id	sid	tid	token	lemma	pos
ap-1263	1	1	ap-5-10.dvi	ap-5-10.dvi	PROPN
ap-1263	1	2	acta	acta	PROPN
ap-1263	1	3	polytechnica	polytechnica	PROPN
ap-1263	1	4	vol	vol	NOUN
ap-1263	1	5	.	.	PROPN
ap-1263	2	1	50	50	NUM
ap-1263	2	2	no	no	NOUN
ap-1263	2	3	.	.	PUNCT
ap-1263	3	1	5/2010	5/2010	NUM
ap-1263	3	2	the	the	DET
ap-1263	3	3	diamond	diamond	NOUN
ap-1263	3	4	lemma	lemma	PROPN
ap-1263	3	5	and	and	CCONJ
ap-1263	3	6	the	the	DET
ap-1263	3	7	pbw	pbw	NOUN
ap-1263	3	8	property	property	NOUN
ap-1263	3	9	in	in	ADP
ap-1263	3	10	quantum	quantum	NOUN
ap-1263	3	11	algebras	algebras	PROPN
ap-1263	3	12	m.	m.	PROPN
ap-1263	3	13	havlíček	havlíček	PROPN
ap-1263	3	14	,	,	PUNCT
ap-1263	3	15	s.	s.	PROPN
ap-1263	3	16	pošta	pošta	PROPN
ap-1263	3	17	abstract	abstract	VERB
ap-1263	3	18	the	the	DET
ap-1263	3	19	use	use	NOUN
ap-1263	3	20	of	of	ADP
ap-1263	3	21	the	the	DET
ap-1263	3	22	diamond	diamond	NOUN
ap-1263	3	23	lemma	lemma	PROPN
ap-1263	3	24	for	for	ADP
ap-1263	3	25	proving	prove	VERB
ap-1263	3	26	various	various	ADJ
ap-1263	3	27	facts	fact	NOUN
ap-1263	3	28	about	about	ADP
ap-1263	3	29	the	the	DET
ap-1263	3	30	center	center	NOUN
ap-1263	3	31	of	of	ADP
ap-1263	3	32	the	the	DET
ap-1263	3	33	algebra	algebra	NOUN
ap-1263	3	34	u	u	NOUN
ap-1263	3	35	′	′	NOUN
ap-1263	3	36	q(so3	q(so3	ADV
ap-1263	3	37	)	)	PUNCT
ap-1263	3	38	is	be	AUX
ap-1263	3	39	demonstrated	demonstrate	VERB
ap-1263	3	40	.	.	PUNCT
ap-1263	4	1	the	the	DET
ap-1263	4	2	approach	approach	NOUN
ap-1263	4	3	presented	present	VERB
ap-1263	4	4	here	here	ADV
ap-1263	4	5	is	be	AUX
ap-1263	4	6	successful	successful	ADJ
ap-1263	4	7	in	in	ADP
ap-1263	4	8	other	other	ADJ
ap-1263	4	9	cases	case	NOUN
ap-1263	4	10	of	of	ADP
ap-1263	4	11	quantum	quantum	NOUN
ap-1263	4	12	algebras	algebra	NOUN
ap-1263	4	13	and	and	CCONJ
ap-1263	4	14	superalgebras	superalgebra	NOUN
ap-1263	4	15	.	.	PUNCT
ap-1263	5	1	keywords	keyword	NOUN
ap-1263	5	2	:	:	PUNCT
ap-1263	5	3	quantum	quantum	ADJ
ap-1263	5	4	algebra	algebra	NOUN
ap-1263	5	5	,	,	PUNCT
ap-1263	5	6	pbw	pbw	NOUN
ap-1263	5	7	property	property	NOUN
ap-1263	5	8	,	,	PUNCT
ap-1263	5	9	center	center	NOUN
ap-1263	5	10	.	.	PUNCT
ap-1263	6	1	1	1	NUM
ap-1263	6	2	introduction	introduction	NOUN
ap-1263	6	3	a	a	DET
ap-1263	6	4	fundamental	fundamental	ADJ
ap-1263	6	5	issue	issue	NOUN
ap-1263	6	6	when	when	SCONJ
ap-1263	6	7	examining	examine	VERB
ap-1263	6	8	quantum	quantum	NOUN
ap-1263	6	9	groups	group	NOUN
ap-1263	6	10	or	or	CCONJ
ap-1263	6	11	similar	similar	ADJ
ap-1263	6	12	structures	structure	NOUN
ap-1263	6	13	is	be	AUX
ap-1263	6	14	to	to	PART
ap-1263	6	15	explore	explore	VERB
ap-1263	6	16	and	and	CCONJ
ap-1263	6	17	classify	classify	VERB
ap-1263	6	18	all	all	DET
ap-1263	6	19	representations	representation	NOUN
ap-1263	6	20	.	.	PUNCT
ap-1263	7	1	usually	usually	ADV
ap-1263	7	2	one	one	NUM
ap-1263	7	3	encounters	encounter	VERB
ap-1263	7	4	two	two	NUM
ap-1263	7	5	main	main	ADJ
ap-1263	7	6	cases	case	NOUN
ap-1263	7	7	which	which	PRON
ap-1263	7	8	are	be	AUX
ap-1263	7	9	of	of	ADP
ap-1263	7	10	different	different	ADJ
ap-1263	7	11	difficulty	difficulty	NOUN
ap-1263	7	12	.	.	PUNCT
ap-1263	8	1	when	when	SCONJ
ap-1263	8	2	the	the	DET
ap-1263	8	3	deformation	deformation	NOUN
ap-1263	8	4	parameter	parameter	NOUN
ap-1263	8	5	,	,	PUNCT
ap-1263	8	6	in	in	ADP
ap-1263	8	7	quantum	quantum	ADJ
ap-1263	8	8	groups	group	NOUN
ap-1263	8	9	typically	typically	ADV
ap-1263	8	10	denoted	denote	VERB
ap-1263	8	11	by	by	ADP
ap-1263	8	12	q	q	PROPN
ap-1263	8	13	,	,	PUNCT
ap-1263	8	14	is	be	AUX
ap-1263	8	15	not	not	PART
ap-1263	8	16	a	a	DET
ap-1263	8	17	root	root	NOUN
ap-1263	8	18	of	of	ADP
ap-1263	8	19	unity	unity	NOUN
ap-1263	8	20	,	,	PUNCT
ap-1263	8	21	i.	i.	PROPN
ap-1263	8	22	e.	e.	PROPN
ap-1263	8	23	when	when	SCONJ
ap-1263	8	24	qn	qn	PROPN
ap-1263	8	25	=	=	NOUN
ap-1263	8	26	1	1	NUM
ap-1263	8	27	for	for	ADP
ap-1263	8	28	all	all	DET
ap-1263	8	29	integers	integer	NOUN
ap-1263	8	30	n	n	CCONJ
ap-1263	8	31	,	,	PUNCT
ap-1263	8	32	the	the	DET
ap-1263	8	33	representation	representation	NOUN
ap-1263	8	34	theory	theory	NOUN
ap-1263	8	35	is	be	AUX
ap-1263	8	36	“	"	PUNCT
ap-1263	8	37	the	the	DET
ap-1263	8	38	same	same	ADJ
ap-1263	8	39	”	"	PUNCT
ap-1263	8	40	as	as	ADP
ap-1263	8	41	in	in	ADP
ap-1263	8	42	the	the	DET
ap-1263	8	43	classical	classical	ADJ
ap-1263	8	44	case	case	NOUN
ap-1263	8	45	,	,	PUNCT
ap-1263	8	46	that	that	PRON
ap-1263	8	47	is	be	AUX
ap-1263	8	48	in	in	ADP
ap-1263	8	49	the	the	DET
ap-1263	8	50	case	case	NOUN
ap-1263	8	51	of	of	ADP
ap-1263	8	52	enveloping	envelop	VERB
ap-1263	8	53	algebras	algebra	NOUN
ap-1263	8	54	of	of	ADP
ap-1263	8	55	classical	classical	ADJ
ap-1263	8	56	lie	lie	NOUN
ap-1263	8	57	algebras	algebra	NOUN
ap-1263	8	58	.	.	PUNCT
ap-1263	9	1	when	when	SCONJ
ap-1263	9	2	q	q	NOUN
ap-1263	9	3	is	be	AUX
ap-1263	9	4	a	a	DET
ap-1263	9	5	root	root	NOUN
ap-1263	9	6	of	of	ADP
ap-1263	9	7	unity	unity	NOUN
ap-1263	9	8	,	,	PUNCT
ap-1263	9	9	it	it	PRON
ap-1263	9	10	is	be	AUX
ap-1263	9	11	not	not	PART
ap-1263	9	12	an	an	DET
ap-1263	9	13	easy	easy	ADJ
ap-1263	9	14	task	task	NOUN
ap-1263	9	15	to	to	PART
ap-1263	9	16	classify	classify	VERB
ap-1263	9	17	finite	finite	ADJ
ap-1263	9	18	dimensional	dimensional	ADJ
ap-1263	9	19	representations	representation	NOUN
ap-1263	9	20	even	even	ADV
ap-1263	9	21	in	in	ADP
ap-1263	9	22	the	the	DET
ap-1263	9	23	lowest	low	ADJ
ap-1263	9	24	dimensions	dimension	NOUN
ap-1263	9	25	.	.	PUNCT
ap-1263	10	1	various	various	ADJ
ap-1263	10	2	preparatory	preparatory	ADJ
ap-1263	10	3	steps	step	NOUN
ap-1263	10	4	must	must	AUX
ap-1263	10	5	be	be	AUX
ap-1263	10	6	taken	take	VERB
ap-1263	10	7	before	before	SCONJ
ap-1263	10	8	one	one	PRON
ap-1263	10	9	can	can	AUX
ap-1263	10	10	investigate	investigate	VERB
ap-1263	10	11	representations	representation	NOUN
ap-1263	10	12	of	of	ADP
ap-1263	10	13	the	the	DET
ap-1263	10	14	considered	consider	VERB
ap-1263	10	15	algebra	algebra	NOUN
ap-1263	10	16	.	.	PUNCT
ap-1263	11	1	important	important	ADJ
ap-1263	11	2	supporting	support	VERB
ap-1263	11	3	knowledge	knowledge	NOUN
ap-1263	11	4	which	which	PRON
ap-1263	11	5	helps	help	VERB
ap-1263	11	6	in	in	ADP
ap-1263	11	7	making	make	VERB
ap-1263	11	8	such	such	DET
ap-1263	11	9	a	a	DET
ap-1263	11	10	classification	classification	NOUN
ap-1263	11	11	is	be	AUX
ap-1263	11	12	detailed	detail	VERB
ap-1263	11	13	information	information	NOUN
ap-1263	11	14	about	about	ADP
ap-1263	11	15	the	the	DET
ap-1263	11	16	center	center	NOUN
ap-1263	11	17	of	of	ADP
ap-1263	11	18	the	the	DET
ap-1263	11	19	considered	consider	VERB
ap-1263	11	20	algebra	algebra	NOUN
ap-1263	11	21	,	,	PUNCT
ap-1263	11	22	because	because	SCONJ
ap-1263	11	23	irreducible	irreducible	ADJ
ap-1263	11	24	representation	representation	NOUN
ap-1263	11	25	operators	operator	NOUN
ap-1263	11	26	which	which	PRON
ap-1263	11	27	belong	belong	VERB
ap-1263	11	28	to	to	ADP
ap-1263	11	29	the	the	DET
ap-1263	11	30	center	center	NOUN
ap-1263	11	31	of	of	ADP
ap-1263	11	32	the	the	DET
ap-1263	11	33	algebra	algebra	NOUN
ap-1263	11	34	(	(	PUNCT
ap-1263	11	35	casimir	casimir	NOUN
ap-1263	11	36	operators	operator	NOUN
ap-1263	11	37	)	)	PUNCT
ap-1263	11	38	are	be	AUX
ap-1263	11	39	represented	represent	VERB
ap-1263	11	40	by	by	ADP
ap-1263	11	41	a	a	DET
ap-1263	11	42	scalar	scalar	ADJ
ap-1263	11	43	multiple	multiple	NOUN
ap-1263	11	44	of	of	ADP
ap-1263	11	45	the	the	DET
ap-1263	11	46	unit	unit	NOUN
ap-1263	11	47	operator	operator	NOUN
ap-1263	11	48	.	.	PUNCT
ap-1263	12	1	the	the	DET
ap-1263	12	2	harish	harish	PROPN
ap-1263	12	3	-	-	PUNCT
ap-1263	12	4	chandra	chandra	PROPN
ap-1263	12	5	homomorphism	homomorphism	PROPN
ap-1263	12	6	(	(	PUNCT
ap-1263	12	7	1951	1951	NUM
ap-1263	12	8	)	)	PUNCT
ap-1263	12	9	is	be	AUX
ap-1263	12	10	an	an	DET
ap-1263	12	11	isomorphism	isomorphism	NOUN
ap-1263	12	12	which	which	PRON
ap-1263	12	13	maps	map	VERB
ap-1263	12	14	the	the	DET
ap-1263	12	15	center	center	NOUN
ap-1263	12	16	z(u(g	z(u(g	PROPN
ap-1263	12	17	)	)	PUNCT
ap-1263	12	18	)	)	PUNCT
ap-1263	12	19	of	of	ADP
ap-1263	12	20	the	the	DET
ap-1263	12	21	universal	universal	ADJ
ap-1263	12	22	enveloping	enveloping	NOUN
ap-1263	12	23	algebra	algebra	NOUN
ap-1263	12	24	u(g	u(g	PROPN
ap-1263	12	25	)	)	PUNCT
ap-1263	12	26	of	of	ADP
ap-1263	12	27	a	a	DET
ap-1263	12	28	semisimple	semisimple	NOUN
ap-1263	12	29	lie	lie	NOUN
ap-1263	12	30	algebra	algebra	NOUN
ap-1263	12	31	g	g	PROPN
ap-1263	12	32	to	to	ADP
ap-1263	12	33	the	the	DET
ap-1263	12	34	elements	element	NOUN
ap-1263	12	35	s(h)w	s(h)w	PROPN
ap-1263	12	36	of	of	ADP
ap-1263	12	37	the	the	DET
ap-1263	12	38	symmetric	symmetric	ADJ
ap-1263	12	39	algebra	algebra	PROPN
ap-1263	12	40	s(h	s(h	PROPN
ap-1263	12	41	)	)	PUNCT
ap-1263	12	42	of	of	ADP
ap-1263	12	43	a	a	DET
ap-1263	12	44	cartan	cartan	ADJ
ap-1263	12	45	subalgebra	subalgebra	NOUN
ap-1263	12	46	h	h	PROPN
ap-1263	12	47	⊂	⊂	PROPN
ap-1263	12	48	g	g	PROPN
ap-1263	12	49	that	that	PRON
ap-1263	12	50	are	be	AUX
ap-1263	12	51	invariant	invariant	ADJ
ap-1263	12	52	under	under	ADP
ap-1263	12	53	the	the	DET
ap-1263	12	54	corresponding	corresponding	ADJ
ap-1263	12	55	weyl	weyl	VERB
ap-1263	12	56	group	group	NOUN
ap-1263	12	57	w	w	PROPN
ap-1263	12	58	.	.	PUNCT
ap-1263	13	1	let	let	VERB
ap-1263	13	2	r	r	NOUN
ap-1263	13	3	be	be	AUX
ap-1263	13	4	the	the	DET
ap-1263	13	5	rank	rank	NOUN
ap-1263	13	6	of	of	ADP
ap-1263	13	7	g	g	NOUN
ap-1263	13	8	,	,	PUNCT
ap-1263	13	9	which	which	PRON
ap-1263	13	10	is	be	AUX
ap-1263	13	11	the	the	DET
ap-1263	13	12	dimension	dimension	NOUN
ap-1263	13	13	of	of	ADP
ap-1263	13	14	the	the	DET
ap-1263	13	15	cartan	cartan	PROPN
ap-1263	13	16	subalgebra	subalgebra	PROPN
ap-1263	13	17	h.	h.	PROPN
ap-1263	13	18	coxeter	coxeter	PROPN
ap-1263	13	19	observed	observe	VERB
ap-1263	13	20	that	that	SCONJ
ap-1263	13	21	s(h)w	s(h)w	PROPN
ap-1263	13	22	is	be	AUX
ap-1263	13	23	a	a	DET
ap-1263	13	24	polynomial	polynomial	ADJ
ap-1263	13	25	algebra	algebra	NOUN
ap-1263	13	26	in	in	ADP
ap-1263	13	27	r	r	NOUN
ap-1263	13	28	variables	variable	NOUN
ap-1263	13	29	.	.	PUNCT
ap-1263	14	1	therefore	therefore	ADV
ap-1263	14	2	,	,	PUNCT
ap-1263	14	3	the	the	DET
ap-1263	14	4	center	center	NOUN
ap-1263	14	5	of	of	ADP
ap-1263	14	6	the	the	DET
ap-1263	14	7	universal	universal	ADJ
ap-1263	14	8	enveloping	enveloping	NOUN
ap-1263	14	9	algebra	algebra	NOUN
