-1259	141	10	1	1	NUM
ap-1259	141	11	.	.	PUNCT
ap-1259	142	1	note	note	VERB
ap-1259	142	2	that	that	SCONJ
ap-1259	142	3	there	there	PRON
ap-1259	142	4	exist	exist	VERB
ap-1259	142	5	more	more	ADJ
ap-1259	142	6	sl2	sl2	NOUN
ap-1259	142	7	-	-	PUNCT
ap-1259	142	8	actions	action	NOUN
ap-1259	142	9	on	on	ADP
ap-1259	142	10	c[x	c[x	NOUN
ap-1259	142	11	,	,	PUNCT
ap-1259	142	12	y	y	NOUN
ap-1259	142	13	]	]	PUNCT
ap-1259	142	14	by	by	ADP
ap-1259	142	15	differentiations	differentiation	NOUN
ap-1259	142	16	(	(	PUNCT
ap-1259	142	17	see	see	VERB
ap-1259	142	18	,	,	PUNCT
ap-1259	143	1	e.g.	e.g.	ADV
ap-1259	143	2	[	[	X
ap-1259	143	3	8	8	NUM
ap-1259	143	4	]	]	SYM
ap-1259	143	5	)	)	PUNCT
ap-1259	143	6	than	than	SCONJ
ap-1259	143	7	one	one	PRON
ap-1259	143	8	can	can	AUX
ap-1259	143	9	see	see	VERB
ap-1259	143	10	in	in	ADP
ap-1259	143	11	table	table	NOUN
ap-1259	143	12	1	1	NUM
ap-1259	143	13	.	.	PUNCT
ap-1259	144	1	it	it	PRON
ap-1259	144	2	follows	follow	VERB
ap-1259	144	3	from	from	ADP
ap-1259	144	4	our	our	PRON
ap-1259	144	5	results	result	NOUN
ap-1259	144	6	that	that	SCONJ
ap-1259	144	7	the	the	DET
ap-1259	144	8	rest	rest	NOUN
ap-1259	144	9	of	of	ADP
ap-1259	144	10	the	the	DET
ap-1259	144	11	classical	classical	ADJ
ap-1259	144	12	actions	action	NOUN
ap-1259	144	13	admit	admit	VERB
ap-1259	144	14	no	no	DET
ap-1259	144	15	quantum	quantum	NOUN
ap-1259	144	16	counterparts	counterpart	NOUN
ap-1259	144	17	.	.	PUNCT
ap-1259	145	1	on	on	ADP
ap-1259	145	2	the	the	DET
ap-1259	145	3	other	other	ADJ
ap-1259	145	4	hand	hand	NOUN
ap-1259	145	5	,	,	PUNCT
ap-1259	145	6	among	among	ADP
ap-1259	145	7	the	the	DET
ap-1259	145	8	quantum	quantum	ADJ
ap-1259	145	9	actions	action	NOUN
ap-1259	145	10	listed	list	VERB
ap-1259	145	11	in	in	ADP
ap-1259	145	12	the	the	DET
ap-1259	145	13	first	first	ADJ
ap-1259	145	14	row	row	NOUN
ap-1259	145	15	of	of	ADP
ap-1259	145	16	table	table	NOUN
ap-1259	145	17	1	1	NUM
ap-1259	145	18	,	,	PUNCT
ap-1259	145	19	the	the	DET
ap-1259	145	20	only	only	ADJ
ap-1259	145	21	one	one	NUM
ap-1259	145	22	to	to	PART
ap-1259	145	23	which	which	PRON
ap-1259	145	24	the	the	DET
ap-1259	145	25	above	above	ADJ
ap-1259	145	26	classical	classical	ADJ
ap-1259	145	27	limit	limit	NOUN
ap-1259	145	28	procedure	procedure	NOUN
ap-1259	145	29	is	be	AUX
ap-1259	145	30	applicable	applicable	ADJ
ap-1259	145	31	,	,	PUNCT
ap-1259	145	32	is	be	AUX
ap-1259	145	33	the	the	DET
ap-1259	145	34	action	action	NOUN
ap-1259	145	35	with	with	ADP
ap-1259	145	36	k(x	k(x	NOUN
ap-1259	145	37	)	)	PUNCT
ap-1259	146	1	=	=	SYM
ap-1259	146	2	x	x	X
ap-1259	146	3	,	,	PUNCT
ap-1259	146	4	k(y	k(y	X
ap-1259	146	5	)	)	PUNCT
ap-1259	146	6	=	=	VERB
ap-1259	147	1	y.	y.	NOUN
ap-1259	147	2	the	the	DET
ap-1259	147	3	remaining	remain	VERB
ap-1259	147	4	three	three	NUM
ap-1259	147	5	actions	action	NOUN
ap-1259	147	6	of	of	ADP
ap-1259	147	7	this	this	DET
ap-1259	147	8	series	series	NOUN
ap-1259	147	9	admit	admit	VERB
ap-1259	147	10	no	no	DET
ap-1259	147	11	classical	classical	ADJ
ap-1259	147	12	limit	limit	NOUN
ap-1259	147	13	in	in	ADP
ap-1259	147	14	the	the	DET
ap-1259	147	15	above	above	ADJ
ap-1259	147	16	sense	sense	NOUN
ap-1259	147	17	.	.	PUNCT
ap-1259	148	1	acknowledgement	acknowledgement	NOUN
ap-1259	148	2	one	one	NUM
ap-1259	148	3	of	of	ADP
ap-1259	148	4	the	the	DET
ap-1259	148	5	authors	author	NOUN
ap-1259	148	6	(	(	PUNCT
ap-1259	148	7	s.d	s.d	PROPN
ap-1259	148	8	.	.	PROPN
ap-1259	148	9	)	)	PUNCT
ap-1259	148	10	is	be	AUX
ap-1259	148	11	grateful	grateful	ADJ
ap-1259	148	12	to	to	ADP
ap-1259	148	13	yu	yu	PROPN
ap-1259	148	14	.	.	PROPN
ap-1259	149	1	bespalov	bespalov	PROPN
ap-1259	149	2	,	,	PUNCT
ap-1259	149	3	j.	j.	PROPN
ap-1259	149	4	cuntz	cuntz	PROPN
ap-1259	149	5	,	,	PUNCT
ap-1259	149	6	b.	b.	PROPN
ap-1259	149	7	dragovich	dragovich	PROPN
ap-1259	149	8	,	,	PUNCT
ap-1259	149	9	j.	j.	PROPN
ap-1259	149	10	fuchs	fuchs	PROPN
ap-1259	149	11	,	,	PUNCT
ap-1259	149	12	a.	a.	NOUN
ap-1259	149	13	gavrilik	gavrilik	PROPN
ap-1259	149	14	,	,	PUNCT
ap-1259	149	15	h.	h.	PROPN
ap-1259	149	16	grosse	grosse	PROPN
ap-1259	149	17	,	,	PUNCT
ap-1259	149	18	d.	d.	PROPN
ap-1259	149	19	gurevich	gurevich	PROPN
ap-1259	149	20	,	,	PUNCT
ap-1259	149	21	j.	j.	PROPN
ap-1259	149	22	lukierski	lukierski	PROPN
ap-1259	149	23	,	,	PUNCT
ap-1259	149	24	m.	m.	PROPN
ap-1259	149	25	pavlov	pavlov	PROPN
ap-1259	149	26	,	,	PUNCT
ap-1259	149	27	h.	h.	PROPN
ap-1259	149	28	steinacker	steinacker	PROPN
ap-1259	149	29	,	,	PUNCT
ap-1259	149	30	z.	z.	PROPN
ap-1259	149	31	rakić	rakić	PROPN
ap-1259	149	32	,	,	PUNCT
ap-1259	149	33	w.	w.	PROPN
ap-1259	149	34	werner	werner	PROPN
ap-1259	149	35	,	,	PUNCT
ap-1259	149	36	and	and	CCONJ
ap-1259	149	37	s.	s.	PROPN
ap-1259	149	38	woronowicz	woronowicz	PROPN
ap-1259	149	39	for	for	ADP
ap-1259	149	40	many	many	ADJ
ap-1259	149	41	fruitful	fruitful	ADJ
ap-1259	149	42	discussions	discussion	NOUN
ap-1259	149	43	.	.	PUNCT
ap-1259	150	1	also	also	ADV
ap-1259	150	2	,	,	PUNCT
ap-1259	150	3	he	he	PRON
ap-1259	150	4	would	would	AUX
ap-1259	150	5	like	like	VERB
ap-1259	150	6	to	to	PART
ap-1259	150	7	thank	thank	VERB
ap-1259	150	8	m.	m.	NOUN
ap-1259	150	9	znojil	znojil	NOUN
ap-1259	150	10	for	for	ADP
ap-1259	150	11	his	his	PRON
ap-1259	150	12	invitation	invitation	NOUN
ap-1259	150	13	to	to	ADP
ap-1259	150	14	the	the	DET