ap-1263	14	10	of	of	ADP
ap-1263	14	11	a	a	DET
ap-1263	14	12	semisimple	semisimple	ADJ
ap-1263	14	13	lie	lie	NOUN
ap-1263	14	14	algebra	algebra	NOUN
ap-1263	14	15	is	be	AUX
ap-1263	14	16	a	a	DET
ap-1263	14	17	free	free	ADJ
ap-1263	14	18	polynomial	polynomial	ADJ
ap-1263	14	19	ring	ring	NOUN
ap-1263	14	20	.	.	PUNCT
ap-1263	15	1	any	any	DET
ap-1263	15	2	casimir	casimir	NOUN
ap-1263	15	3	operator	operator	NOUN
ap-1263	15	4	is	be	AUX
ap-1263	15	5	an	an	DET
ap-1263	15	6	arbitrary	arbitrary	ADJ
ap-1263	15	7	polynomial	polynomial	NOUN
ap-1263	15	8	in	in	ADP
ap-1263	15	9	basic	basic	ADJ
ap-1263	15	10	algebra	algebra	NOUN
ap-1263	15	11	invariants	invariant	NOUN
ap-1263	15	12	.	.	PUNCT
ap-1263	16	1	the	the	DET
ap-1263	16	2	number	number	NOUN
ap-1263	16	3	and	and	CCONJ
ap-1263	16	4	degrees	degree	NOUN
ap-1263	16	5	of	of	ADP
ap-1263	16	6	these	these	DET
ap-1263	16	7	fundamental	fundamental	ADJ
ap-1263	16	8	invariants	invariant	NOUN
ap-1263	16	9	are	be	AUX
ap-1263	16	10	shown	show	VERB
ap-1263	16	11	in	in	ADP
ap-1263	16	12	table	table	NOUN
ap-1263	16	13	1	1	NUM
ap-1263	16	14	.	.	PUNCT
ap-1263	17	1	in	in	ADP
ap-1263	17	2	the	the	DET
ap-1263	17	3	case	case	NOUN
ap-1263	17	4	of	of	ADP
ap-1263	17	5	standard	standard	ADJ
ap-1263	17	6	drinfeld	drinfeld	PROPN
ap-1263	17	7	-	-	PUNCT
ap-1263	17	8	jimbo	jimbo	PROPN
ap-1263	17	9	quantum	quantum	NOUN
ap-1263	17	10	groups	group	NOUN
ap-1263	17	11	,	,	PUNCT
ap-1263	17	12	we	we	PRON
ap-1263	17	13	have	have	VERB
ap-1263	17	14	an	an	DET
ap-1263	17	15	analogy	analogy	NOUN
ap-1263	17	16	to	to	ADP
ap-1263	17	17	the	the	DET
ap-1263	17	18	non	non	ADJ
ap-1263	17	19	-	-	ADJ
ap-1263	17	20	deformed	deform	VERB
ap-1263	17	21	case	case	NOUN
ap-1263	17	22	.	.	PUNCT
ap-1263	18	1	when	when	SCONJ
ap-1263	18	2	deformation	deformation	NOUN
ap-1263	18	3	parameter	parameter	NOUN
ap-1263	18	4	q	q	PROPN
ap-1263	18	5	is	be	AUX
ap-1263	18	6	not	not	PART
ap-1263	18	7	a	a	DET
ap-1263	18	8	root	root	NOUN
ap-1263	18	9	of	of	ADP
ap-1263	18	10	unity	unity	NOUN
ap-1263	18	11	,	,	PUNCT
ap-1263	18	12	a	a	DET
ap-1263	18	13	modified	modify	VERB
ap-1263	18	14	version	version	NOUN
ap-1263	18	15	of	of	ADP
ap-1263	18	16	the	the	DET
ap-1263	18	17	harish	harish	PROPN
ap-1263	18	18	-	-	PUNCT
ap-1263	18	19	chandra	chandra	PROPN
ap-1263	18	20	homomorphism	homomorphism	NOUN
ap-1263	18	21	exists	exist	VERB
ap-1263	18	22	and	and	CCONJ
ap-1263	18	23	the	the	DET
ap-1263	18	24	center	center	NOUN
ap-1263	18	25	is	be	AUX
ap-1263	18	26	again	again	ADV
ap-1263	18	27	isomorphic	isomorphic	ADJ
ap-1263	18	28	to	to	ADP
ap-1263	18	29	the	the	DET
ap-1263	18	30	ring	ring	NOUN
ap-1263	18	31	of	of	ADP
ap-1263	18	32	polynomials	polynomial	NOUN
ap-1263	18	33	of	of	ADP
ap-1263	18	34	the	the	DET
ap-1263	18	35	fundamental	fundamental	ADJ
ap-1263	18	36	invariants	invariant	NOUN
ap-1263	18	37	(	(	PUNCT
ap-1263	18	38	see	see	VERB
ap-1263	18	39	[	[	X
ap-1263	18	40	1	1	NUM
ap-1263	18	41	]	]	NUM
ap-1263	18	42	)	)	PUNCT
ap-1263	18	43	.	.	PUNCT
ap-1263	19	1	table	table	NOUN
ap-1263	19	2	1	1	NUM
ap-1263	19	3	:	:	PUNCT
ap-1263	19	4	degrees	degree	NOUN
ap-1263	19	5	of	of	ADP
ap-1263	19	6	the	the	DET
ap-1263	19	7	fundamental	fundamental	ADJ
ap-1263	19	8	invariants	invariant	NOUN
ap-1263	19	9	ar	ar	PROPN
ap-1263	19	10	2	2	NUM
ap-1263	19	11	,	,	PUNCT
ap-1263	19	12	3	3	NUM
ap-1263	19	13	,	,	PUNCT
ap-1263	19	14	4	4	NUM
ap-1263	19	15	,	,	PUNCT
ap-1263	19	16	...	...	PUNCT
ap-1263	19	17	,	,	PUNCT
ap-1263	19	18	n+	n+	PUNCT
ap-1263	19	19	1	1	NUM
ap-1263	19	20	br	br	NOUN
ap-1263	19	21	2	2	NUM
ap-1263	19	22	,	,	PUNCT
ap-1263	19	23	4	4	NUM
ap-1263	19	24	,	,	PUNCT
ap-1263	19	25	6	6	NUM
ap-1263	19	26	,	,	PUNCT
ap-1263	19	27	...	...	PUNCT
ap-1263	19	28	,	,	PUNCT
ap-1263	19	29	2n	2n	NUM
ap-1263	19	30	cr	cr	ADP
ap-1263	19	31	2	2	NUM
ap-1263	19	32	,	,	PUNCT
ap-1263	19	33	4	4	NUM
ap-1263	19	34	,	,	PUNCT
ap-1263	19	35	6	6	NUM
ap-1263	19	36	,	,	PUNCT
ap-1263	19	37	...	...	PUNCT
ap-1263	19	38	,	,	PUNCT
ap-1263	19	39	2n	2n	NUM
ap-1263	19	40	dr	dr	PROPN
ap-1263	19	41	n	n	NUM
ap-1263	19	42	;	;	PUNCT
ap-1263	19	43	2	2	NUM
ap-1263	19	44	,	,	PUNCT
ap-1263	19	45	4	4	NUM
ap-1263	19	46	,	,	PUNCT
ap-1263	19	47	6	6	NUM
ap-1263	19	48	,	,	PUNCT
ap-1263	19	49	...	...	PUNCT
ap-1263	19	50	,	,	PUNCT
ap-1263	19	51	2n	2n	NUM
ap-1263	19	52	−	−	NOUN
ap-1263	19	53	2	2	NUM
ap-1263	19	54	e6	e6	NOUN
ap-1263	19	55	2	2	NUM
ap-1263	19	56	,	,	PUNCT
ap-1263	19	57	5	5	NUM
ap-1263	19	58	,	,	PUNCT
ap-1263	19	59	6	6	NUM
ap-1263	19	60	,	,	PUNCT
ap-1263	19	61	8	8	NUM
ap-1263	19	62	,	,	PUNCT
ap-1263	19	63	9	9	NUM
ap-1263	19	64	,	,	PUNCT
ap-1263	19	65	12	12	NUM
ap-1263	19	66	e7	e7	PROPN
ap-1263	19	67	2	2	NUM
ap-1263	19	68	,	,	PUNCT
ap-1263	19	69	6	6	NUM
ap-1263	19	70	,	,	PUNCT
ap-1263	19	71	8	8	NUM
ap-1263	19	72	,	,	PUNCT
ap-1263	19	73	10	10	NUM
ap-1263	19	74	,	,	PUNCT
ap-1263	19	75	12	12	NUM
ap-1263	19	76	,	,	PUNCT
ap-1263	19	77	14	14	NUM
ap-1263	19	78	,	,	PUNCT
ap-1263	19	79	18	18	NUM
ap-1263	19	80	e8	e8	PROPN
ap-1263	19	81	2	2	NUM
ap-1263	19	82	,	,	PUNCT
ap-1263	19	83	8	8	NUM
ap-1263	19	84	,	,	PUNCT
ap-1263	19	85	12	12	NUM
ap-1263	19	86	,	,	PUNCT
ap-1263	19	87	14	14	NUM
ap-1263	19	88	,	,	PUNCT
ap-1263	19	89	18	18	NUM
ap-1263	19	90	,	,	PUNCT
ap-1263	19	91	20	20	NUM
ap-1263	19	92	,	,	PUNCT
ap-1263	19	93	24	24	NUM
ap-1263	19	94	,	,	PUNCT
ap-1263	19	95	30	30	NUM
ap-1263	19	96	f4	f4	PROPN
ap-1263	19	97	2	2	NUM
ap-1263	19	98	,	,	PUNCT
ap-1263	19	99	6	6	NUM
ap-1263	19	100	,	,	PUNCT
ap-1263	19	101	8	8	NUM
ap-1263	19	102	,	,	PUNCT
ap-1263	19	103	12	12	NUM
ap-1263	19	104	g2	g2	PROPN
ap-1263	19	105	2	2	NUM
ap-1263	19	106	,	,	PUNCT
ap-1263	19	107	6	6	NUM
ap-1263	19	108	for	for	ADP
ap-1263	19	109	example	example	NOUN
ap-1263	19	110	,	,	PUNCT
ap-1263	19	111	in	in	ADP
ap-1263	19	112	the	the	DET
ap-1263	19	113	simplest	simple	ADJ
ap-1263	19	114	case	case	NOUN
ap-1263	19	115	of	of	ADP
ap-1263	19	116	the	the	DET
ap-1263	19	117	algebra	algebra	NOUN
ap-1263	19	118	uq(sl2	uq(sl2	PROPN
ap-1263	19	119	)	)	PUNCT
ap-1263	19	120	,	,	PUNCT
ap-1263	19	121	generated	generate	VERB
ap-1263	19	122	by	by	ADP
ap-1263	19	123	four	four	NUM
ap-1263	19	124	letters	letter	NOUN
ap-1263	19	125	(	(	PUNCT
ap-1263	19	126	generators	generator	NOUN
ap-1263	19	127	)	)	PUNCT
ap-1263	19	128	denoted	denote	VERB
ap-1263	19	129	by	by	ADP
ap-1263	19	130	e	e	PROPN
ap-1263	19	131	,	,	PUNCT
ap-1263	19	132	f	f	PROPN
ap-1263	19	133	,	,	PUNCT
ap-1263	19	134	k	k	PROPN
ap-1263	19	135	,	,	PUNCT
ap-1263	19	136	k−1	k−1	PROPN
ap-1263	19	137	and	and	CCONJ
ap-1263	19	138	relations	relation	NOUN
ap-1263	19	139	kk−1	kk−1	PROPN
ap-1263	19	140	=	=	PUNCT
ap-1263	19	141	k−1k	k−1k	NOUN
ap-1263	19	142	=	=	SYM
ap-1263	19	143	1	1	NUM
ap-1263	19	144	,	,	PUNCT
ap-1263	19	145	kek−1	kek−1	PROPN
ap-1263	19	146	=	=	PUNCT
ap-1263	19	147	q2e	q2e	PROPN
ap-1263	19	148	,	,	PUNCT
ap-1263	19	149	kfk−1	kfk−1	PROPN
ap-1263	19	150	=	=	SYM
ap-1263	19	151	q−2f	q−2f	NOUN
ap-1263	19	152	,	,	PUNCT
ap-1263	19	153	[	[	X
ap-1263	19	154	e	e	X
ap-1263	19	155	,	,	PUNCT
ap-1263	19	156	f	f	PROPN
ap-1263	19	157	]	]	PUNCT
ap-1263	19	158	≡	≡	PROPN
ap-1263	19	159	ef	ef	PROPN
ap-1263	19	160	−	−	PROPN
ap-1263	19	161	fe	fe	X
ap-1263	20	1	=	=	PUNCT
ap-1263	21	1	[	[	X
ap-1263	21	2	k]q	k]q	X
ap-1263	21	3	≡	≡	PROPN
ap-1263	21	4	k	k	PROPN
ap-1263	22	1	−	−	PROPN
ap-1263	22	2	k−1	k−1	PROPN
ap-1263	22	3	q	q	PROPN
ap-1263	23	1	−	−	PROPN
ap-1263	23	2	q−1	q−1	PROPN
ap-1263	23	3	,	,	PUNCT
ap-1263	23	4	the	the	DET
ap-1263	23	5	center	center	NOUN
ap-1263	23	6	is	be	AUX
ap-1263	23	7	generated	generate	VERB
ap-1263	23	8	by	by	ADP
ap-1263	23	9	the	the	DET
ap-1263	23	10	casimir	casimir	PROPN
ap-1263	23	11	element	element	PROPN
ap-1263	23	12	cq	cq	PROPN
ap-1263	24	1	=	=	PROPN
ap-1263	24	2	ef	ef	PROPN
ap-1263	25	1	+	+	CCONJ
ap-1263	26	1	kq−1	kq−1	PROPN
ap-1263	26	2	+	+	PROPN
ap-1263	26	3	k−1q	k−1q	NOUN
ap-1263	26	4	(	(	PUNCT
ap-1263	26	5	q	q	NOUN
ap-1263	26	6	−	−	X
ap-1263	26	7	q−1)2	q−1)2	NOUN
ap-1263	26	8	(	(	PUNCT
ap-1263	26	9	1	1	NUM
ap-1263	26	10	)	)	PUNCT
ap-1263	26	11	(	(	PUNCT
ap-1263	26	12	for	for	ADP
ap-1263	26	13	the	the	DET
ap-1263	26	14	standard	standard	ADJ
ap-1263	26	15	proof	proof	NOUN
ap-1263	26	16	of	of	ADP
ap-1263	26	17	this	this	DET
ap-1263	26	18	fact	fact	NOUN
ap-1263	26	19	see	see	VERB
ap-1263	26	20	[	[	X
ap-1263	26	21	2	2	NUM
ap-1263	26	22	]	]	PUNCT
ap-1263	26	23	,	,	PUNCT
ap-1263	26	24	theorem	theorem	VERB
ap-1263	26	25	45	45	NUM
ap-1263	26	26	)	)	PUNCT
ap-1263	26	27	.	.	PUNCT
ap-1263	27	1	when	when	SCONJ
ap-1263	27	2	q	q	NOUN
ap-1263	27	3	is	be	AUX
ap-1263	27	4	a	a	DET
ap-1263	27	5	primitive	primitive	ADJ
ap-1263	27	6	root	root	NOUN
ap-1263	27	7	of	of	ADP
ap-1263	27	8	unity	unity	NOUN
ap-1263	27	9	,	,	PUNCT
ap-1263	27	10	say	say	VERB
ap-1263	27	11	qn	qn	NOUN
ap-1263	27	12	=	=	NOUN
ap-1263	27	13	1	1	NUM
ap-1263	27	14	,	,	PUNCT
ap-1263	27	15	n	n	CCONJ
ap-1263	27	16	>	>	X
ap-1263	27	17	1	1	NUM
ap-1263	27	18	,	,	PUNCT
ap-1263	27	19	qm	qm	PROPN
ap-1263	27	20	=	=	NOUN
ap-1263	27	21	1	1	NUM
ap-1263	27	22	for	for	ADP
ap-1263	27	23	m	m	PROPN
ap-1263	27	24	<	<	X
ap-1263	27	25	n	n	CCONJ
ap-1263	27	26	,	,	PUNCT
ap-1263	27	27	the	the	DET
ap-1263	27	28	situation	situation	NOUN
ap-1263	27	29	is	be	AUX
ap-1263	27	30	much	much	ADV
ap-1263	27	31	more	more	ADV
ap-1263	27	32	difficult	difficult	ADJ
ap-1263	27	33	.	.	PUNCT
ap-1263	28	1	the	the	DET
ap-1263	28	2	center	center	NOUN
ap-1263	28	3	is	be	AUX
ap-1263	28	4	typically	typically	ADV
ap-1263	28	5	much	much	ADV
ap-1263	28	6	larger	large	ADJ
ap-1263	28	7	and	and	CCONJ
ap-1263	28	8	the	the	DET
ap-1263	28	9	central	central	ADJ
ap-1263	28	10	elements	element	NOUN
ap-1263	28	11	satisfy	satisfy	VERB
ap-1263	28	12	nontrivial	nontrivial	ADJ
ap-1263	28	13	polynomial	polynomial	ADJ
ap-1263	28	14	relations	relation	NOUN
ap-1263	28	15	[	[	X
ap-1263	28	16	3	3	NUM
ap-1263	28	17	]	]	PUNCT
ap-1263	28	18	.	.	PUNCT
ap-1263	29	1	in	in	ADP
ap-1263	29	2	the	the	DET
ap-1263	29	3	case	case	NOUN
ap-1263	29	4	of	of	ADP
ap-1263	29	5	uq(sl2	uq(sl2	PROPN
ap-1263	29	6	)	)	PUNCT
ap-1263	29	7	,	,	PUNCT
ap-1263	29	8	there	there	PRON
ap-1263	29	9	are	be	VERB
ap-1263	29	10	four	four	NUM
ap-1263	29	11	more	more	ADV
ap-1263	29	12	additional	additional	ADJ
ap-1263	29	13	elements	element	NOUN
ap-1263	29	14	in	in	ADP
ap-1263	29	15	the	the	DET
ap-1263	29	16	center	center	NOUN