ap-1259	150	15	conference	conference	NOUN
ap-1259	150	16	“	"	PUNCT
ap-1259	150	17	analytic	analytic	ADJ
ap-1259	150	18	and	and	CCONJ
ap-1259	150	19	algebraic	algebraic	ADJ
ap-1259	150	20	methods	method	NOUN
ap-1259	150	21	vi	vi	PROPN
ap-1259	150	22	”	"	PUNCT
ap-1259	150	23	,	,	PUNCT
ap-1259	150	24	villa	villa	PROPN
ap-1259	150	25	lanna	lanna	PROPN
ap-1259	150	26	,	,	PUNCT
ap-1259	150	27	prague	prague	NOUN
ap-1259	150	28	,	,	PUNCT
ap-1259	150	29	and	and	CCONJ
ap-1259	150	30	kind	kind	ADJ
ap-1259	150	31	hospitality	hospitality	NOUN
ap-1259	150	32	at	at	ADP
ap-1259	150	33	the	the	DET
ap-1259	150	34	doppler	doppler	NOUN
ap-1259	150	35	institute	institute	NOUN
ap-1259	150	36	in	in	ADP
ap-1259	150	37	rez	rez	PROPN
ap-1259	150	38	.	.	PUNCT
ap-1259	151	1	references	reference	NOUN
ap-1259	151	2	[	[	X
ap-1259	151	3	1	1	NUM
ap-1259	151	4	]	]	SYM
ap-1259	151	5	manin	manin	PROPN
ap-1259	151	6	,	,	PUNCT
ap-1259	151	7	y.	y.	PROPN
ap-1259	151	8	i.	i.	PROPN
ap-1259	151	9	:	:	PUNCT
ap-1259	151	10	topics	topic	NOUN
ap-1259	151	11	in	in	ADP
ap-1259	151	12	noncommutative	noncommutative	ADJ
ap-1259	151	13	differential	differential	PROPN
ap-1259	151	14	geometry	geometry	NOUN
ap-1259	151	15	,	,	PUNCT
ap-1259	151	16	princeton	princeton	PROPN
ap-1259	151	17	university	university	PROPN
ap-1259	151	18	press	press	PROPN
ap-1259	151	19	,	,	PUNCT
ap-1259	151	20	princeton	princeton	PROPN
ap-1259	151	21	,	,	PUNCT
ap-1259	151	22	1991	1991	NUM
ap-1259	151	23	.	.	PUNCT
ap-1259	152	1	[	[	X
ap-1259	152	2	2	2	NUM
ap-1259	152	3	]	]	X
ap-1259	152	4	castellani	castellani	PROPN
ap-1259	152	5	,	,	PUNCT
ap-1259	152	6	l.	l.	PROPN
ap-1259	152	7	,	,	PUNCT
ap-1259	152	8	wess	wess	PROPN
ap-1259	152	9	,	,	PUNCT
ap-1259	152	10	j.	j.	PROPN
ap-1259	152	11	(	(	PUNCT
ap-1259	152	12	eds	eds	PROPN
ap-1259	152	13	.	.	PROPN
ap-1259	152	14	):	):	PUNCT
ap-1259	152	15	quantum	quantum	ADJ
ap-1259	152	16	groups	group	NOUN
ap-1259	152	17	and	and	CCONJ
ap-1259	152	18	their	their	PRON
ap-1259	152	19	applications	application	NOUN
ap-1259	152	20	in	in	ADP
ap-1259	152	21	physics	physics	NOUN
ap-1259	152	22	,	,	PUNCT
ap-1259	152	23	ios	ios	PROPN
ap-1259	152	24	press	press	NOUN
ap-1259	152	25	,	,	PUNCT
ap-1259	152	26	amsterdam	amsterdam	PROPN
ap-1259	152	27	,	,	PUNCT
ap-1259	152	28	1996	1996	NUM
ap-1259	152	29	.	.	PUNCT
ap-1259	153	1	[	[	X
ap-1259	153	2	3	3	NUM
ap-1259	153	3	]	]	X
ap-1259	153	4	kassel	kassel	PROPN
ap-1259	153	5	,	,	PUNCT
ap-1259	153	6	c.	c.	PROPN
ap-1259	153	7	:	:	PUNCT
ap-1259	153	8	quantum	quantum	ADJ
ap-1259	153	9	groups	group	NOUN
ap-1259	153	10	,	,	PUNCT
ap-1259	153	11	springer	springer	NOUN