ap-1263	29	17	,	,	PUNCT
ap-1263	29	18	namely	namely	ADV
ap-1263	29	19	ep	ep	PROPN
ap-1263	29	20	,	,	PUNCT
ap-1263	29	21	f	f	PROPN
ap-1263	29	22	p	p	X
ap-1263	29	23	,	,	PUNCT
ap-1263	29	24	kp	kp	PROPN
ap-1263	29	25	,	,	PUNCT
ap-1263	29	26	k−p	k−p	PROPN
ap-1263	29	27	,	,	PUNCT
ap-1263	29	28	where	where	SCONJ
ap-1263	29	29	p	p	NOUN
ap-1263	29	30	=	=	X
ap-1263	29	31	n	n	PROPN
ap-1263	29	32	if	if	SCONJ
ap-1263	29	33	n	n	NOUN
ap-1263	29	34	is	be	AUX
ap-1263	29	35	odd	odd	ADJ
ap-1263	29	36	and	and	CCONJ
ap-1263	29	37	p	p	X
ap-1263	29	38	=	=	PROPN
ap-1263	29	39	n	n	NUM
ap-1263	29	40	2	2	NUM
ap-1263	29	41	if	if	SCONJ
ap-1263	29	42	n	n	PRON
ap-1263	29	43	is	be	AUX
ap-1263	29	44	even	even	ADV
ap-1263	29	45	.	.	PUNCT
ap-1263	30	1	these	these	DET
ap-1263	30	2	five	five	NUM
ap-1263	30	3	elements	element	NOUN
ap-1263	30	4	(	(	PUNCT
ap-1263	30	5	together	together	ADV
ap-1263	30	6	with	with	ADP
ap-1263	30	7	(	(	PUNCT
ap-1263	30	8	1	1	NUM
ap-1263	30	9	)	)	PUNCT
ap-1263	30	10	)	)	PUNCT
ap-1263	30	11	are	be	AUX
ap-1263	30	12	no	no	ADV
ap-1263	30	13	longer	long	ADV
ap-1263	30	14	algebraically	algebraically	ADV
ap-1263	30	15	independent	independent	ADJ
ap-1263	30	16	.	.	PUNCT
ap-1263	31	1	one	one	PRON
ap-1263	31	2	can	can	AUX
ap-1263	31	3	show	show	VERB
ap-1263	31	4	by	by	ADP
ap-1263	31	5	induction	induction	NOUN
ap-1263	31	6	40	40	NUM
ap-1263	31	7	acta	acta	PROPN
ap-1263	31	8	polytechnica	polytechnica	PROPN
ap-1263	31	9	vol	vol	NOUN
ap-1263	31	10	.	.	PROPN
ap-1263	32	1	50	50	NUM
ap-1263	32	2	no	no	NOUN
ap-1263	32	3	.	.	PUNCT
ap-1263	33	1	5/2010	5/2010	NUM
ap-1263	34	1	that	that	SCONJ
ap-1263	34	2	p−1∏	p−1∏	PROPN
ap-1263	34	3	j=0	j=0	AUX
ap-1263	34	4	(	(	PUNCT
ap-1263	34	5	cq	cq	NOUN
ap-1263	34	6	−	−	PROPN
ap-1263	34	7	(	(	PUNCT
ap-1263	34	8	q	q	NOUN
ap-1263	34	9	−	−	X
ap-1263	34	10	q−1)−2(kqj+1	q−1)−2(kqj+1	PROPN
ap-1263	34	11	+	+	PROPN
ap-1263	34	12	k−1q−j−1	k−1q−j−1	PROPN
ap-1263	34	13	)	)	PUNCT
ap-1263	34	14	)	)	PUNCT
ap-1263	35	1	=	=	VERB
ap-1263	36	1	epf	epf	VERB
ap-1263	36	2	p	p	X
ap-1263	36	3	,	,	PUNCT
ap-1263	36	4	which	which	PRON
ap-1263	36	5	implies	imply	VERB
ap-1263	36	6	cp	cp	PRON
ap-1263	36	7	q	q	PROPN
ap-1263	37	1	+	+	NUM
ap-1263	37	2	γ1c	γ1c	PROPN
ap-1263	37	3	p−1	p−1	PROPN
ap-1263	37	4	q	q	PROPN
ap-1263	38	1	+	+	CCONJ
ap-1263	38	2	.	.	PUNCT
ap-1263	38	3	.	.	PUNCT
ap-1263	39	1	.+	.+	NOUN
ap-1263	39	2	γp−1cq	γp−1cq	NUM
ap-1263	39	3	+	+	CCONJ
ap-1263	39	4	(	(	PUNCT
ap-1263	39	5	−1)p(q	−1)p(q	NUM
ap-1263	39	6	−	−	NOUN
ap-1263	39	7	q−1)−2p(kp	q−1)−2p(kp	NUM
ap-1263	39	8	−	−	NOUN
ap-1263	39	9	k−p	k−p	NOUN
ap-1263	39	10	)	)	PUNCT
ap-1263	39	11	=	=	VERB
ap-1263	39	12	epf	epf	VERB
ap-1263	39	13	p	p	X
ap-1263	39	14	,	,	PUNCT
ap-1263	39	15	where	where	SCONJ
ap-1263	39	16	γi	γi	NOUN
ap-1263	39	17	are	be	AUX
ap-1263	39	18	certain	certain	ADJ
ap-1263	39	19	complex	complex	ADJ
ap-1263	39	20	coefficients	coefficient	NOUN
ap-1263	39	21	.	.	PUNCT
ap-1263	40	1	quantum	quantum	ADJ
ap-1263	40	2	groups	group	NOUN
ap-1263	40	3	are	be	AUX
ap-1263	40	4	not	not	PART
ap-1263	40	5	the	the	DET
ap-1263	40	6	only	only	ADJ
ap-1263	40	7	kind	kind	NOUN
ap-1263	40	8	of	of	ADP
ap-1263	40	9	quantum	quantum	NOUN
ap-1263	40	10	deformations	deformation	NOUN
ap-1263	40	11	.	.	PUNCT
ap-1263	41	1	there	there	PRON
ap-1263	41	2	exist	exist	VERB
ap-1263	41	3	also	also	ADV
ap-1263	41	4	other	other	ADJ
ap-1263	41	5	,	,	PUNCT
ap-1263	41	6	nonstandard	nonstandard	ADJ
ap-1263	41	7	deformations	deformation	NOUN
ap-1263	41	8	.	.	PUNCT
ap-1263	42	1	for	for	ADP
ap-1263	42	2	example	example	NOUN
ap-1263	42	3	,	,	PUNCT
ap-1263	42	4	q	q	ADJ
ap-1263	42	5	-	-	PUNCT
ap-1263	42	6	deformation	deformation	NOUN
ap-1263	42	7	u	u	NOUN
ap-1263	42	8	′	′	NOUN
ap-1263	42	9	q(so3	q(so3	ADV
ap-1263	42	10	)	)	PUNCT
ap-1263	42	11	of	of	ADP
ap-1263	42	12	the	the	DET
ap-1263	42	13	universal	universal	ADJ
ap-1263	42	14	enveloping	enveloping	NOUN
ap-1263	42	15	algebra	algebra	NOUN
ap-1263	42	16	u(so3	u(so3	NOUN
ap-1263	42	17	)	)	PUNCT
ap-1263	42	18	,	,	PUNCT
ap-1263	42	19	which	which	PRON
ap-1263	42	20	does	do	AUX
ap-1263	42	21	not	not	PART
ap-1263	42	22	coincide	coincide	VERB
ap-1263	42	23	with	with	ADP
ap-1263	42	24	the	the	DET
ap-1263	42	25	drinfeld	drinfeld	PROPN
ap-1263	42	26	-	-	PUNCT
ap-1263	42	27	jimbo	jimbo	PROPN
ap-1263	42	28	quantum	quantum	PROPN
ap-1263	42	29	algebra	algebra	NOUN
ap-1263	42	30	uq(so3	uq(so3	PART
ap-1263	42	31	)	)	PUNCT
ap-1263	42	32	is	be	AUX
ap-1263	42	33	constructed	construct	VERB
ap-1263	42	34	without	without	ADP
ap-1263	42	35	using	use	VERB
ap-1263	42	36	the	the	DET
ap-1263	42	37	cartan	cartan	ADJ
ap-1263	42	38	subalgebra	subalgebra	NOUN
ap-1263	42	39	and	and	CCONJ
ap-1263	42	40	roots	root	NOUN
ap-1263	42	41	by	by	ADP
ap-1263	42	42	deforming	deform	VERB
ap-1263	42	43	serre	serre	ADJ
ap-1263	42	44	-	-	ADJ
ap-1263	42	45	type	type	NOUN
ap-1263	42	46	relations	relation	NOUN
ap-1263	42	47	directly	directly	ADV
ap-1263	42	48	.	.	PUNCT
ap-1263	43	1	we	we	PRON
ap-1263	43	2	substitute	substitute	VERB
ap-1263	43	3	simply	simply	ADV
ap-1263	43	4	2	2	NUM
ap-1263	43	5	→	→	SYM
ap-1263	43	6	[	[	X
ap-1263	43	7	2]q	2]q	NUM
ap-1263	43	8	=	=	SYM
ap-1263	43	9	q	q	PROPN
ap-1263	44	1	+	+	NUM
ap-1263	44	2	q−1	q−1	PROPN
ap-1263	44	3	in	in	ADP
ap-1263	44	4	cubic	cubic	ADJ
ap-1263	44	5	defining	define	VERB
ap-1263	44	6	relations	relation	NOUN
ap-1263	44	7	of	of	ADP
ap-1263	44	8	u(so3	u(so3	NOUN
ap-1263	44	9	)	)	PUNCT
ap-1263	44	10	.	.	PUNCT
ap-1263	45	1	as	as	ADP
ap-1263	45	2	a	a	DET
ap-1263	45	3	result	result	NOUN
ap-1263	45	4	we	we	PRON
ap-1263	45	5	obtain	obtain	VERB
ap-1263	45	6	a	a	DET
ap-1263	45	7	complex	complex	ADJ
ap-1263	45	8	associative	associative	ADJ
ap-1263	45	9	algebra	algebra	NOUN
ap-1263	45	10	with	with	ADP
ap-1263	45	11	unity	unity	NOUN
ap-1263	45	12	generated	generate	VERB
ap-1263	45	13	by	by	ADP
ap-1263	45	14	elements	element	NOUN
ap-1263	45	15	i21	i21	NOUN
ap-1263	45	16	,	,	PUNCT
ap-1263	45	17	i32	i32	NOUN
ap-1263	45	18	satisfying	satisfy	VERB
ap-1263	45	19	the	the	DET
ap-1263	45	20	relations	relation	NOUN
ap-1263	45	21	i221i32	i221i32	NOUN
ap-1263	45	22	−	−	PROPN
ap-1263	45	23	(	(	PUNCT
ap-1263	45	24	q	q	X
ap-1263	46	1	+	+	CCONJ
ap-1263	47	1	q−1)i21i32i21	q−1)i21i32i21	PUNCT
ap-1263	47	2	+	+	PUNCT
ap-1263	47	3	i32i	i32i	ADJ
ap-1263	47	4	2	2	NUM
ap-1263	47	5	21	21	NUM
ap-1263	47	6	=	=	SYM
ap-1263	47	7	−i32	−i32	NOUN
ap-1263	47	8	,	,	PUNCT
ap-1263	47	9	i21i	i21i	X
ap-1263	47	10	2	2	NUM
ap-1263	47	11	32	32	NUM
ap-1263	47	12	−	−	NOUN
ap-1263	47	13	(	(	PUNCT
ap-1263	47	14	q	q	PROPN
ap-1263	47	15	+	+	PUNCT
ap-1263	47	16	q−1)i32i21i32	q−1)i32i21i32	ADJ
ap-1263	47	17	+	+	CCONJ
ap-1263	47	18	i232i21	i232i21	VERB
ap-1263	47	19	=	=	SYM
ap-1263	47	20	−i21	−i21	X
ap-1263	47	21	.	.	PUNCT
ap-1263	48	1	it	it	PRON
ap-1263	48	2	can	can	AUX
ap-1263	48	3	be	be	AUX
ap-1263	48	4	shown	show	VERB
ap-1263	48	5	that	that	SCONJ
ap-1263	48	6	this	this	PRON
ap-1263	48	7	is	be	AUX
ap-1263	48	8	isomorphic	isomorphic	ADJ
ap-1263	48	9	to	to	ADP
ap-1263	48	10	an	an	DET
ap-1263	48	11	algebra	algebra	NOUN
ap-1263	48	12	generated	generate	VERB
ap-1263	48	13	by	by	ADP
ap-1263	48	14	three	three	NUM
ap-1263	48	15	generators	generator	NOUN
ap-1263	48	16	i1	i1	PROPN
ap-1263	48	17	,	,	PUNCT
ap-1263	48	18	i2	i2	PROPN
ap-1263	48	19	,	,	PUNCT
ap-1263	48	20	i3	i3	NOUN
ap-1263	48	21	and	and	CCONJ
ap-1263	48	22	relations	relation	NOUN
ap-1263	48	23	[	[	X
ap-1263	48	24	5	5	NUM
ap-1263	48	25	]	]	SYM
ap-1263	48	26	q	q	X
ap-1263	48	27	1	1	NUM
ap-1263	48	28	2	2	NUM
ap-1263	48	29	i1i2	i1i2	NOUN
ap-1263	48	30	−	−	ADP
ap-1263	48	31	q−	q−	PROPN
ap-1263	48	32	1	1	NUM
ap-1263	48	33	2	2	NUM
ap-1263	48	34	i2i1	i2i1	NOUN
ap-1263	48	35	=	=	NOUN
ap-1263	48	36	i3	i3	NOUN
ap-1263	48	37	,	,	PUNCT
ap-1263	48	38	q	q	NOUN
ap-1263	48	39	1	1	NUM
ap-1263	48	40	2	2	NUM
ap-1263	48	41	i2i3	i2i3	NOUN
ap-1263	48	42	−	−	NOUN
ap-1263	48	43	q−	q−	PROPN
ap-1263	48	44	1	1	NUM
ap-1263	48	45	2	2	NUM
ap-1263	48	46	i3i2	i3i2	PROPN
ap-1263	48	47	=	=	PROPN
ap-1263	48	48	i1	i1	PROPN
ap-1263	48	49	,	,	PUNCT
ap-1263	48	50	(	(	PUNCT
ap-1263	48	51	2	2	X
ap-1263	48	52	)	)	PUNCT
ap-1263	48	53	q	q	NOUN
ap-1263	48	54	1	1	NUM
ap-1263	48	55	2	2	NUM
ap-1263	48	56	i3i1	i3i1	NOUN
ap-1263	48	57	−	−	NOUN
ap-1263	49	1	q−	q−	PROPN
ap-1263	49	2	1	1	NUM
ap-1263	49	3	2	2	NUM
ap-1263	49	4	i1i3	i1i3	NOUN
ap-1263	49	5	=	=	PROPN
ap-1263	49	6	i2	i2	PROPN
ap-1263	49	7	.	.	PUNCT
ap-1263	50	1	one	one	PRON
ap-1263	50	2	can	can	AUX
ap-1263	50	3	quickly	quickly	ADV
ap-1263	50	4	explore	explore	VERB
ap-1263	50	5	the	the	DET
ap-1263	50	6	following	follow	VERB
ap-1263	50	7	casimir	casimir	NOUN
ap-1263	50	8	element	element	NOUN
ap-1263	50	9	,	,	PUNCT
ap-1263	50	10	which	which	PRON
ap-1263	50	11	belongs	belong	VERB
ap-1263	50	12	to	to	ADP
ap-1263	50	13	the	the	DET
ap-1263	50	14	center	center	NOUN
ap-1263	50	15	of	of	ADP
ap-1263	50	16	this	this	DET
ap-1263	50	17	algebra	algebra	NOUN
ap-1263	50	18	:	:	PUNCT
ap-1263	50	19	c	c	X
ap-1263	50	20	=	=	PUNCT
ap-1263	50	21	q2i21	q2i21	NOUN
ap-1263	50	22	+	+	CCONJ
ap-1263	50	23	i22	i22	NOUN
ap-1263	50	24	+	+	CCONJ
ap-1263	50	25	q2i23	q2i23	ADJ
ap-1263	50	26	−	−	PROPN
ap-1263	50	27	(	(	PUNCT
ap-1263	50	28	q	q	PROPN
ap-1263	50	29	52	52	NUM
ap-1263	50	30	−	−	NOUN
ap-1263	50	31	q	q	NOUN
ap-1263	50	32	1	1	NUM
ap-1263	50	33	2	2	NUM
ap-1263	50	34	)	)	PUNCT
ap-1263	50	35	i1i2i3	i1i2i3	PROPN
ap-1263	50	36	.	.	PROPN
ap-1263	51	1	(	(	PUNCT
ap-1263	51	2	3	3	X
ap-1263	51	3	)	)	PUNCT
ap-1263	51	4	similarly	similarly	ADV
ap-1263	51	5	as	as	ADP
ap-1263	51	6	in	in	ADP
ap-1263	51	7	the	the	DET
ap-1263	51	8	case	case	NOUN
ap-1263	51	9	of	of	ADP
ap-1263	51	10	ordinary	ordinary	ADJ
ap-1263	51	11	hopf	hopf	ADJ
ap-1263	51	12	quantum	quantum	ADJ
ap-1263	51	13	groups	group	NOUN
ap-1263	51	14	,	,	PUNCT
ap-1263	51	15	one	one	PRON
ap-1263	51	16	can	can	AUX
ap-1263	51	17	expect	expect	VERB
ap-1263	51	18	that	that	SCONJ
ap-1263	51	19	when	when	SCONJ
ap-1263	51	20	q	q	NOUN
ap-1263	51	21	is	be	AUX
ap-1263	51	22	not	not	PART
ap-1263	51	23	a	a	DET
ap-1263	51	24	root	root	NOUN
ap-1263	51	25	of	of	ADP
ap-1263	51	26	unity	unity	NOUN
ap-1263	51	27	,	,	PUNCT
ap-1263	51	28	this	this	DET
ap-1263	51	29	element	element	NOUN
ap-1263	51	30	generates	generate	VERB
ap-1263	51	31	the	the	DET
ap-1263	51	32	center	center	NOUN
ap-1263	51	33	of	of	ADP
ap-1263	51	34	the	the	DET
ap-1263	51	35	algebra	algebra	NOUN
ap-1263	51	36	u	u	NOUN
ap-1263	51	37	′	′	NUM
ap-1263	51	38	q(so3	q(so3	ADV
ap-1263	51	39	)	)	PUNCT
ap-1263	51	40	.	.	PUNCT
ap-1263	52	1	however	however	ADV
ap-1263	52	2	,	,	PUNCT
ap-1263	52	3	there	there	PRON
ap-1263	52	4	is	be	VERB
ap-1263	52	5	no	no	DET
ap-1263	52	6	analogy	analogy	NOUN
ap-1263	52	7	of	of	ADP
ap-1263	52	8	harishchandra	harishchandra	NOUN
ap-1263	52	9	homomorphism	homomorphism	PROPN
ap-1263	52	10	here	here	ADV
ap-1263	52	11	so	so	SCONJ
ap-1263	52	12	one	one	PRON
ap-1263	52	13	must	must	AUX
ap-1263	52	14	prove	prove	VERB
ap-1263	52	15	this	this	DET
ap-1263	52	16	fact	fact	NOUN
ap-1263	52	17	by	by	ADP
ap-1263	52	18	other	other	ADJ
ap-1263	52	19	methods	method	NOUN
ap-1263	52	20	.	.	PUNCT
ap-1263	53	1	as	as	SCONJ
ap-1263	53	2	is	be	AUX
ap-1263	53	3	shown	show	VERB
ap-1263	53	4	below	below	ADP
ap-1263	53	5	,	,	PUNCT
ap-1263	53	6	these	these	DET
ap-1263	53	7	methods	method	NOUN
ap-1263	53	8	are	be	AUX
ap-1263	53	9	useful	useful	ADJ
ap-1263	53	10	even	even	ADV
ap-1263	53	11	in	in	ADP
ap-1263	53	12	the	the	DET
ap-1263	53	13	more	more	ADV
ap-1263	53	14	complicated	complicated	ADJ
ap-1263	53	15	case	case	NOUN
ap-1263	53	16	when	when	SCONJ
ap-1263	53	17	q	q	NOUN
ap-1263	53	18	is	be	AUX
ap-1263	53	19	a	a	DET
ap-1263	53	20	root	root	NOUN
ap-1263	53	21	of	of	ADP
ap-1263	53	22	unity	unity	NOUN
ap-1263	53	23	.	.	PUNCT
ap-1263	54	1	2	2	NUM
ap-1263	54	2	the	the	DET
ap-1263	54	3	diamond	diamond	NOUN
ap-1263	54	4	lemma	lemma	PROPN
ap-1263	54	5	in	in	ADP
ap-1263	54	6	1978	1978	NUM
ap-1263	54	7	,	,	PUNCT
ap-1263	54	8	m.	m.	NOUN
ap-1263	54	9	bergmann	bergmann	PROPN
ap-1263	54	10	recalled	recall	VERB
ap-1263	54	11	a	a	DET
ap-1263	54	12	rather	rather	ADV
ap-1263	54	13	deep	deep	ADJ
ap-1263	54	14	and	and	CCONJ
ap-1263	54	15	forgotten	forget	VERB
ap-1263	54	16	result	result	NOUN
ap-1263	54	17	of	of	ADP
ap-1263	54	18	newman	newman	PROPN
ap-1263	54	19	from	from	ADP
ap-1263	54	20	graph	graph	NOUN
ap-1263	54	21	theory	theory	NOUN
ap-1263	54	22	,	,	PUNCT
ap-1263	54	23	often	often	ADV
ap-1263	54	24	called	call	VERB
ap-1263	54	25	the	the	DET
ap-1263	54	26	diamond	diamond	NOUN
ap-1263	54	27	lemma	lemma	PROPN
ap-1263	54	28	.	.	PUNCT
ap-1263	55	1	he	he	PRON
ap-1263	55	2	showed	show	VERB
ap-1263	55	3	its	its	PRON
ap-1263	55	4	usefulness	usefulness	NOUN
ap-1263	55	5	for	for	ADP
ap-1263	55	6	other	other	ADJ
ap-1263	55	7	fields	field	NOUN
ap-1263	55	8	of	of	ADP
ap-1263	55	9	mathematics	mathematic	NOUN
ap-1263	55	10	also	also	ADV
ap-1263	55	11	,	,	PUNCT
ap-1263	55	12	namely	namely	ADV
ap-1263	55	13	for	for	ADP
ap-1263	55	14	the	the	DET
ap-1263	55	15	theory	theory	NOUN
ap-1263	55	16	of	of	ADP
ap-1263	55	17	associative	associative	ADJ
ap-1263	55	18	algebras	algebra	NOUN
ap-1263	55	19	.	.	PUNCT
ap-1263	56	1	the	the	DET
ap-1263	56	2	original	original	ADJ
ap-1263	56	3	newman	newman	PROPN
ap-1263	56	4	formulation	formulation	NOUN
ap-1263	56	5	was	be	AUX
ap-1263	56	6	as	as	SCONJ
ap-1263	56	7	follows	follow	VERB
ap-1263	56	8	(	(	PUNCT
ap-1263	56	9	see	see	VERB
ap-1263	56	10	[	[	X
ap-1263	56	11	6	6	NUM
ap-1263	56	12	]	]	NUM
ap-1263	56	13	)	)	PUNCT
ap-1263	56	14	.	.	PUNCT
ap-1263	57	1	let	let	VERB
ap-1263	57	2	g	g	PRON
ap-1263	57	3	be	be	AUX
ap-1263	57	4	an	an	DET
ap-1263	57	5	oriented	orient	VERB
ap-1263	57	6	graph	graph	NOUN
ap-1263	57	7	.	.	PUNCT
ap-1263	58	1	now	now	ADV
ap-1263	58	2	suppose	suppose	VERB
ap-1263	58	3	that	that	SCONJ
ap-1263	58	4	1	1	X
ap-1263	58	5	)	)	PUNCT
ap-1263	58	6	the	the	DET
ap-1263	58	7	oriented	orient	VERB
ap-1263	58	8	graph	graph	NOUN
ap-1263	58	9	g	g	PROPN
ap-1263	58	10	has	have	VERB
ap-1263	58	11	the	the	DET
ap-1263	58	12	descending	descend	VERB
ap-1263	58	13	chain	chain	NOUN
ap-1263	58	14	condition	condition	NOUN
ap-1263	58	15	.	.	PUNCT
ap-1263	59	1	that	that	PRON
ap-1263	59	2	is	is	ADV
ap-1263	59	3	,	,	PUNCT
ap-1263	59	4	all	all	DET
ap-1263	59	5	positively	positively	ADV
ap-1263	59	6	oriented	orient	VERB
ap-1263	59	7	paths	path	NOUN
ap-1263	59	8	in	in	ADP
ap-1263	59	9	g	g	NOUN
ap-1263	59	10	terminate	terminate	NOUN
ap-1263	59	11	,	,	PUNCT
ap-1263	59	12	in	in	ADP
ap-1263	59	13	other	other	ADJ
ap-1263	59	14	words	word	NOUN
ap-1263	59	15	,	,	PUNCT
ap-1263	59	16	there	there	PRON
ap-1263	59	17	are	be	VERB
ap-1263	59	18	no	no	DET
ap-1263	59	19	circles	circle	NOUN
ap-1263	59	20	in	in	ADP
ap-1263	59	21	the	the	DET
ap-1263	59	22	graph	graph	NOUN
ap-1263	59	23	.	.	PUNCT
ap-1263	60	1	2	2	X
ap-1263	60	2	)	)	PUNCT
ap-1263	60	3	whenever	whenever	SCONJ
ap-1263	60	4	two	two	NUM
ap-1263	60	5	edges	edge	NOUN
ap-1263	60	6	,	,	PUNCT
ap-1263	60	7	e	e	NOUN
ap-1263	60	8	and	and	CCONJ
ap-1263	60	9	e′	e′	PROPN
ap-1263	60	10	,	,	PUNCT
ap-1263	60	11	proceed	proceed	VERB
ap-1263	60	12	from	from	ADP
ap-1263	60	13	one	one	NUM
ap-1263	60	14	vertex	vertex	NOUN
ap-1263	60	15	a	a	PRON
ap-1263	60	16	of	of	ADP
ap-1263	60	17	g	g	NOUN
ap-1263	60	18	,	,	PUNCT
ap-1263	60	19	there	there	PRON
ap-1263	60	20	exist	exist	VERB
ap-1263	60	21	positively	positively	ADV
ap-1263	60	22	oriented	orient	VERB
ap-1263	60	23	paths	path	NOUN
ap-1263	60	24	p	p	NOUN
ap-1263	60	25	,	,	PUNCT
ap-1263	60	26	p′	p′	NOUN
ap-1263	60	27	in	in	ADP
ap-1263	60	28	g	g	NOUN
ap-1263	60	29	leading	lead	VERB
ap-1263	60	30	from	from	ADP
ap-1263	60	31	the	the	DET
ap-1263	60	32	endpoints	endpoint	NOUN
ap-1263	60	33	b	b	PROPN
ap-1263	60	34	,	,	PUNCT
ap-1263	60	35	b′	b′	NUM
ap-1263	60	36	of	of	ADP
ap-1263	60	37	these	these	DET
ap-1263	60	38	edges	edge	NOUN
ap-1263	60	39	to	to	ADP
ap-1263	60	40	a	a	DET
ap-1263	60	41	common	common	ADJ
ap-1263	60	42	vertex	vertex	NOUN
ap-1263	60	43	c.	c.	NOUN
ap-1263	60	44	(	(	PUNCT
ap-1263	60	45	this	this	PRON
ap-1263	60	46	is	be	AUX
ap-1263	60	47	often	often	ADV
ap-1263	60	48	called	call	VERB
ap-1263	60	49	the	the	DET
ap-1263	60	50	“	"	PUNCT
ap-1263	60	51	confluence	confluence	NOUN
ap-1263	60	52	”	"	PUNCT
ap-1263	60	53	or	or	CCONJ
ap-1263	60	54	“	"	PUNCT
ap-1263	60	55	diamond	diamond	NOUN
ap-1263	60	56	”	"	PUNCT
ap-1263	60	57	condition	condition	NOUN
ap-1263	60	58	,	,	PUNCT
ap-1263	60	59	see	see	VERB
ap-1263	60	60	fig	fig	NOUN
ap-1263	60	61	.	.	PUNCT
ap-1263	61	1	1	1	NUM
ap-1263	61	2	.	.	NUM
ap-1263	61	3	)	)	PUNCT
ap-1263	61	4	fig	fig	NOUN
ap-1263	61	5	.	.	PUNCT
ap-1263	62	1	1	1	NUM
ap-1263	62	2	:	:	PUNCT
ap-1263	62	3	diamond	diamond	NOUN
ap-1263	62	4	condition	condition	NOUN
ap-1263	62	5	then	then	ADV
ap-1263	62	6	one	one	PRON
ap-1263	62	7	can	can	AUX
ap-1263	62	8	show	show	VERB
ap-1263	62	9	that	that	SCONJ
ap-1263	62	10	every	every	DET
ap-1263	62	11	connected	connected	ADJ
ap-1263	62	12	component	component	NOUN
ap-1263	62	13	c	c	NOUN
ap-1263	62	14	of	of	ADP
ap-1263	62	15	g	g	PROPN
ap-1263	62	16	has	have	VERB
ap-1263	62	17	a	a	DET
ap-1263	62	18	unique	unique	ADJ
ap-1263	62	19	minimal	minimal	ADJ
ap-1263	62	20	vertex	vertex	NOUN
ap-1263	62	21	mc	mc	PROPN
ap-1263	62	22	.	.	PUNCT
ap-1263	63	1	this	this	PRON
ap-1263	63	2	means	mean	VERB
ap-1263	63	3	that	that	SCONJ
ap-1263	63	4	every	every	DET
ap-1263	63	5	maximal	maximal	ADJ
ap-1263	63	6	positively	positively	ADV
ap-1263	63	7	oriented	orient	VERB
ap-1263	63	8	path	path	NOUN
ap-1263	63	9	beginning	begin	VERB
ap-1263	63	10	at	at	ADP
ap-1263	63	11	a	a	DET
ap-1263	63	12	point	point	NOUN
ap-1263	63	13	of	of	ADP
ap-1263	63	14	c	c	NOUN
ap-1263	63	15	will	will	AUX
ap-1263	63	16	terminate	terminate	VERB
ap-1263	63	17	at	at	ADP
ap-1263	63	18	mc	mc	PROPN
ap-1263	63	19	.	.	PUNCT
ap-1263	64	1	let	let	VERB
ap-1263	64	2	us	we	PRON
ap-1263	64	3	now	now	ADV
ap-1263	64	4	describe	describe	VERB
ap-1263	64	5	the	the	DET
ap-1263	64	6	version	version	NOUN
ap-1263	64	7	of	of	ADP
ap-1263	64	8	the	the	DET
ap-1263	64	9	diamond	diamond	NOUN
ap-1263	64	10	lemma	lemma	PROPN
ap-1263	64	11	in	in	ADP
ap-1263	64	12	the	the	DET
ap-1263	64	13	theory	theory	NOUN
ap-1263	64	14	of	of	ADP
ap-1263	64	15	associative	associative	ADJ
ap-1263	64	16	algebras	algebra	NOUN
ap-1263	64	17	.	.	PUNCT
ap-1263	65	1	let	let	VERB
ap-1263	65	2	r	r	PRON
ap-1263	65	3	be	be	AUX
ap-1263	65	4	an	an	DET
ap-1263	65	5	associative	associative	ADJ
ap-1263	65	6	algebra	algebra	NOUN
ap-1263	65	7	with	with	ADP
ap-1263	65	8	unity	unity	NOUN
ap-1263	65	9	over	over	ADP
ap-1263	65	10	complex	complex	ADJ
ap-1263	65	11	numbers	number	NOUN
ap-1263	65	12	,	,	PUNCT
ap-1263	65	13	given	give	VERB
ap-1263	65	14	by	by	ADP
ap-1263	65	15	the	the	DET
ap-1263	65	16	finite	finite	ADJ
ap-1263	65	17	set	set	NOUN
ap-1263	65	18	of	of	ADP
ap-1263	65	19	generators	generator	NOUN
ap-1263	65	20	x	x	PUNCT
ap-1263	65	21	and	and	CCONJ
ap-1263	65	22	the	the	DET
ap-1263	65	23	set	set	NOUN
ap-1263	65	24	of	of	ADP
ap-1263	65	25	relations	relation	NOUN
ap-1263	65	26	s	s	PART
ap-1263	65	27	=	=	PUNCT
ap-1263	65	28	{	{	PUNCT
ap-1263	65	29	wσ	wσ	PROPN
ap-1263	65	30	=	=	PUNCT
ap-1263	66	1	fσ|σ	fσ|σ	PROPN
ap-1263	66	2	∈	∈	PROPN
ap-1263	66	3	σ	σ	PROPN
ap-1263	66	4	}	}	PUNCT
ap-1263	66	5	,	,	PUNCT
ap-1263	66	6	where	where	SCONJ
ap-1263	66	7	wσ	wσ	ADJ
ap-1263	66	8	is	be	AUX
ap-1263	66	9	monomial	monomial	ADJ
ap-1263	66	10	(	(	PUNCT
ap-1263	66	11	the	the	DET
ap-1263	66	12	product	product	NOUN
ap-1263	66	13	of	of	ADP
ap-1263	66	14	a	a	DET
ap-1263	66	15	finite	finite	ADJ
ap-1263	66	16	number	number	NOUN
ap-1263	66	17	of	of	ADP
ap-1263	66	18	generators	generator	NOUN
ap-1263	66	19	from	from	ADP
ap-1263	66	20	x	x	NOUN
ap-1263	66	21	)	)	PUNCT
ap-1263	66	22	and	and	CCONJ
ap-1263	66	23	fσ	fσ	PRON
ap-1263	66	24	is	be	AUX
ap-1263	66	25	a	a	DET
ap-1263	66	26	complex	complex	ADJ
ap-1263	66	27	linear	linear	ADJ
ap-1263	66	28	combination	combination	NOUN
ap-1263	66	29	of	of	ADP
ap-1263	66	30	monomials	monomial	NOUN
ap-1263	66	31	.	.	PUNCT
ap-1263	67	1	let	let	VERB
ap-1263	67	2	us	we	PRON
ap-1263	67	3	have	have	VERB
ap-1263	67	4	partial	partial	ADJ
ap-1263	67	5	ordering	ordering	NOUN
ap-1263	67	6	<	<	X
ap-1263	67	7	defined	define	VERB
ap-1263	67	8	on	on	ADP
ap-1263	67	9	monomials	monomial	NOUN
ap-1263	67	10	which	which	PRON
ap-1263	67	11	satisfies	satisfy	VERB
ap-1263	67	12	three	three	NUM
ap-1263	67	13	conditions	condition	NOUN
ap-1263	67	14	:	:	PUNCT
ap-1263	67	15	it	it	PRON
ap-1263	67	16	is	be	AUX
ap-1263	67	17	invariant	invariant	ADJ
ap-1263	67	18	with	with	ADP
ap-1263	67	19	respect	respect	NOUN