ap-1259	153	12	-	-	PUNCT
ap-1259	153	13	verlag	verlag	PROPN
ap-1259	153	14	,	,	PUNCT
ap-1259	153	15	new	new	PROPN
ap-1259	153	16	york	york	PROPN
ap-1259	153	17	,	,	PUNCT
ap-1259	153	18	1995	1995	NUM
ap-1259	153	19	.	.	PUNCT
ap-1259	154	1	[	[	X
ap-1259	154	2	4	4	NUM
ap-1259	154	3	]	]	X
ap-1259	154	4	sweedler	sweedler	NOUN
ap-1259	154	5	,	,	PUNCT
ap-1259	154	6	m.	m.	NOUN
ap-1259	154	7	e.	e.	PROPN
ap-1259	154	8	:	:	PUNCT
ap-1259	154	9	hopf	hopf	PROPN
ap-1259	154	10	algebras	algebras	PROPN
ap-1259	154	11	,	,	PUNCT
ap-1259	154	12	benjamin	benjamin	PROPN
ap-1259	154	13	,	,	PUNCT
ap-1259	154	14	new	new	PROPN
ap-1259	154	15	york	york	PROPN
ap-1259	154	16	,	,	PUNCT
ap-1259	154	17	1969	1969	NUM
ap-1259	154	18	.	.	PUNCT
ap-1259	155	1	[	[	X
ap-1259	155	2	5	5	NUM
ap-1259	155	3	]	]	PUNCT
ap-1259	155	4	alev	alev	ADJ
ap-1259	155	5	,	,	PUNCT
ap-1259	155	6	j.	j.	PROPN
ap-1259	155	7	,	,	PUNCT
ap-1259	155	8	chamarie	chamarie	VERB
ap-1259	155	9	,	,	PUNCT
ap-1259	155	10	m.	m.	NOUN
ap-1259	155	11	:	:	PUNCT
ap-1259	155	12	dérivations	dérivations	PROPN
ap-1259	155	13	et	et	PROPN
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ap-1259	155	15	de	de	PROPN
ap-1259	155	16	quelques	quelques	PROPN
ap-1259	155	17	algèbres	algèbre	NOUN
ap-1259	155	18	quantiques	quantique	NOUN
ap-1259	155	19	,	,	PUNCT
ap-1259	155	20	comm	comm	NOUN
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ap-1259	156	2	20	20	NUM
ap-1259	156	3	,	,	PUNCT
ap-1259	156	4	1787–1802	1787–1802	NUM
ap-1259	156	5	(	(	PUNCT
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ap-1259	156	7	)	)	PUNCT
ap-1259	156	8	.	.	PUNCT
ap-1259	157	1	[	[	X
ap-1259	157	2	6	6	NUM
ap-1259	157	3	]	]	X
ap-1259	157	4	montgomery	montgomery	PROPN
ap-1259	157	5	,	,	PUNCT
ap-1259	157	6	s.	s.	PROPN
ap-1259	157	7	,	,	PUNCT
ap-1259	157	8	smith	smith	PROPN
ap-1259	157	9	,	,	PUNCT
ap-1259	157	10	s.	s.	PROPN
ap-1259	157	11	p.	p.	PROPN
ap-1259	157	12	:	:	PUNCT
ap-1259	157	13	skew	skew	ADJ
ap-1259	157	14	derivations	derivation	NOUN
ap-1259	157	15	and	and	CCONJ
ap-1259	157	16	uq(sl(2	uq(sl(2	NUM
ap-1259	157	17	)	)	PUNCT
ap-1259	157	18	)	)	PUNCT
ap-1259	157	19	,	,	PUNCT
ap-1259	157	20	israel	israel	PROPN
ap-1259	157	21	j.	j.	PROPN
ap-1259	157	22	math	math	PROPN
ap-1259	157	23	.	.	PUNCT
ap-1259	158	1	72	72	NUM
ap-1259	158	2	,	,	PUNCT
ap-1259	158	3	158–166	158–166	NUM
ap-1259	158	4	(	(	PUNCT
ap-1259	158	5	1990	1990	NUM
ap-1259	158	6	)	)	PUNCT
ap-1259	158	7	.	.	PUNCT
ap-1259	159	1	[	[	X
ap-1259	159	2	7	7	NUM
ap-1259	159	3	]	]	X
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ap-1259	159	5	,	,	PUNCT
ap-1259	159	6	l.	l.	PROPN
ap-1259	159	7	a.	a.	PROPN
ap-1259	159	8	,	,	PUNCT