ap-1263	67	20	to	to	ADP
ap-1263	67	21	multiplication	multiplication	NOUN
ap-1263	67	22	,	,	PUNCT
ap-1263	67	23	i.	i.	PROPN
ap-1263	67	24	e.	e.	PROPN
ap-1263	67	25	for	for	ADP
ap-1263	67	26	each	each	DET
ap-1263	67	27	monomial	monomial	NOUN
ap-1263	67	28	a	a	DET
ap-1263	67	29	,	,	PUNCT
ap-1263	67	30	b	b	NOUN
ap-1263	67	31	,	,	PUNCT
ap-1263	67	32	b′	b′	NUM
ap-1263	67	33	,	,	PUNCT
ap-1263	67	34	c	c	AUX
ap-1263	67	35	we	we	PRON
ap-1263	67	36	have	have	VERB
ap-1263	67	37	b	b	NUM
ap-1263	67	38	<	<	X
ap-1263	67	39	b′	b′	NUM
ap-1263	67	40	=	=	NOUN
ap-1263	67	41	⇒	⇒	VERB
ap-1263	67	42	abc	abc	X
ap-1263	67	43	<	<	X
ap-1263	67	44	ab′c	ab′c	PROPN
ap-1263	67	45	,	,	PUNCT
ap-1263	67	46	it	it	PRON
ap-1263	67	47	is	be	AUX
ap-1263	67	48	s	s	NOUN
ap-1263	67	49	-	-	ADJ
ap-1263	67	50	compatible	compatible	ADJ
ap-1263	67	51	(	(	PUNCT
ap-1263	67	52	i.	i.	PROPN
ap-1263	67	53	e.	e.	PROPN
ap-1263	67	54	fσ	fσ	PROPN
ap-1263	67	55	is	be	AUX
ap-1263	67	56	a	a	DET
ap-1263	67	57	linear	linear	ADJ
ap-1263	67	58	combination	combination	NOUN
ap-1263	67	59	of	of	ADP
ap-1263	67	60	elements	element	NOUN
ap-1263	67	61	being	be	AUX
ap-1263	67	62	less	less	ADJ
ap-1263	67	63	than	than	SCONJ
ap-1263	67	64	wσ	wσ	VERB
ap-1263	67	65	for	for	ADP
ap-1263	67	66	each	each	DET
ap-1263	67	67	σ	σ	PROPN
ap-1263	67	68	∈	∈	PROPN
ap-1263	67	69	σ	σ	PROPN
ap-1263	67	70	)	)	PUNCT
ap-1263	67	71	and	and	CCONJ
ap-1263	67	72	fulfils	fulfil	VERB
ap-1263	67	73	dcc	dcc	PROPN
ap-1263	67	74	(	(	PUNCT
ap-1263	67	75	the	the	DET
ap-1263	67	76	descending	descend	VERB
ap-1263	67	77	chain	chain	NOUN
ap-1263	67	78	condition	condition	NOUN
ap-1263	67	79	,	,	PUNCT
ap-1263	67	80	which	which	PRON
ap-1263	67	81	is	be	AUX
ap-1263	67	82	the	the	DET
ap-1263	67	83	nonexistence	nonexistence	NOUN
ap-1263	67	84	of	of	ADP
ap-1263	67	85	an	an	DET
ap-1263	67	86	infinite	infinite	ADJ
ap-1263	67	87	sequence	sequence	NOUN
ap-1263	68	1	x1	x1	PROPN
ap-1263	68	2	>	>	X
ap-1263	69	1	x2	x2	INTJ
ap-1263	69	2	>	>	X
ap-1263	69	3	...	...	PUNCT
ap-1263	69	4	)	)	PUNCT
ap-1263	69	5	.	.	PUNCT
ap-1263	70	1	furthermore	furthermore	ADV
ap-1263	70	2	,	,	PUNCT
ap-1263	70	3	let	let	VERB
ap-1263	70	4	all	all	DET
ap-1263	70	5	monomials	monomial	NOUN
ap-1263	70	6	which	which	PRON
ap-1263	70	7	can	can	AUX
ap-1263	70	8	be	be	AUX
ap-1263	70	9	written	write	VERB
ap-1263	70	10	as	as	ADP
ap-1263	70	11	product	product	NOUN
ap-1263	70	12	abc	abc	PROPN
ap-1263	70	13	,	,	PUNCT
ap-1263	70	14	where	where	SCONJ
ap-1263	70	15	ab	ab	PROPN
ap-1263	70	16	=	=	PUNCT
ap-1263	70	17	wσ	wσ	PROPN
ap-1263	70	18	and	and	CCONJ
ap-1263	70	19	bc	bc	PROPN
ap-1263	70	20	=	=	PROPN
ap-1263	70	21	wτ	wτ	PROPN
ap-1263	70	22	,	,	PUNCT
ap-1263	70	23	b	b	PROPN
ap-1263	70	24	=	=	SYM
ap-1263	70	25	1	1	NUM
ap-1263	70	26	,	,	PUNCT
ap-1263	70	27	σ	σ	PROPN
ap-1263	70	28	,	,	PUNCT
ap-1263	70	29	τ	τ	PROPN
ap-1263	70	30	∈	∈	PROPN
ap-1263	70	31	σ	σ	NOUN
ap-1263	70	32	or	or	CCONJ
ap-1263	70	33	in	in	ADP
ap-1263	70	34	the	the	DET
ap-1263	70	35	form	form	NOUN
ap-1263	70	36	abc	abc	X
ap-1263	70	37	=	=	PUNCT
ap-1263	70	38	wσ	wσ	PROPN
ap-1263	70	39	and	and	CCONJ
ap-1263	70	40	b	b	X
ap-1263	70	41	=	=	SYM
ap-1263	70	42	wτ	wτ	PROPN
ap-1263	70	43	,	,	PUNCT
ap-1263	70	44	σ	σ	PROPN
ap-1263	70	45	=	=	SYM
ap-1263	70	46	τ	τ	PROPN
ap-1263	70	47	(	(	PUNCT
ap-1263	70	48	these	these	DET
ap-1263	70	49	monomials	monomial	NOUN
ap-1263	70	50	are	be	AUX
ap-1263	70	51	called	call	VERB
ap-1263	70	52	ambiguities	ambiguity	NOUN
ap-1263	70	53	)	)	PUNCT
ap-1263	70	54	be	be	AUX
ap-1263	70	55	reduced	reduce	VERB
ap-1263	70	56	by	by	ADP
ap-1263	70	57	the	the	DET
ap-1263	70	58	relations	relation	NOUN
ap-1263	70	59	in	in	ADP
ap-1263	70	60	s	s	PRON
ap-1263	70	61	to	to	ADP
ap-1263	70	62	a	a	DET
ap-1263	70	63	common	common	ADJ
ap-1263	70	64	value	value	NOUN
ap-1263	70	65	.	.	PUNCT
ap-1263	71	1	then	then	ADV
ap-1263	71	2	the	the	DET
ap-1263	71	3	diamond	diamond	NOUN
ap-1263	71	4	lemma	lemma	PROPN
ap-1263	71	5	states	state	VERB
ap-1263	71	6	that	that	SCONJ
ap-1263	71	7	all	all	DET
ap-1263	71	8	irreducible	irreducible	ADJ
ap-1263	71	9	(	(	PUNCT
ap-1263	71	10	i.	i.	PROPN
ap-1263	71	11	e.	e.	PROPN
ap-1263	71	12	completely	completely	ADV
ap-1263	71	13	reduced	reduce	VERB
ap-1263	71	14	,	,	PUNCT
ap-1263	71	15	to	to	PART
ap-1263	71	16	which	which	PRON
ap-1263	71	17	one	one	PRON
ap-1263	71	18	can	can	AUX
ap-1263	71	19	not	not	PART
ap-1263	71	20	apply	apply	VERB
ap-1263	71	21	any	any	DET
ap-1263	71	22	relation	relation	NOUN
ap-1263	71	23	from	from	ADP
ap-1263	71	24	s	s	NOUN
ap-1263	71	25	)	)	PUNCT
ap-1263	71	26	monomials	monomial	NOUN
ap-1263	71	27	form	form	VERB
ap-1263	71	28	a	a	DET
ap-1263	71	29	basis	basis	NOUN
ap-1263	71	30	of	of	ADP
ap-1263	71	31	algebra	algebra	PROPN
ap-1263	71	32	r.	r.	PROPN
ap-1263	71	33	41	41	NUM
ap-1263	71	34	acta	acta	PROPN
ap-1263	71	35	polytechnica	polytechnica	PROPN
ap-1263	71	36	vol	vol	NOUN
ap-1263	71	37	.	.	PROPN
ap-1263	72	1	50	50	NUM
ap-1263	72	2	no	no	NOUN
ap-1263	72	3	.	.	PUNCT
ap-1263	73	1	5/2010	5/2010	NUM
ap-1263	73	2	the	the	DET
ap-1263	73	3	diamond	diamond	NOUN
ap-1263	73	4	lemma	lemma	PROPN
ap-1263	73	5	can	can	AUX
ap-1263	73	6	be	be	AUX
ap-1263	73	7	effectively	effectively	ADV
ap-1263	73	8	used	use	VERB
ap-1263	73	9	for	for	ADP
ap-1263	73	10	deciding	decide	VERB
ap-1263	73	11	various	various	ADJ
ap-1263	73	12	kinds	kind	NOUN
ap-1263	73	13	of	of	ADP
ap-1263	73	14	problems	problem	NOUN
ap-1263	73	15	.	.	PUNCT
ap-1263	74	1	the	the	DET
ap-1263	74	2	typical	typical	ADJ
ap-1263	74	3	problem	problem	NOUN
ap-1263	74	4	,	,	PUNCT
ap-1263	74	5	as	as	SCONJ
ap-1263	74	6	mentioned	mention	VERB
ap-1263	74	7	in	in	ADP
ap-1263	74	8	[	[	X
ap-1263	74	9	6	6	NUM
ap-1263	74	10	]	]	PUNCT
ap-1263	74	11	,	,	PUNCT
ap-1263	74	12	is	be	AUX
ap-1263	74	13	as	as	SCONJ
ap-1263	74	14	follows	follow	VERB
ap-1263	74	15	.	.	PUNCT
ap-1263	75	1	let	let	VERB
ap-1263	75	2	us	we	PRON
ap-1263	75	3	have	have	VERB
ap-1263	75	4	an	an	DET
ap-1263	75	5	algebra	algebra	NOUN
ap-1263	75	6	with	with	ADP
ap-1263	75	7	generators	generator	NOUN
ap-1263	75	8	a	a	DET
ap-1263	75	9	,	,	PUNCT
ap-1263	75	10	b	b	NOUN
ap-1263	75	11	,	,	PUNCT
ap-1263	75	12	c	c	PROPN
ap-1263	75	13	and	and	CCONJ
ap-1263	75	14	the	the	DET
ap-1263	75	15	relations	relation	NOUN
ap-1263	75	16	a2	a2	PROPN
ap-1263	75	17	=	=	SYM
ap-1263	75	18	a	a	PROPN
ap-1263	75	19	,	,	PUNCT
ap-1263	75	20	b2	b2	NOUN
ap-1263	75	21	=	=	SYM
ap-1263	75	22	b	b	PROPN
ap-1263	75	23	,	,	PUNCT
ap-1263	75	24	c2	c2	PROPN
ap-1263	75	25	=	=	SYM
ap-1263	75	26	c	c	PROPN
ap-1263	75	27	,	,	PUNCT
ap-1263	75	28	(	(	PUNCT
ap-1263	75	29	4	4	NUM
ap-1263	75	30	)	)	PUNCT
ap-1263	75	31	(	(	PUNCT
ap-1263	75	32	a+	a+	X
ap-1263	75	33	b+	b+	X
ap-1263	75	34	c)2	c)2	PROPN
ap-1263	75	35	=	=	PRON
ap-1263	75	36	a+	a+	X
ap-1263	75	37	b+	b+	X
ap-1263	75	38	c.	c.	PROPN
ap-1263	75	39	(	(	PUNCT
ap-1263	75	40	5	5	NUM
ap-1263	75	41	)	)	PUNCT
ap-1263	75	42	now	now	ADV
ap-1263	75	43	the	the	DET
ap-1263	75	44	problem	problem	NOUN
ap-1263	75	45	is	be	AUX
ap-1263	75	46	to	to	PART
ap-1263	75	47	answer	answer	VERB
ap-1263	75	48	the	the	DET
ap-1263	75	49	question	question	NOUN
ap-1263	75	50	whether	whether	SCONJ
ap-1263	75	51	it	it	PRON
ap-1263	75	52	follows	follow	VERB
ap-1263	75	53	from	from	ADP
ap-1263	75	54	these	these	DET
ap-1263	75	55	relations	relation	NOUN
ap-1263	75	56	that	that	PRON
ap-1263	75	57	ab	ab	PROPN
ap-1263	75	58	=	=	NOUN
ap-1263	75	59	0	0	PROPN
ap-1263	75	60	.	.	PUNCT
ap-1263	76	1	the	the	DET
ap-1263	76	2	second	second	ADJ
ap-1263	76	3	relation	relation	NOUN
ap-1263	76	4	(	(	PUNCT
ap-1263	76	5	5	5	NUM
ap-1263	76	6	)	)	PUNCT
ap-1263	76	7	can	can	AUX
ap-1263	76	8	be	be	AUX
ap-1263	76	9	rewritten	rewrite	VERB
ap-1263	76	10	as	as	ADP
ap-1263	76	11	cb	cb	PROPN
ap-1263	76	12	=	=	PROPN
ap-1263	76	13	−ab	−ab	PROPN
ap-1263	76	14	−	−	PROPN
ap-1263	76	15	ba	ba	PROPN
ap-1263	76	16	−	−	PROPN
ap-1263	77	1	ac	ac	PROPN
ap-1263	78	1	−	−	PROPN
ap-1263	78	2	ca	can	AUX
ap-1263	78	3	−	−	PROPN
ap-1263	78	4	bc	bc	PROPN
ap-1263	78	5	.	.	PROPN
ap-1263	79	1	(	(	PUNCT
ap-1263	79	2	6	6	NUM
ap-1263	79	3	)	)	PUNCT
ap-1263	79	4	now	now	ADV
ap-1263	79	5	we	we	PRON
ap-1263	79	6	test	test	VERB
ap-1263	79	7	whether	whether	SCONJ
ap-1263	79	8	(	(	PUNCT
ap-1263	79	9	4	4	NUM
ap-1263	79	10	)	)	PUNCT
ap-1263	79	11	,	,	PUNCT
ap-1263	79	12	(	(	PUNCT
ap-1263	79	13	5	5	NUM
ap-1263	79	14	)	)	PUNCT
ap-1263	79	15	and	and	CCONJ
ap-1263	79	16	(	(	PUNCT
ap-1263	79	17	6	6	NUM
ap-1263	79	18	)	)	PUNCT
ap-1263	79	19	imply	imply	VERB
ap-1263	79	20	a	a	DET
ap-1263	79	21	unique	unique	ADJ
ap-1263	79	22	canonical	canonical	ADJ
ap-1263	79	23	form	form	NOUN
ap-1263	79	24	of	of	ADP
ap-1263	79	25	the	the	DET
ap-1263	79	26	elements	element	NOUN
ap-1263	79	27	of	of	ADP
ap-1263	79	28	the	the	DET
ap-1263	79	29	considered	consider	VERB
ap-1263	79	30	algebra	algebra	NOUN
ap-1263	79	31	.	.	PUNCT
ap-1263	80	1	we	we	PRON
ap-1263	80	2	must	must	AUX
ap-1263	80	3	examine	examine	VERB
ap-1263	80	4	the	the	DET
ap-1263	80	5	following	follow	VERB
ap-1263	80	6	ambiguities	ambiguity	NOUN
ap-1263	80	7	:	:	PUNCT
ap-1263	80	8	a3	a3	NOUN
ap-1263	80	9	,	,	PUNCT
ap-1263	80	10	b3	b3	PROPN
ap-1263	80	11	,	,	PUNCT
ap-1263	80	12	c3	c3	PROPN
ap-1263	80	13	,	,	PUNCT
ap-1263	80	14	cb2	cb2	PROPN
ap-1263	80	15	,	,	PUNCT
ap-1263	80	16	c2b	c2b	PROPN
ap-1263	80	17	.	.	PUNCT
ap-1263	81	1	the	the	DET
ap-1263	81	2	first	first	ADJ
ap-1263	81	3	three	three	NUM
ap-1263	81	4	are	be	AUX
ap-1263	81	5	trivial	trivial	ADJ
ap-1263	81	6	to	to	PART
ap-1263	81	7	reduce	reduce	VERB
ap-1263	81	8	,	,	PUNCT
ap-1263	81	9	and	and	CCONJ
ap-1263	81	10	the	the	DET
ap-1263	81	11	fourth	fourth	ADJ
ap-1263	81	12	,	,	PUNCT
ap-1263	81	13	reduced	reduce	VERB
ap-1263	81	14	in	in	ADP
ap-1263	81	15	two	two	NUM
ap-1263	81	16	possible	possible	ADJ
ap-1263	81	17	ways	way	NOUN
ap-1263	81	18	,	,	PUNCT
ap-1263	81	19	gives	give	VERB
ap-1263	81	20	us	we	PRON
ap-1263	81	21	the	the	DET
ap-1263	81	22	following	follow	VERB
ap-1263	81	23	:	:	PUNCT
ap-1263	81	24	c(bb	c(bb	X
ap-1263	81	25	)	)	PUNCT
ap-1263	81	26	=	=	PUNCT
ap-1263	81	27	cb	cb	NOUN
ap-1263	82	1	=	=	SYM
ap-1263	82	2	−ab	−ab	PROPN
ap-1263	82	3	−	−	PROPN
ap-1263	82	4	ba	ba	PROPN
ap-1263	82	5	−	−	PROPN
ap-1263	82	6	ac	ac	PROPN
ap-1263	83	1	−	−	PROPN
ap-1263	83	2	ca	can	AUX
ap-1263	83	3	−	−	PROPN
ap-1263	83	4	bc	bc	PROPN