ap-1259	159	9	radford	radford	PROPN
ap-1259	159	10	,	,	PUNCT
ap-1259	159	11	d.	d.	PROPN
ap-1259	159	12	e.	e.	PROPN
ap-1259	159	13	:	:	PUNCT
ap-1259	159	14	introduction	introduction	NOUN
ap-1259	159	15	to	to	ADP
ap-1259	159	16	the	the	DET
ap-1259	159	17	quantum	quantum	PROPN
ap-1259	159	18	yang	yang	PROPN
ap-1259	159	19	-	-	PUNCT
ap-1259	159	20	baxter	baxter	PROPN
ap-1259	159	21	equation	equation	NOUN
ap-1259	159	22	and	and	CCONJ
ap-1259	159	23	quantum	quantum	NOUN
ap-1259	159	24	groups	group	NOUN
ap-1259	159	25	:	:	PUNCT
ap-1259	159	26	an	an	DET
ap-1259	159	27	algebraic	algebraic	ADJ
ap-1259	159	28	approach	approach	NOUN
ap-1259	159	29	,	,	PUNCT
ap-1259	159	30	kluwer	kluwer	NOUN
ap-1259	159	31	,	,	PUNCT
ap-1259	159	32	dordrecht	dordrecht	PROPN
ap-1259	159	33	,	,	PUNCT
ap-1259	159	34	1997	1997	NUM
ap-1259	159	35	.	.	PUNCT
ap-1259	160	1	[	[	X
ap-1259	160	2	8	8	NUM
ap-1259	160	3	]	]	X
ap-1259	160	4	gonzález	gonzález	NOUN
ap-1259	160	5	-	-	PUNCT
ap-1259	160	6	lópez	lópez	ADV
ap-1259	160	7	,	,	PUNCT
ap-1259	160	8	a.	a.	PROPN
ap-1259	160	9	,	,	PUNCT
ap-1259	160	10	kamran	kamran	PROPN
ap-1259	160	11	,	,	PUNCT
ap-1259	160	12	n.	n.	PROPN
ap-1259	160	13	,	,	PUNCT
ap-1259	160	14	olver	olver	ADV
ap-1259	160	15	,	,	PUNCT
ap-1259	160	16	p.	p.	NOUN
ap-1259	160	17	:	:	PUNCT
ap-1259	160	18	quasi	quasi	ADJ
ap-1259	160	19	-	-	ADJ
ap-1259	160	20	exactly	exactly	ADV
ap-1259	160	21	solvable	solvable	ADJ
ap-1259	160	22	lie	lie	NOUN
ap-1259	160	23	algebras	algebra	NOUN
ap-1259	160	24	of	of	ADP
ap-1259	160	25	differential	differential	ADJ
ap-1259	160	26	operators	operator	NOUN
ap-1259	160	27	in	in	ADP
ap-1259	160	28	two	two	NUM
ap-1259	160	29	complex	complex	ADJ
ap-1259	160	30	variables	variable	NOUN
ap-1259	160	31	,	,	PUNCT
ap-1259	160	32	j.	j.	PROPN
ap-1259	160	33	phys	phys	PROPN
ap-1259	160	34	.	.	PUNCT
ap-1259	161	1	a	a	DET
ap-1259	161	2	:	:	PUNCT
ap-1259	161	3	math	math	NOUN
ap-1259	161	4	.	.	PUNCT
ap-1259	162	1	gen	gen	PROPN
ap-1259	162	2	.	.	PROPN
ap-1259	162	3	24	24	NUM
ap-1259	162	4	,	,	PUNCT
ap-1259	162	5	3	3	NUM
ap-1259	162	6	995–4	995–4	NOUN
ap-1259	162	7	078	078	NUM
ap-1259	162	8	(	(	PUNCT
ap-1259	162	9	1991	1991	NUM
ap-1259	162	10	)	)	PUNCT
ap-1259	162	11	.	.	PUNCT
ap-1259	163	1	28	28	NUM
ap-1259	163	2	acta	acta	PROPN
ap-1259	163	3	polytechnica	polytechnica	PROPN
ap-1259	163	4	vol	vol	NOUN
ap-1259	163	5	.	.	PROPN
ap-1259	164	1	50	50	NUM
ap-1259	164	2	no	no	NOUN
ap-1259	164	3	.	.	PUNCT
ap-1259	165	1	5/2010	5/2010	NUM
ap-1259	165	2	table	table	NOUN
ap-1259	165	3	1	1	NUM
ap-1259	165	4	:	:	PUNCT
ap-1259	165	5	symbolic	symbolic	ADJ
ap-1259	165	6	matrices	matrix	NOUN
ap-1259	165	7	uq	uq	NOUN
ap-1259	165	8	-	-	PUNCT
ap-1259	165	9	module	module	NOUN
ap-1259	165	10	algebra	algebra	NOUN
ap-1259	165	11	structures	structure	VERB
ap-1259	165	12	classical	classical	ADJ
ap-1259	165	13	limit	limit	NOUN
ap-1259	165	14	sl2	sl2	PROPN
ap-1259	165	15	-	-	PUNCT
ap-1259	165	16	actions	action	NOUN
ap-1259	165	17	by	by	ADP
ap-1259	165	18	differentiations	differentiation	NOUN
ap-1259	165	19	[	[	X
ap-1259	165	20	(	(	PUNCT
ap-1259	165	21	0	0	NUM
ap-1259	165	22	0	0	NUM
ap-1259	165	23	0	0	NUM
ap-1259	165	24	0	0	NUM
ap-1259	165	25	)	)	PUNCT
ap-1259	165	26	0	0	NUM
ap-1259	165	27	;	;	PUNCT
ap-1259	165	28	(	(	PUNCT
ap-1259	165	29	0	0	NUM
ap-1259	165	30	0	0	NUM
ap-1259	165	31	0	0	NUM
ap-1259	165	32	0	0	NUM
ap-1259	165	33	)	)	PUNCT
ap-1259	165	34	1	1	NUM
ap-1259	165	35	]	]	PUNCT
ap-1259	165	36	k	k	X
ap-1259	165	37	(	(	PUNCT
ap-1259	165	38	x	x	X
ap-1259	165	39	)	)	PUNCT
ap-1259	165	40	=	=	SYM
ap-1259	165	41	±x	±x	PROPN
ap-1259	165	42	,	,	PUNCT
ap-1259	165	43	k	k	PROPN
ap-1259	165	44	(	(	PUNCT
ap-1259	165	45	y	y	NOUN
ap-1259	165	46	)	)	PUNCT
ap-1259	165	47	=	=	SYM
ap-1259	165	48	±y	±y	NUM
ap-1259	165	49	,	,	PUNCT
ap-1259	165	50	e	e	X
ap-1259	165	51	(	(	PUNCT
ap-1259	165	52	x	x	X
ap-1259	165	53	)	)	PUNCT
ap-1259	165	54	=	=	SYM
ap-1259	165	55	e	e	X
ap-1259	165	56	(	(	PUNCT
ap-1259	165	57	y	y	NOUN
ap-1259	165	58	)	)	PUNCT
ap-1259	165	59	=	=	SYM
ap-1259	165	60	0	0	NUM
ap-1259	165	61	,	,	PUNCT
ap-1259	165	62	f	f	PROPN
ap-1259	165	63	(	(	PUNCT
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ap-1259	165	65	)	)	PUNCT
ap-1259	165	66	=	=	SYM
ap-1259	165	67	f	f	PROPN
ap-1259	165	68	(	(	PUNCT
ap-1259	165	69	y	y	NOUN
ap-1259	165	70	)	)	PUNCT
ap-1259	165	71	=	=	SYM
ap-1259	165	72	0	0	NUM
ap-1259	165	73	,	,	PUNCT
ap-1259	165	74	h	h	NOUN
ap-1259	165	75	(	(	PUNCT
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ap-1259	165	77	)	)	PUNCT
ap-1259	165	78	=	=	SYM
ap-1259	165	79	0	0	NUM
ap-1259	165	80	,	,	PUNCT
ap-1259	165	81	h	h	NOUN
ap-1259	165	82	(	(	PUNCT
ap-1259	165	83	y	y	NOUN
ap-1259	165	84	)	)	PUNCT
ap-1259	165	85	=	=	SYM
ap-1259	165	86	0	0	NUM
ap-1259	165	87	,	,	PUNCT
ap-1259	165	88	e	e	X
ap-1259	165	89	(	(	PUNCT
ap-1259	165	90	x	x	X
ap-1259	165	91	)	)	PUNCT
ap-1259	165	92	=	=	SYM
ap-1259	165	93	e	e	X
ap-1259	165	94	(	(	PUNCT
ap-1259	165	95	y	y	NOUN
ap-1259	165	96	)	)	PUNCT
ap-1259	165	97	=	=	SYM
ap-1259	165	98	0	0	NUM
ap-1259	165	99	,	,	PUNCT
ap-1259	165	100	f	f	PROPN
ap-1259	165	101	(	(	PUNCT
ap-1259	165	102	x	x	X
ap-1259	165	103	)	)	PUNCT
ap-1259	165	104	=	=	SYM
ap-1259	165	105	f	f	PROPN
ap-1259	165	106	(	(	PUNCT
ap-1259	165	107	y	y	NOUN
ap-1259	165	108	)	)	PUNCT