ap-1263	83	5	and	and	CCONJ
ap-1263	83	6	(	(	PUNCT
ap-1263	83	7	cb)b	cb)b	PROPN
ap-1263	83	8	=	=	SYM
ap-1263	83	9	(	(	PUNCT
ap-1263	83	10	−ab	−ab	NOUN
ap-1263	83	11	−	−	PROPN
ap-1263	84	1	ba	ba	PROPN
ap-1263	85	1	−	−	PROPN
ap-1263	86	1	ac	ac	PROPN
ap-1263	87	1	−	−	PROPN
ap-1263	87	2	ca	ca	NOUN
ap-1263	88	1	−	−	NOUN
ap-1263	88	2	bc)b	bc)b	PROPN
ap-1263	88	3	=	=	PUNCT
ap-1263	88	4	−ab2	−ab2	PROPN
ap-1263	88	5	−	−	PROPN
ap-1263	88	6	bab	bab	PROPN
ap-1263	88	7	−	−	PROPN
ap-1263	89	1	acb	acb	PROPN
ap-1263	89	2	−	−	PROPN
ap-1263	89	3	cab	cab	NOUN
ap-1263	89	4	−	−	PROPN
ap-1263	89	5	bcb	bcb	PROPN
ap-1263	89	6	=	=	SYM
ap-1263	89	7	−ab	−ab	PROPN
ap-1263	89	8	−	−	PROPN
ap-1263	89	9	bab	bab	PROPN
ap-1263	89	10	−	−	PROPN
ap-1263	89	11	a(−ab	a(−ab	NOUN
ap-1263	89	12	−	−	PROPN
ap-1263	89	13	ba	ba	PROPN
ap-1263	89	14	−	−	PROPN
ap-1263	89	15	ac	ac	PROPN
ap-1263	89	16	−	−	PROPN
ap-1263	89	17	ca	can	AUX
ap-1263	89	18	−	−	PROPN
ap-1263	89	19	bc)−	bc)−	ADJ
ap-1263	89	20	cab	cab	NOUN
ap-1263	89	21	−	−	PROPN
ap-1263	89	22	b(−ab	b(−ab	NOUN
ap-1263	89	23	−	−	PROPN
ap-1263	89	24	ba	ba	PROPN
ap-1263	90	1	−	−	PROPN
ap-1263	90	2	ac	ac	PROPN
ap-1263	90	3	−	−	PROPN
ap-1263	90	4	ca	can	AUX
ap-1263	90	5	−	−	PROPN
ap-1263	90	6	bc	bc	PROPN
ap-1263	90	7	)	)	PUNCT
ap-1263	90	8	=	=	SYM
ap-1263	91	1	−ab	−ab	NOUN
ap-1263	91	2	−	−	X
ap-1263	91	3	bab+	bab+	NOUN
ap-1263	91	4	a2b+	a2b+	ADP
ap-1263	91	5	aba+	aba+	ADJ
ap-1263	91	6	a2c+	a2c+	X
ap-1263	91	7	aca+	aca+	NOUN
ap-1263	91	8	abc	abc	NOUN
ap-1263	91	9	−	−	PROPN
ap-1263	91	10	cab+	cab+	NOUN
ap-1263	91	11	bab+	bab+	NOUN
ap-1263	91	12	b2a+	b2a+	VERB
ap-1263	91	13	bac+	bac+	PROPN
ap-1263	91	14	bca+	bca+	PROPN
ap-1263	91	15	b2c	b2c	PROPN
ap-1263	91	16	=	=	SYM
ap-1263	91	17	−ab	−ab	NOUN
ap-1263	92	1	−	−	X
ap-1263	92	2	bab+	bab+	NOUN
ap-1263	92	3	ab+	ab+	NOUN
ap-1263	92	4	aba+	aba+	ADJ
ap-1263	92	5	ac+	ac+	PROPN
ap-1263	92	6	aca+	aca+	PROPN
ap-1263	92	7	abc	abc	PROPN
ap-1263	92	8	−	−	PROPN
ap-1263	92	9	cab+	cab+	NOUN
ap-1263	92	10	bab+	bab+	VERB
ap-1263	92	11	ba+	ba+	ADJ
ap-1263	92	12	bac+	bac+	PROPN
ap-1263	92	13	bca+	bca+	PROPN
ap-1263	92	14	bc	bc	PROPN
ap-1263	92	15	=	=	SYM
ap-1263	92	16	aba+	aba+	ADJ
ap-1263	92	17	ac+	ac+	NOUN
ap-1263	92	18	aca+	aca+	PROPN
ap-1263	92	19	abc	abc	PROPN
ap-1263	92	20	−	−	PROPN
ap-1263	92	21	cab+	cab+	PROPN
ap-1263	92	22	ba+	ba+	ADV
ap-1263	92	23	bac+	bac+	PROPN
ap-1263	92	24	bca+	bca+	PROPN
ap-1263	92	25	bc	bc	PROPN
ap-1263	92	26	.	.	PUNCT
ap-1263	93	1	so	so	ADV
ap-1263	93	2	we	we	PRON
ap-1263	93	3	have	have	VERB
ap-1263	93	4	−ab	−ab	NUM
ap-1263	94	1	−	−	PROPN
ap-1263	94	2	ba	ba	PROPN
ap-1263	95	1	−	−	PROPN
ap-1263	96	1	ac	ac	PROPN
ap-1263	97	1	−	−	PROPN
ap-1263	97	2	ca	can	AUX
ap-1263	97	3	−	−	PROPN
ap-1263	97	4	bc	bc	PROPN
ap-1263	97	5	=	=	SYM
ap-1263	97	6	aba+	aba+	ADJ
ap-1263	97	7	ac+	ac+	NOUN
ap-1263	97	8	aca+	aca+	PROPN
ap-1263	97	9	abc	abc	PROPN
ap-1263	97	10	−	−	PROPN
ap-1263	97	11	cab+	cab+	PROPN
ap-1263	97	12	ba+	ba+	ADV
ap-1263	97	13	bac+	bac+	PROPN
ap-1263	97	14	bca+	bca+	PROPN
ap-1263	97	15	bc	bc	PROPN
ap-1263	97	16	.	.	PUNCT
ap-1263	98	1	this	this	DET
ap-1263	98	2	equality	equality	NOUN
ap-1263	98	3	can	can	AUX
ap-1263	98	4	be	be	AUX
ap-1263	98	5	rewritten	rewrite	VERB
ap-1263	98	6	as	as	ADP
ap-1263	98	7	cab	cab	NOUN
ap-1263	98	8	=	=	SYM
ap-1263	98	9	aba+	aba+	ADJ
ap-1263	98	10	2ac+	2ac+	NOUN
ap-1263	98	11	aca+	aca+	NOUN
ap-1263	98	12	abc+	abc+	PROPN
ap-1263	98	13	(	(	PUNCT
ap-1263	98	14	7	7	NUM
ap-1263	98	15	)	)	PUNCT
ap-1263	98	16	2ba+	2ba+	NOUN
ap-1263	98	17	bac+	bac+	PROPN
ap-1263	98	18	bca+	bca+	PROPN
ap-1263	98	19	2bc+	2bc+	PROPN
ap-1263	98	20	ab+	ab+	NOUN
ap-1263	98	21	ca	can	AUX
ap-1263	98	22	.	.	PUNCT
ap-1263	99	1	reducing	reduce	VERB
ap-1263	99	2	the	the	DET
ap-1263	99	3	fifth	fifth	ADJ
ap-1263	99	4	ambiguity	ambiguity	NOUN
ap-1263	99	5	c(cb	c(cb	PROPN
ap-1263	99	6	)	)	PUNCT
ap-1263	99	7	=	=	PUNCT
ap-1263	99	8	(	(	PUNCT
ap-1263	99	9	cc)b	cc)b	PROPN
ap-1263	99	10	leads	lead	VERB
ap-1263	99	11	to	to	ADP
ap-1263	99	12	the	the	DET
ap-1263	99	13	same	same	ADJ
ap-1263	99	14	relation	relation	NOUN
ap-1263	99	15	.	.	PUNCT
ap-1263	100	1	now	now	ADV
ap-1263	100	2	what	what	PRON
ap-1263	100	3	happens	happen	VERB
ap-1263	100	4	if	if	SCONJ
ap-1263	100	5	we	we	PRON
ap-1263	100	6	add	add	VERB
ap-1263	100	7	(	(	PUNCT
ap-1263	100	8	7	7	NUM
ap-1263	100	9	)	)	PUNCT
ap-1263	100	10	to	to	ADP
ap-1263	100	11	the	the	DET
ap-1263	100	12	list	list	NOUN
ap-1263	100	13	of	of	ADP
ap-1263	100	14	relations	relation	NOUN
ap-1263	100	15	?	?	PUNCT
ap-1263	101	1	the	the	DET
ap-1263	101	2	ambiguities	ambiguity	NOUN
ap-1263	101	3	cb2	cb2	PROPN
ap-1263	101	4	and	and	CCONJ
ap-1263	101	5	c2b	c2b	PROPN
ap-1263	101	6	now	now	ADV
ap-1263	101	7	reduce	reduce	VERB
ap-1263	101	8	automatically	automatically	ADV
ap-1263	101	9	to	to	ADP
ap-1263	101	10	a	a	DET
ap-1263	101	11	common	common	ADJ
ap-1263	101	12	value	value	NOUN
ap-1263	101	13	.	.	PUNCT
ap-1263	102	1	but	but	CCONJ
ap-1263	102	2	two	two	NUM
ap-1263	102	3	new	new	ADJ
ap-1263	102	4	ambiguities	ambiguity	NOUN
ap-1263	102	5	of	of	ADP
ap-1263	102	6	higher	high	ADJ
ap-1263	102	7	degree	degree	NOUN
ap-1263	102	8	arise	arise	NOUN
ap-1263	102	9	:	:	PUNCT
ap-1263	102	10	c2ab	c2ab	NOUN
ap-1263	102	11	,	,	PUNCT
ap-1263	102	12	cab2	cab2	ADJ
ap-1263	102	13	.	.	PUNCT
ap-1263	103	1	we	we	PRON
ap-1263	103	2	therefore	therefore	ADV
ap-1263	103	3	test	test	VERB
ap-1263	103	4	again	again	ADV
ap-1263	103	5	:	:	PUNCT
ap-1263	103	6	we	we	PRON
ap-1263	103	7	have	have	VERB
ap-1263	103	8	(	(	PUNCT
ap-1263	103	9	cc)ab	cc)ab	NOUN
ap-1263	103	10	=	=	SYM
ap-1263	103	11	cab	cab	NOUN
ap-1263	103	12	=	=	PUNCT
ap-1263	103	13	aba+	aba+	ADJ
ap-1263	103	14	2ac+	2ac+	NOUN
ap-1263	103	15	aca+	aca+	NOUN
ap-1263	103	16	abc+	abc+	PROPN
ap-1263	103	17	2ba+	2ba+	NUM
ap-1263	103	18	bac+	bac+	PROPN
ap-1263	103	19	bca+	bca+	PROPN
ap-1263	103	20	2bc+	2bc+	PROPN
ap-1263	103	21	ab+	ab+	NOUN
ap-1263	103	22	ca	can	AUX
ap-1263	103	23	,	,	PUNCT
ap-1263	103	24	and	and	CCONJ
ap-1263	103	25	,	,	PUNCT
ap-1263	103	26	after	after	ADP
ap-1263	103	27	some	some	DET
ap-1263	103	28	computation	computation	NOUN
ap-1263	103	29	,	,	PUNCT
ap-1263	103	30	c(cab	c(cab	NOUN
ap-1263	103	31	)	)	PUNCT
ap-1263	103	32	=	=	PUNCT
ap-1263	103	33	.	.	PUNCT
ap-1263	103	34	.	.	PUNCT
ap-1263	103	35	.	.	PUNCT
ap-1263	104	1	=	=	PUNCT
ap-1263	104	2	aba+	aba+	ADJ
ap-1263	104	3	2ac+	2ac+	NOUN
ap-1263	104	4	aca+	aca+	NOUN
ap-1263	104	5	abc+	abc+	PROPN
ap-1263	104	6	2ba+	2ba+	NUM
ap-1263	104	7	bac+	bac+	PROPN
ap-1263	104	8	bca+	bca+	PROPN
ap-1263	104	9	2bc+	2bc+	PROPN
ap-1263	104	10	ab+	ab+	NOUN
ap-1263	104	11	ca	can	AUX
ap-1263	104	12	.	.	PUNCT
ap-1263	105	1	the	the	DET
ap-1263	105	2	second	second	ADJ
ap-1263	105	3	ambiguity	ambiguity	NOUN
ap-1263	105	4	reduces	reduce	VERB
ap-1263	105	5	to	to	ADP
ap-1263	105	6	a	a	DET
ap-1263	105	7	common	common	ADJ
ap-1263	105	8	value	value	NOUN
ap-1263	105	9	,	,	PUNCT
ap-1263	105	10	too	too	ADV
ap-1263	105	11	.	.	PUNCT
ap-1263	106	1	the	the	DET
ap-1263	106	2	basis	basis	NOUN
ap-1263	106	3	of	of	ADP
ap-1263	106	4	the	the	DET
ap-1263	106	5	considered	consider	VERB
ap-1263	106	6	algebra	algebra	NOUN
ap-1263	106	7	consists	consist	VERB
ap-1263	106	8	of	of	ADP
ap-1263	106	9	all	all	DET
ap-1263	106	10	words	word	NOUN
ap-1263	106	11	consisting	consist	VERB
ap-1263	106	12	of	of	ADP
ap-1263	106	13	letters	letter	NOUN
ap-1263	106	14	a	a	DET
ap-1263	106	15	,	,	PUNCT
ap-1263	106	16	b	b	NOUN
ap-1263	106	17	,	,	PUNCT
ap-1263	106	18	c	c	AUX
ap-1263	106	19	not	not	PART
ap-1263	106	20	containing	contain	VERB
ap-1263	106	21	substrings	substring	NOUN
ap-1263	106	22	a2	a2	PROPN
ap-1263	106	23	,	,	PUNCT
ap-1263	106	24	b2	b2	NOUN
ap-1263	106	25	,	,	PUNCT
ap-1263	106	26	c2	c2	PROPN
ap-1263	106	27	,	,	PUNCT
ap-1263	106	28	cab	cab	NOUN
ap-1263	106	29	and	and	CCONJ
ap-1263	106	30	cb	cb	PROPN
ap-1263	106	31	.	.	PROPN
ap-1263	107	1	therefore	therefore	ADV
ap-1263	107	2	the	the	DET
ap-1263	107	3	word	word	NOUN
ap-1263	107	4	ab	ab	PROPN
ap-1263	107	5	is	be	AUX
ap-1263	107	6	irreducible	irreducible	ADJ
ap-1263	107	7	,	,	PUNCT
ap-1263	107	8	hence	hence	ADV
ap-1263	107	9	nonzero	nonzero	ADJ
ap-1263	107	10	.	.	PUNCT
ap-1263	108	1	3	3	NUM
ap-1263	108	2	pbw	pbw	NOUN
ap-1263	108	3	property	property	NOUN
ap-1263	108	4	one	one	NUM
ap-1263	108	5	of	of	ADP
ap-1263	108	6	simple	simple	ADJ
ap-1263	108	7	consequences	consequence	NOUN
ap-1263	108	8	of	of	ADP
ap-1263	108	9	the	the	DET
ap-1263	108	10	diamond	diamond	NOUN
ap-1263	108	11	lemma	lemma	PROPN
ap-1263	108	12	is	be	AUX
ap-1263	108	13	the	the	DET
ap-1263	108	14	poincaré-birkhoff	poincaré-birkhoff	NOUN
ap-1263	108	15	-	-	PUNCT
ap-1263	108	16	witt	witt	VERB
ap-1263	108	17	property	property	NOUN
ap-1263	108	18	of	of	ADP
ap-1263	108	19	universal	universal	ADJ
ap-1263	108	20	enveloping	enveloping	NOUN
ap-1263	108	21	algebras	algebra	NOUN
ap-1263	108	22	and	and	CCONJ
ap-1263	108	23	its	its	PRON
ap-1263	108	24	analogy	analogy	NOUN
ap-1263	108	25	in	in	ADP
ap-1263	108	26	the	the	DET
ap-1263	108	27	case	case	NOUN
ap-1263	108	28	of	of	ADP
ap-1263	108	29	quantum	quantum	NOUN
ap-1263	108	30	deformations	deformation	NOUN
ap-1263	108	31	.	.	PUNCT
ap-1263	109	1	as	as	ADP
ap-1263	109	2	a	a	DET
ap-1263	109	3	simple	simple	ADJ
ap-1263	109	4	example	example	NOUN
ap-1263	109	5	,	,	PUNCT
ap-1263	109	6	let	let	VERB
ap-1263	109	7	us	we	PRON
ap-1263	109	8	have	have	VERB
ap-1263	109	9	an	an	DET
ap-1263	109	10	enveloping	enveloping	NOUN
ap-1263	109	11	algebra	algebra	NOUN
ap-1263	109	12	u(sl2	u(sl2	NOUN
ap-1263	109	13	)	)	PUNCT
ap-1263	109	14	of	of	ADP
ap-1263	109	15	lie	lie	NOUN
ap-1263	109	16	algebra	algebra	PROPN
ap-1263	109	17	sl2	sl2	PROPN
ap-1263	109	18	which	which	PRON
ap-1263	109	19	is	be	AUX
ap-1263	109	20	given	give	VERB
ap-1263	109	21	by	by	ADP
ap-1263	109	22	three	three	NUM
ap-1263	109	23	generators	generator	NOUN
ap-1263	109	24	e	e	NOUN
ap-1263	109	25	,	,	PUNCT
ap-1263	109	26	f	f	X
ap-1263	109	27	,	,	PUNCT
ap-1263	110	1	h	h	NOUN
ap-1263	110	2	satisfying	satisfy	VERB
ap-1263	110	3	the	the	DET
ap-1263	110	4	relations	relation	NOUN
ap-1263	111	1	[	[	X
ap-1263	111	2	e	e	NOUN
ap-1263	111	3	,	,	PUNCT
ap-1263	111	4	f	f	X
ap-1263	111	5	]	]	PUNCT
ap-1263	111	6	=	=	PUNCT
ap-1263	111	7	ef	ef	PROPN
ap-1263	111	8	−	−	PROPN
ap-1263	111	9	fe	fe	X