ap-1259	165	109	=	=	SYM
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ap-1259	165	111	,	,	PUNCT
ap-1259	165	112	[	[	X
ap-1259	165	113	(	(	PUNCT
ap-1259	165	114	0	0	NUM
ap-1259	165	115	�	�	PROPN
ap-1259	165	116	0	0	NUM
ap-1259	165	117	0	0	NUM
ap-1259	165	118	)	)	PUNCT
ap-1259	165	119	0	0	NUM
ap-1259	165	120	;	;	PUNCT
ap-1259	165	121	(	(	PUNCT
ap-1259	165	122	0	0	NUM
ap-1259	165	123	0	0	NUM
ap-1259	165	124	0	0	NUM
ap-1259	165	125	0	0	NUM
ap-1259	165	126	)	)	PUNCT
ap-1259	165	127	1	1	NUM
ap-1259	165	128	]	]	PUNCT
ap-1259	165	129	k	k	X
ap-1259	165	130	(	(	PUNCT
ap-1259	165	131	x	x	X
ap-1259	165	132	)	)	PUNCT
ap-1259	165	133	=	=	SYM
ap-1259	166	1	qx	qx	INTJ
ap-1259	166	2	,	,	PUNCT
ap-1259	166	3	k	k	PROPN
ap-1259	166	4	(	(	PUNCT
ap-1259	166	5	y	y	NOUN
ap-1259	166	6	)	)	PUNCT
ap-1259	166	7	=	=	SYM
ap-1259	167	1	q−2y	q−2y	PROPN
ap-1259	167	2	,	,	PUNCT
ap-1259	167	3	e	e	X
ap-1259	167	4	(	(	PUNCT
ap-1259	167	5	x	x	X
ap-1259	167	6	)	)	PUNCT
ap-1259	167	7	=	=	SYM
ap-1259	167	8	0	0	NUM
ap-1259	167	9	,	,	PUNCT
ap-1259	167	10	e	e	X
ap-1259	167	11	(	(	PUNCT
ap-1259	167	12	y	y	NOUN
ap-1259	167	13	)	)	PUNCT
ap-1259	167	14	=	=	SYM
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ap-1259	167	16	,	,	PUNCT
ap-1259	167	17	f	f	PROPN
ap-1259	167	18	(	(	PUNCT
ap-1259	167	19	x	x	X
ap-1259	167	20	)	)	PUNCT
ap-1259	167	21	=	=	VERB
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ap-1259	168	1	xy	xy	PROPN
ap-1259	168	2	,	,	PUNCT
ap-1259	168	3	f	f	PROPN
ap-1259	168	4	(	(	PUNCT
ap-1259	168	5	y	y	NOUN
ap-1259	168	6	)	)	PUNCT
ap-1259	168	7	=	=	PRON
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ap-1259	168	9	y2	y2	INTJ
ap-1259	168	10	h	h	NOUN
ap-1259	168	11	(	(	PUNCT
ap-1259	168	12	x	x	NOUN
ap-1259	168	13	)	)	PUNCT
ap-1259	168	14	=	=	SYM
ap-1259	168	15	x	x	NOUN
ap-1259	168	16	,	,	PUNCT
ap-1259	168	17	h	h	PROPN
ap-1259	168	18	(	(	PUNCT
ap-1259	168	19	y	y	NOUN
ap-1259	168	20	)	)	PUNCT
ap-1259	168	21	=	=	SYM
ap-1259	169	1	−2y	−2y	PROPN
ap-1259	169	2	,	,	PUNCT
ap-1259	169	3	e	e	X
ap-1259	169	4	(	(	PUNCT
ap-1259	169	5	x	x	X
ap-1259	169	6	)	)	PUNCT
ap-1259	169	7	=	=	SYM
ap-1259	169	8	0	0	NUM
ap-1259	169	9	,	,	PUNCT
ap-1259	169	10	e	e	X
ap-1259	169	11	(	(	PUNCT
ap-1259	169	12	y	y	NOUN
ap-1259	169	13	)	)	PUNCT
ap-1259	169	14	=	=	SYM
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ap-1259	169	16	,	,	PUNCT
ap-1259	169	17	f	f	PROPN
ap-1259	169	18	(	(	PUNCT
ap-1259	169	19	x	x	X
ap-1259	169	20	)	)	PUNCT
ap-1259	169	21	=	=	VERB
ap-1259	169	22	b−10	b−10	VERB
ap-1259	170	1	xy	xy	PROPN
ap-1259	170	2	,	,	PUNCT
ap-1259	170	3	f	f	PROPN
ap-1259	170	4	(	(	PUNCT
ap-1259	170	5	y	y	NOUN
ap-1259	170	6	)	)	PUNCT
ap-1259	170	7	=	=	PUNCT
ap-1259	171	1	−b−10	−b−10	NOUN
ap-1259	171	2	y2	y2	INTJ
ap-1259	172	1	[	[	X
ap-1259	172	2	(	(	PUNCT
ap-1259	172	3	0	0	NUM
ap-1259	172	4	0	0	NUM
ap-1259	172	5	�	�	PROPN
ap-1259	172	6	0	0	NUM
ap-1259	172	7	)	)	PUNCT
ap-1259	172	8	0	0	NUM
ap-1259	172	9	;	;	PUNCT
ap-1259	172	10	(	(	PUNCT
ap-1259	172	11	0	0	NUM
ap-1259	172	12	0	0	NUM
ap-1259	172	13	0	0	NUM
ap-1259	172	14	0	0	NUM
ap-1259	172	15	)	)	PUNCT
ap-1259	172	16	1	1	NUM
ap-1259	172	17	]	]	PUNCT
ap-1259	172	18	k	k	X
ap-1259	172	19	(	(	PUNCT
ap-1259	172	20	x	x	X
ap-1259	172	21	)	)	PUNCT
ap-1259	172	22	=	=	SYM
ap-1259	173	1	q2x	q2x	NOUN
ap-1259	173	2	,	,	PUNCT
ap-1259	173	3	k	k	PROPN
ap-1259	173	4	(	(	PUNCT
ap-1259	173	5	y	y	NOUN
ap-1259	173	6	)	)	PUNCT
ap-1259	173	7	=	=	SYM
ap-1259	174	1	q−1y	q−1y	NOUN
ap-1259	174	2	,	,	PUNCT
ap-1259	174	3	e	e	X
ap-1259	174	4	(	(	PUNCT
ap-1259	174	5	x	x	X
ap-1259	174	6	)	)	PUNCT
ap-1259	174	7	=	=	SYM
ap-1259	174	8	−qc−10	−qc−10	NUM
ap-1259	174	9	x2	x2	NOUN
ap-1259	174	10	,	,	PUNCT
ap-1259	174	11	e	e	X
ap-1259	174	12	(	(	PUNCT
ap-1259	174	13	y	y	NOUN
ap-1259	174	14	)	)	PUNCT
ap-1259	174	15	=	=	PRON
ap-1259	174	16	c−10	c−10	PROPN
ap-1259	174	17	xy	xy	ADJ
ap-1259	174	18	,	,	PUNCT
ap-1259	174	19	f	f	PROPN
ap-1259	174	20	(	(	PUNCT
ap-1259	174	21	x	x	NOUN
ap-1259	174	22	)	)	PUNCT
ap-1259	174	23	=	=	SYM
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ap-1259	174	25	,	,	PUNCT
ap-1259	174	26	f	f	PROPN
ap-1259	174	27	(	(	PUNCT
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ap-1259	174	29	)	)	PUNCT
ap-1259	174	30	=	=	SYM
ap-1259	175	1	0	0	NUM
ap-1259	175	2	,	,	PUNCT
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ap-1259	178	24	,	,	PUNCT
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ap-1259	185	2	0	0	NUM
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ap-1259	187	2	(	(	PUNCT
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ap-1259	187	19	(	(	PUNCT
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ap-1259	188	3	,	,	PUNCT
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ap-1259	188	17	0	0	NUM
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ap-1259	188	21	,	,	PUNCT
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ap-1259	188	28	0	0	NUM
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ap-1259	188	46	,	,	PUNCT
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ap-1259	191	2	,	,	PUNCT
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ap-1259	191	4	(	(	PUNCT
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ap-1259	191	44	,	,	PUNCT
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