ap-1263	111	10	=	=	SYM
ap-1263	111	11	h	h	PROPN
ap-1263	111	12	,	,	PUNCT
ap-1263	112	1	[	[	X
ap-1263	112	2	h	h	X
ap-1263	112	3	,	,	PUNCT
ap-1263	112	4	e	e	X
ap-1263	112	5	]	]	X
ap-1263	112	6	=	=	SYM
ap-1263	112	7	2e	2e	NUM
ap-1263	112	8	,	,	PUNCT
ap-1263	112	9	(	(	PUNCT
ap-1263	112	10	8)	8)	NUM
ap-1263	112	11	[	[	X
ap-1263	112	12	h	h	NOUN
ap-1263	112	13	,	,	PUNCT
ap-1263	112	14	f	f	X
ap-1263	112	15	]	]	PUNCT
ap-1263	113	1	=	=	PUNCT
ap-1263	113	2	−2f	−2f	PROPN
ap-1263	113	3	.	.	PUNCT
ap-1263	114	1	we	we	PRON
ap-1263	114	2	define	define	VERB
ap-1263	114	3	the	the	DET
ap-1263	114	4	total	total	ADJ
ap-1263	114	5	ordering	ordering	NOUN
ap-1263	114	6	≺	≺	NOUN
ap-1263	114	7	of	of	ADP
ap-1263	114	8	the	the	DET
ap-1263	114	9	generators	generator	NOUN
ap-1263	114	10	as	as	SCONJ
ap-1263	114	11	it	it	PRON
ap-1263	114	12	is	be	AUX
ap-1263	114	13	in	in	ADP
ap-1263	114	14	the	the	DET
ap-1263	114	15	alphabet	alphabet	NOUN
ap-1263	114	16	,	,	PUNCT
ap-1263	114	17	i.	i.	PROPN
ap-1263	114	18	e.	e.	PROPN
ap-1263	114	19	e	e	PROPN
ap-1263	114	20	≺	≺	NOUN
ap-1263	114	21	f	f	PROPN
ap-1263	114	22	≺	≺	NOUN
ap-1263	114	23	h	h	NOUN
ap-1263	114	24	.	.	PUNCT
ap-1263	115	1	partial	partial	ADJ
ap-1263	115	2	ordering	ordering	NOUN
ap-1263	115	3	among	among	ADP
ap-1263	115	4	monomials	monomial	NOUN
ap-1263	115	5	is	be	AUX
ap-1263	115	6	defined	define	VERB
ap-1263	115	7	in	in	ADP
ap-1263	115	8	such	such	ADJ
ap-1263	115	9	way	way	NOUN
ap-1263	115	10	thatx	thatx	NOUN
ap-1263	115	11	<	<	X
ap-1263	115	12	y	y	PROPN
ap-1263	115	13	,	,	PUNCT
ap-1263	115	14	when	when	SCONJ
ap-1263	115	15	the	the	DET
ap-1263	115	16	length	length	NOUN
ap-1263	115	17	of	of	ADP
ap-1263	115	18	x	x	SYM
ap-1263	115	19	(	(	PUNCT
ap-1263	115	20	the	the	DET
ap-1263	115	21	number	number	NOUN
ap-1263	115	22	of	of	ADP
ap-1263	115	23	letters	letter	NOUN
ap-1263	115	24	in	in	ADP
ap-1263	115	25	the	the	DET
ap-1263	115	26	product	product	NOUN
ap-1263	115	27	x	x	X
ap-1263	115	28	)	)	PUNCT
ap-1263	115	29	is	be	AUX
ap-1263	115	30	less	less	ADJ
ap-1263	115	31	than	than	ADP
ap-1263	115	32	the	the	DET
ap-1263	115	33	length	length	NOUN
ap-1263	115	34	of	of	ADP
ap-1263	115	35	y	y	PROPN
ap-1263	115	36	,	,	PUNCT
ap-1263	115	37	or	or	CCONJ
ap-1263	115	38	when	when	SCONJ
ap-1263	115	39	x	x	PRON
ap-1263	115	40	is	be	AUX
ap-1263	115	41	a	a	DET
ap-1263	115	42	permutation	permutation	NOUN
ap-1263	115	43	of	of	ADP
ap-1263	115	44	the	the	DET
ap-1263	115	45	letters	letter	NOUN
ap-1263	115	46	from	from	ADP
ap-1263	115	47	y	y	PROPN
ap-1263	115	48	,	,	PUNCT
ap-1263	115	49	but	but	CCONJ
ap-1263	115	50	has	have	VERB
ap-1263	115	51	a	a	DET
ap-1263	115	52	lower	low	ADJ
ap-1263	115	53	number	number	NOUN
ap-1263	115	54	of	of	ADP
ap-1263	115	55	inverses	inverse	NOUN
ap-1263	115	56	(	(	PUNCT
ap-1263	115	57	the	the	DET
ap-1263	115	58	monomial	monomial	NOUN
ap-1263	115	59	x	x	X
ap-1263	116	1	=	=	SYM
ap-1263	116	2	x1	x1	PROPN
ap-1263	116	3	.	.	PUNCT
ap-1263	116	4	.	.	PUNCT
ap-1263	116	5	.	.	PUNCT
ap-1263	117	1	xs	xs	PROPN
ap-1263	117	2	has	have	VERB
ap-1263	117	3	inverse	inverse	NOUN
ap-1263	117	4	(	(	PUNCT
ap-1263	117	5	i	i	PROPN
ap-1263	117	6	,	,	PUNCT
ap-1263	117	7	j	j	PROPN
ap-1263	117	8	)	)	PUNCT
ap-1263	117	9	,	,	PUNCT
ap-1263	117	10	1	1	NUM
ap-1263	117	11	≤	≤	X
ap-1263	117	12	i	i	PRON
ap-1263	117	13	,	,	PUNCT
ap-1263	117	14	j	j	PROPN
ap-1263	117	15	≤	≤	PROPN
ap-1263	117	16	s	s	PROPN
ap-1263	117	17	,	,	PUNCT
ap-1263	118	1	when	when	SCONJ
ap-1263	118	2	i	i	PRON
ap-1263	118	3	<	<	X
ap-1263	118	4	j	j	PROPN
ap-1263	118	5	and	and	CCONJ
ap-1263	118	6	xi	xi	PROPN
ap-1263	118	7	�	�	PROPN
ap-1263	118	8	xj	xj	PROPN
ap-1263	118	9	)	)	PUNCT
ap-1263	118	10	.	.	PUNCT
ap-1263	119	1	one	one	PRON
ap-1263	119	2	can	can	AUX
ap-1263	119	3	easily	easily	ADV
ap-1263	119	4	see	see	VERB
ap-1263	119	5	that	that	SCONJ
ap-1263	119	6	this	this	DET
ap-1263	119	7	partial	partial	ADJ
ap-1263	119	8	ordering	ordering	NOUN
ap-1263	119	9	is	be	AUX
ap-1263	119	10	compatible	compatible	ADJ
ap-1263	119	11	with	with	ADP
ap-1263	119	12	relations	relation	NOUN
ap-1263	119	13	(	(	PUNCT
ap-1263	119	14	8)	8)	NUM
ap-1263	119	15	,	,	PUNCT
ap-1263	119	16	which	which	PRON
ap-1263	119	17	we	we	PRON
ap-1263	119	18	present	present	VERB
ap-1263	119	19	in	in	ADP
ap-1263	119	20	a	a	DET
ap-1263	119	21	more	more	ADV
ap-1263	119	22	suitable	suitable	ADJ
ap-1263	119	23	form	form	NOUN
ap-1263	119	24	of	of	ADP
ap-1263	119	25	“	"	PUNCT
ap-1263	119	26	rewriting	rewrite	VERB
ap-1263	119	27	rules	rule	NOUN
ap-1263	119	28	”	"	PUNCT
ap-1263	119	29	:	:	PUNCT
ap-1263	119	30	fe	fe	X
ap-1263	119	31	→	→	SYM
ap-1263	119	32	ef	ef	PROPN
ap-1263	119	33	−	−	PROPN
ap-1263	119	34	h	h	NOUN
ap-1263	119	35	,	,	PUNCT
ap-1263	119	36	he	he	PRON
ap-1263	119	37	→	→	PUNCT
ap-1263	119	38	eh	eh	INTJ
ap-1263	119	39	+	+	NUM
ap-1263	119	40	2e	2e	NUM
ap-1263	119	41	,	,	PUNCT
ap-1263	119	42	(	(	PUNCT
ap-1263	119	43	9	9	NUM
ap-1263	119	44	)	)	PUNCT
ap-1263	119	45	hf	hf	NOUN
ap-1263	119	46	→	→	SYM
ap-1263	119	47	fh	fh	PROPN
ap-1263	119	48	−	−	PRON
ap-1263	119	49	2f	2f	NOUN
ap-1263	119	50	.	.	PUNCT
ap-1263	120	1	one	one	PRON
ap-1263	120	2	can	can	AUX
ap-1263	120	3	also	also	ADV
ap-1263	120	4	easily	easily	ADV
ap-1263	120	5	check	check	VERB
ap-1263	120	6	that	that	SCONJ
ap-1263	120	7	the	the	DET
ap-1263	120	8	ordering	ordering	NOUN
ap-1263	120	9	fulfils	fulfil	VERB
ap-1263	120	10	dcc	dcc	PROPN
ap-1263	120	11	.	.	PUNCT
ap-1263	121	1	simple	simple	ADJ
ap-1263	121	2	computation	computation	NOUN
ap-1263	121	3	gives	give	VERB
ap-1263	121	4	us	we	PRON
ap-1263	121	5	(	(	PUNCT
ap-1263	121	6	hf	hf	NOUN
ap-1263	121	7	)	)	PUNCT
ap-1263	121	8	e	e	X
ap-1263	121	9	=	=	SYM
ap-1263	121	10	(	(	PUNCT
ap-1263	121	11	fh	fh	INTJ
ap-1263	121	12	−	−	PROPN
ap-1263	121	13	2f	2f	NOUN
ap-1263	121	14	)	)	PUNCT
ap-1263	121	15	e	e	X
ap-1263	121	16	=	=	SYM
ap-1263	121	17	fhe	fhe	NOUN
ap-1263	121	18	−	−	NOUN
ap-1263	121	19	2fe	2fe	NOUN
ap-1263	121	20	=	=	PUNCT
ap-1263	121	21	f	f	X
ap-1263	121	22	(	(	PUNCT
ap-1263	121	23	eh	eh	INTJ
ap-1263	121	24	+	+	NUM
ap-1263	121	25	2e)−	2e)−	NUM
ap-1263	121	26	2fe	2fe	NOUN
ap-1263	121	27	=	=	PUNCT
ap-1263	121	28	feh	feh	X
ap-1263	121	29	=	=	SYM
ap-1263	121	30	(	(	PUNCT
ap-1263	121	31	ef	ef	PROPN
ap-1263	121	32	−	−	PROPN
ap-1263	121	33	h)h	h)h	X
ap-1263	121	34	=	=	PUNCT
ap-1263	121	35	efh	efh	NOUN
ap-1263	121	36	−	−	PROPN
ap-1263	121	37	h2	h2	NOUN
ap-1263	121	38	,	,	PUNCT
ap-1263	121	39	h(fe	h(fe	NOUN
ap-1263	121	40	)	)	PUNCT
ap-1263	121	41	=	=	SYM
ap-1263	122	1	h(ef	h(ef	PROPN
ap-1263	122	2	−	−	PROPN
ap-1263	122	3	h	h	NOUN
ap-1263	122	4	)	)	PUNCT
ap-1263	122	5	=	=	SYM
ap-1263	122	6	hef	hef	X
ap-1263	122	7	−	−	PROPN
ap-1263	122	8	h2	h2	NOUN
ap-1263	122	9	=	=	SYM
ap-1263	122	10	(	(	PUNCT
ap-1263	122	11	eh	eh	INTJ
ap-1263	122	12	+	+	NUM
ap-1263	122	13	2e)f	2e)f	NUM
ap-1263	122	14	−	−	NOUN
ap-1263	122	15	h2	h2	NOUN
ap-1263	122	16	=	=	SYM
ap-1263	122	17	ehf	ehf	PROPN
ap-1263	123	1	+	+	CCONJ
ap-1263	123	2	2ef	2ef	ADJ
ap-1263	123	3	−	−	NOUN
ap-1263	123	4	h2	h2	NOUN
ap-1263	123	5	=	=	SYM
ap-1263	123	6	e(fh	e(fh	NOUN
ap-1263	123	7	−	−	PROPN
ap-1263	123	8	2f	2f	NUM
ap-1263	123	9	)	)	PUNCT
ap-1263	124	1	+	+	CCONJ
ap-1263	124	2	2ef	2ef	ADJ
ap-1263	124	3	−	−	NOUN
ap-1263	124	4	h2	h2	NOUN
ap-1263	124	5	=	=	SYM
ap-1263	124	6	efh	efh	NOUN
ap-1263	124	7	−	−	PROPN
ap-1263	124	8	2ef	2ef	NOUN
ap-1263	125	1	+	+	CCONJ
ap-1263	125	2	2ef	2ef	ADJ
ap-1263	125	3	−	−	NOUN
ap-1263	125	4	h2	h2	NOUN
ap-1263	125	5	=	=	SYM
ap-1263	125	6	efh	efh	NOUN
ap-1263	125	7	−	−	PROPN
ap-1263	125	8	h2	h2	NOUN
ap-1263	125	9	.	.	PUNCT
ap-1263	126	1	42	42	NUM
ap-1263	126	2	acta	acta	PROPN
ap-1263	126	3	polytechnica	polytechnica	PROPN
ap-1263	126	4	vol	vol	NOUN
ap-1263	126	5	.	.	PROPN
ap-1263	127	1	50	50	NUM
ap-1263	127	2	no	no	NOUN
ap-1263	127	3	.	.	PUNCT
ap-1263	128	1	5/2010	5/2010	NUM
ap-1263	128	2	we	we	PRON
ap-1263	128	3	see	see	VERB
ap-1263	128	4	that	that	SCONJ
ap-1263	128	5	the	the	DET
ap-1263	128	6	ambiguity	ambiguity	NOUN
ap-1263	128	7	hfe	hfe	PROPN
ap-1263	128	8	is	be	AUX
ap-1263	128	9	reduced	reduce	VERB
ap-1263	128	10	to	to	ADP
ap-1263	128	11	a	a	DET
ap-1263	128	12	common	common	ADJ
ap-1263	128	13	value	value	NOUN
ap-1263	128	14	.	.	PUNCT
ap-1263	129	1	one	one	PRON
ap-1263	129	2	can	can	AUX
ap-1263	129	3	easily	easily	ADV
ap-1263	129	4	list	list	VERB
ap-1263	129	5	all	all	DET
ap-1263	129	6	irreducible	irreducible	ADJ
ap-1263	129	7	monomials	monomial	NOUN
ap-1263	129	8	.	.	PUNCT
ap-1263	130	1	these	these	PRON
ap-1263	130	2	are	be	AUX
ap-1263	130	3	precisely	precisely	ADV
ap-1263	130	4	eαf	eαf	ADJ
ap-1263	130	5	βhγ	βhγ	NOUN
ap-1263	130	6	,	,	PUNCT
ap-1263	130	7	α	α	PROPN
ap-1263	130	8	,	,	PUNCT
ap-1263	130	9	β	β	X
ap-1263	130	10	,	,	PUNCT
ap-1263	130	11	γ	γ	X
ap-1263	130	12	≥	≥	NUM
ap-1263	130	13	0	0	NUM
ap-1263	130	14	.	.	PUNCT
ap-1263	131	1	the	the	DET
ap-1263	131	2	diamond	diamond	NOUN
ap-1263	131	3	lemma	lemma	PROPN
ap-1263	131	4	states	state	VERB
ap-1263	131	5	that	that	SCONJ
ap-1263	131	6	these	these	DET
ap-1263	131	7	monomials	monomial	NOUN
ap-1263	131	8	form	form	VERB
ap-1263	131	9	the	the	DET
ap-1263	131	10	basis	basis	NOUN
ap-1263	131	11	of	of	ADP
ap-1263	131	12	the	the	DET
ap-1263	131	13	algebra	algebra	NOUN
ap-1263	131	14	u(sl2	u(sl2	PROPN
ap-1263	131	15	)	)	PUNCT
ap-1263	131	16	(	(	PUNCT
ap-1263	131	17	as	as	SCONJ
ap-1263	131	18	stated	state	VERB
ap-1263	131	19	by	by	ADP
ap-1263	131	20	the	the	DET
ap-1263	131	21	well	well	ADV
ap-1263	131	22	known	know	VERB
ap-1263	131	23	pbw	pbw	NOUN
ap-1263	131	24	theorem	theorem	NOUN
ap-1263	131	25	)	)	PUNCT
ap-1263	131	26	.	.	PUNCT
ap-1263	132	1	4	4	NUM
ap-1263	132	2	center	center	NOUN
ap-1263	132	3	of	of	ADP
ap-1263	132	4	u(sl2	u(sl2	PROPN
ap-1263	132	5	)	)	PUNCT
ap-1263	132	6	as	as	SCONJ
ap-1263	132	7	was	be	AUX
ap-1263	132	8	said	say	VERB
ap-1263	132	9	in	in	ADP
ap-1263	132	10	the	the	DET
ap-1263	132	11	introduction	introduction	NOUN
ap-1263	132	12	,	,	PUNCT
ap-1263	132	13	there	there	PRON
ap-1263	132	14	is	be	VERB
ap-1263	132	15	a	a	DET
ap-1263	132	16	standard	standard	ADJ
ap-1263	132	17	way	way	NOUN
ap-1263	132	18	to	to	PART
ap-1263	132	19	explore	explore	VERB
ap-1263	132	20	the	the	DET
ap-1263	132	21	structure	structure	NOUN
ap-1263	132	22	of	of	ADP
ap-1263	132	23	the	the	DET
ap-1263	132	24	center	center	NOUN
ap-1263	132	25	of	of	ADP
ap-1263	132	26	the	the	DET
ap-1263	132	27	algebra	algebra	NOUN
ap-1263	132	28	u(sl2	u(sl2	PROPN
ap-1263	132	29	)	)	PUNCT
ap-1263	132	30	.	.	PUNCT
ap-1263	133	1	let	let	VERB
ap-1263	133	2	us	we	PRON
ap-1263	133	3	find	find	VERB
ap-1263	133	4	this	this	DET
ap-1263	133	5	structure	structure	NOUN
ap-1263	133	6	now	now	ADV
ap-1263	133	7	using	use	VERB
ap-1263	133	8	the	the	DET
ap-1263	133	9	diammond	diammond	NOUN
ap-1263	133	10	lemma	lemma	PROPN
ap-1263	133	11	.	.	PUNCT
ap-1263	134	1	this	this	DET
ap-1263	134	2	procedure	procedure	NOUN
ap-1263	134	3	can	can	AUX
ap-1263	134	4	then	then	ADV
ap-1263	134	5	be	be	AUX
ap-1263	134	6	generalized	generalize	VERB
ap-1263	134	7	to	to	ADP
ap-1263	134	8	other	other	ADJ
ap-1263	134	9	algebras	algebra	NOUN
ap-1263	134	10	where	where	SCONJ
ap-1263	134	11	standard	standard	ADJ
ap-1263	134	12	tools	tool	NOUN
ap-1263	134	13	like	like	ADP
ap-1263	134	14	the	the	DET
ap-1263	134	15	harish	harish	PROPN
ap-1263	134	16	-	-	PUNCT
ap-1263	134	17	chandra	chandra	PROPN
ap-1263	134	18	homomorphism	homomorphism	NOUN
ap-1263	134	19	can	can	AUX
ap-1263	134	20	not	not	PART
ap-1263	134	21	be	be	AUX
ap-1263	134	22	used	use	VERB
ap-1263	134	23	.	.	PUNCT
ap-1263	135	1	the	the	DET
ap-1263	135	2	problem	problem	NOUN
ap-1263	135	3	is	be	AUX
ap-1263	135	4	to	to	PART
ap-1263	135	5	find	find	VERB
ap-1263	135	6	all	all	DET
ap-1263	135	7	elementsx	elementsx	NOUN
ap-1263	135	8	from	from	ADP
ap-1263	135	9	u(sl2	u(sl2	PROPN
ap-1263	135	10	)	)	PUNCT
ap-1263	135	11	,	,	PUNCT
ap-1263	135	12	for	for	ADP
ap-1263	135	13	which	which	PRON
ap-1263	135	14	we	we	PRON
ap-1263	135	15	have	have	VERB
ap-1263	135	16	[	[	X
ap-1263	135	17	x	x	X
ap-1263	135	18	,	,	PUNCT
ap-1263	135	19	a	a	PRON
ap-1263	135	20	]	]	X
ap-1263	135	21	≡	≡	PROPN
ap-1263	135	22	xa	xa	PROPN
ap-1263	136	1	−	−	PROPN
ap-1263	136	2	ax	ax	NOUN
ap-1263	136	3	=	=	NOUN
ap-1263	136	4	0	0	NUM
ap-1263	136	5	for	for	ADP
ap-1263	136	6	all	all	DET
ap-1263	136	7	a	a	DET
ap-1263	136	8	∈	∈	NOUN
ap-1263	136	9	u(sl2	u(sl2	NOUN
ap-1263	136	10	)	)	PUNCT
ap-1263	136	11	.	.	PUNCT
ap-1263	137	1	this	this	DET
ap-1263	137	2	condition	condition	NOUN
ap-1263	137	3	is	be	AUX
ap-1263	137	4	clearly	clearly	ADV
ap-1263	137	5	equivalent	equivalent	ADJ
ap-1263	137	6	to	to	ADP
ap-1263	137	7	[	[	X
ap-1263	137	8	x	x	X
ap-1263	137	9	,	,	PUNCT
ap-1263	137	10	e	e	X
ap-1263	137	11	]	]	PUNCT
ap-1263	137	12	=	=	PUNCT
ap-1263	138	1	[	[	X
ap-1263	138	2	x	x	X
ap-1263	138	3	,	,	PUNCT
ap-1263	138	4	f	f	X
ap-1263	138	5	]	]	PUNCT
ap-1263	139	1	=	=	PUNCT
ap-1263	140	1	[	[	X
ap-1263	140	2	x	x	X
ap-1263	140	3	,	,	PUNCT
ap-1263	140	4	h	h	NOUN
ap-1263	140	5	]	]	X
ap-1263	140	6	=	=	PUNCT
ap-1263	140	7	0	0	NUM
ap-1263	140	8	,	,	PUNCT
ap-1263	140	9	(	(	PUNCT
ap-1263	140	10	10	10	NUM
ap-1263	140	11	)	)	PUNCT
ap-1263	140	12	that	that	PRON
ap-1263	140	13	is	is	ADV
ap-1263	140	14	,	,	PUNCT
ap-1263	140	15	one	one	PRON
ap-1263	140	16	can	can	AUX
ap-1263	140	17	restrict	restrict	VERB
ap-1263	140	18	oneself	oneself	PRON
ap-1263	140	19	to	to	ADP
ap-1263	140	20	making	make	VERB
ap-1263	140	21	commutations	commutation	NOUN
ap-1263	140	22	with	with	ADP
ap-1263	140	23	generators	generator	NOUN
ap-1263	140	24	only	only	ADV
ap-1263	140	25	.	.	PUNCT
ap-1263	141	1	let	let	VERB
ap-1263	141	2	us	we	PRON
ap-1263	141	3	take	take	VERB
ap-1263	141	4	a	a	DET
ap-1263	141	5	general	general	ADJ
ap-1263	141	6	element	element	NOUN
ap-1263	141	7	of	of	ADP
ap-1263	141	8	the	the	DET
ap-1263	141	9	form	form	NOUN
ap-1263	141	10	x	x	PUNCT
ap-1263	142	1	=	=	SYM
ap-1263	142	2	n∑	n∑	PROPN
ap-1263	143	1	i	i	PROPN
ap-1263	143	2	,	,	PUNCT
ap-1263	143	3	j	j	PROPN
ap-1263	143	4	,	,	PUNCT
ap-1263	143	5	k=0	k=0	PROPN
ap-1263	143	6	αi	αi	PROPN
ap-1263	143	7	,	,	PUNCT
ap-1263	143	8	j	j	PROPN
ap-1263	143	9	,	,	PUNCT
ap-1263	143	10	keif	keif	VERB
ap-1263	143	11	jhk	jhk	NOUN
ap-1263	143	12	for	for	ADP
ap-1263	143	13	some	some	DET
ap-1263	143	14	small	small	ADJ
ap-1263	143	15	values	value	NOUN
ap-1263	143	16	of	of	ADP
ap-1263	143	17	n	n	CCONJ
ap-1263	143	18	,	,	PUNCT
ap-1263	143	19	let	let	VERB
ap-1263	143	20	us	we	PRON
ap-1263	143	21	generally	generally	ADV
ap-1263	143	22	compute	compute	VERB
ap-1263	143	23	commutators	commutator	NOUN
ap-1263	144	1	[	[	X
ap-1263	144	2	x	x	X
ap-1263	144	3	,	,	PUNCT
ap-1263	144	4	e	e	NOUN
ap-1263	144	5	]	]	X
ap-1263	144	6	,	,	PUNCT
ap-1263	145	1	[	[	X
ap-1263	145	2	x	x	X
ap-1263	145	3	,	,	PUNCT
ap-1263	145	4	f	f	X
ap-1263	145	5	]	]	X
ap-1263	145	6	a	a	DET
ap-1263	145	7	[	[	X
ap-1263	145	8	x	x	X
ap-1263	145	9	,	,	PUNCT
ap-1263	145	10	h	h	NOUN
ap-1263	145	11	]	]	PUNCT
ap-1263	145	12	and	and	CCONJ
ap-1263	145	13	solve	solve	VERB
ap-1263	145	14	a	a	DET
ap-1263	145	15	system	system	NOUN
ap-1263	145	16	of	of	ADP
ap-1263	145	17	linear	linear	ADJ
ap-1263	145	18	equations	equation	NOUN
ap-1263	145	19	(	(	PUNCT
ap-1263	145	20	10	10	NUM
ap-1263	145	21	)	)	PUNCT
ap-1263	145	22	for	for	ADP
ap-1263	145	23	coefficients	coefficient	NOUN
ap-1263	145	24	αi	αi	PROPN
ap-1263	145	25	,	,	PUNCT
ap-1263	145	26	j	j	PROPN
ap-1263	145	27	,	,	PUNCT
ap-1263	145	28	k.	k.	PROPN
ap-1263	145	29	for	for	ADP
ap-1263	145	30	n	n	NOUN
ap-1263	145	31	=	=	SYM
ap-1263	145	32	1	1	NUM
ap-1263	145	33	we	we	PRON
ap-1263	145	34	get	get	VERB
ap-1263	145	35	nothing	nothing	PRON
ap-1263	145	36	(	(	PUNCT
ap-1263	145	37	trivial	trivial	ADJ
ap-1263	145	38	zero	zero	NUM
ap-1263	145	39	solution	solution	NOUN
ap-1263	145	40	only	only	ADV
ap-1263	145	41	)	)	PUNCT
ap-1263	145	42	.	.	PUNCT
ap-1263	146	1	for	for	ADP
ap-1263	146	2	n	n	NOUN
ap-1263	146	3	=	=	SYM
ap-1263	146	4	2	2	NUM
ap-1263	146	5	we	we	PRON
ap-1263	146	6	get	get	VERB
ap-1263	146	7	any	any	DET
ap-1263	146	8	scalar	scalar	ADJ
ap-1263	146	9	multiple	multiple	NOUN
ap-1263	146	10	of	of	ADP
ap-1263	146	11	x	x	PUNCT
ap-1263	146	12	=	=	SYM
ap-1263	146	13	h2	h2	PROPN
ap-1263	146	14	+	+	CCONJ
ap-1263	146	15	4ef	4ef	ADJ
ap-1263	146	16	−	−	PROPN
ap-1263	146	17	2h	2h	NUM
ap-1263	146	18	≡	≡	PROPN
ap-1263	146	19	c.	c.	PROPN
ap-1263	146	20	for	for	ADP
ap-1263	146	21	higher	high	ADJ
ap-1263	146	22	n	n	NOUN
ap-1263	146	23	we	we	PRON
ap-1263	146	24	get	get	VERB
ap-1263	146	25	elements	element	NOUN
ap-1263	146	26	of	of	ADP
ap-1263	146	27	the	the	DET
ap-1263	146	28	form	form	NOUN
ap-1263	146	29	αc	αc	VERB
ap-1263	147	1	+	+	CCONJ
ap-1263	147	2	βc2	βc2	X
ap-1263	147	3	,	,	PUNCT
ap-1263	147	4	then	then	ADV
ap-1263	147	5	αc	αc	VERB
ap-1263	147	6	+	+	CCONJ
ap-1263	147	7	βc2	βc2	PROPN
ap-1263	147	8	+	+	NUM
ap-1263	147	9	γc3	γc3	PROPN
ap-1263	147	10	,	,	PUNCT
ap-1263	147	11	etc	etc	X
ap-1263	147	12	.	.	X
ap-1263	147	13	,	,	PUNCT
ap-1263	147	14	where	where	SCONJ
ap-1263	147	15	α	α	X
ap-1263	147	16	,	,	PUNCT
ap-1263	147	17	β	β	X
ap-1263	147	18	,	,	PUNCT
ap-1263	147	19	γ	γ	X
ap-1263	147	20	,	,	PUNCT
ap-1263	147	21	.	.	PUNCT
ap-1263	147	22	.	.	PUNCT
ap-1263	148	1	.	.	PUNCT
ap-1263	149	1	are	be	AUX
ap-1263	149	2	arbitrary	arbitrary	ADJ
ap-1263	149	3	complex	complex	ADJ
ap-1263	149	4	coefficients	coefficient	NOUN
ap-1263	149	5	.	.	PUNCT
ap-1263	150	1	of	of	ADV
ap-1263	150	2	course	course	ADV
ap-1263	150	3	this	this	PRON
ap-1263	150	4	leads	lead	VERB
ap-1263	150	5	to	to	ADP
ap-1263	150	6	the	the	DET
ap-1263	150	7	hypothesis	hypothesis	NOUN
ap-1263	150	8	that	that	PRON
ap-1263	150	9	any	any	DET
ap-1263	150	10	element	element	NOUN
ap-1263	150	11	x	x	PUNCT
ap-1263	150	12	which	which	PRON
ap-1263	150	13	commutes	commute	VERB
ap-1263	150	14	with	with	ADP
ap-1263	150	15	e	e	NOUN
ap-1263	150	16	,	,	PUNCT
ap-1263	150	17	f	f	PROPN
ap-1263	150	18	and	and	CCONJ
ap-1263	150	19	h	h	NOUN
ap-1263	150	20	is	be	AUX
ap-1263	150	21	of	of	ADP
ap-1263	150	22	the	the	DET
ap-1263	150	23	form	form	NOUN
ap-1263	150	24	p(c	p(c	PROPN
ap-1263	150	25	)	)	PUNCT
ap-1263	150	26	,	,	PUNCT
ap-1263	150	27	where	where	SCONJ
ap-1263	150	28	p	p	NOUN
ap-1263	150	29	is	be	AUX
ap-1263	150	30	an	an	DET
ap-1263	150	31	arbitrary	arbitrary	ADJ
ap-1263	150	32	complex	complex	ADJ
ap-1263	150	33	polynomial	polynomial	NOUN
ap-1263	150	34	.	.	PUNCT
ap-1263	151	1	the	the	DET
ap-1263	151	2	proof	proof	NOUN
ap-1263	151	3	is	be	AUX
ap-1263	151	4	based	base	VERB
ap-1263	151	5	on	on	ADP
ap-1263	151	6	the	the	DET
ap-1263	151	7	change	change	NOUN
ap-1263	151	8	of	of	ADP
ap-1263	151	9	the	the	DET
ap-1263	151	10	original	original	ADJ
ap-1263	151	11	basis	basis	NOUN
ap-1263	151	12	{	{	PUNCT
ap-1263	151	13	eαf	eαf	NOUN
ap-1263	151	14	βhγ	βhγ	PROPN
ap-1263	151	15	}	}	PUNCT
ap-1263	151	16	.	.	PUNCT
ap-1263	152	1	we	we	PRON
ap-1263	152	2	add	add	VERB
ap-1263	152	3	to	to	ADP
ap-1263	152	4	generators	generator	NOUN
ap-1263	152	5	e	e	PROPN
ap-1263	152	6	,	,	PUNCT
ap-1263	152	7	f	f	PROPN
ap-1263	152	8	and	and	CCONJ
ap-1263	152	9	h	h	DET
ap-1263	152	10	another	another	DET
ap-1263	152	11	letter	letter	NOUN
ap-1263	152	12	c	c	PROPN
ap-1263	152	13	and	and	CCONJ
ap-1263	152	14	to	to	ADP
ap-1263	152	15	the	the	DET
ap-1263	152	16	rewriting	rewrite	VERB
ap-1263	152	17	rules	rule	NOUN
ap-1263	152	18	(	(	PUNCT
ap-1263	152	19	9	9	X
ap-1263	152	20	)	)	PUNCT
ap-1263	152	21	we	we	PRON
ap-1263	152	22	add	add	VERB
ap-1263	152	23	the	the	DET
ap-1263	152	24	following	following	NOUN
ap-1263	152	25	:	:	PUNCT
ap-1263	152	26	ef	ef	PROPN
ap-1263	152	27	→	→	SYM
ap-1263	152	28	1	1	NUM
ap-1263	152	29	4	4	NUM
ap-1263	152	30	(	(	PUNCT
ap-1263	152	31	c	c	NOUN
ap-1263	152	32	+	+	SYM
ap-1263	152	33	2h	2h	NUM
ap-1263	152	34	−	−	PROPN
ap-1263	152	35	h2	h2	PROPN
ap-1263	152	36	)	)	PUNCT
ap-1263	152	37	,	,	PUNCT
ap-1263	152	38	ec	ec	PROPN
ap-1263	152	39	→	→	SYM
ap-1263	152	40	ce	ce	PROPN
ap-1263	152	41	,	,	PUNCT
ap-1263	152	42	fc	fc	PROPN
ap-1263	152	43	→	→	SYM
ap-1263	152	44	cf	cf	PROPN
ap-1263	152	45	,	,	PUNCT
ap-1263	152	46	hc	hc	PROPN
ap-1263	152	47	→	→	SYM
ap-1263	152	48	ch	ch	NOUN
ap-1263	152	49	.	.	PUNCT
ap-1263	153	1	the	the	DET
ap-1263	153	2	basis	basis	NOUN
ap-1263	153	3	now	now	ADV
ap-1263	153	4	consists	consist	VERB
ap-1263	153	5	of	of	ADP
ap-1263	153	6	irreducible	irreducible	ADJ
ap-1263	153	7	elements	element	NOUN
ap-1263	153	8	,	,	PUNCT
ap-1263	153	9	i.	i.	PROPN
ap-1263	153	10	e.	e.	PROPN
ap-1263	153	11	{	{	PUNCT
ap-1263	153	12	cjekhm|j	cjekhm|j	PROPN
ap-1263	153	13	,	,	PUNCT
ap-1263	153	14	k	k	PROPN
ap-1263	153	15	,	,	PUNCT
ap-1263	153	16	m	m	VERB
ap-1263	153	17	≥	≥	NOUN
ap-1263	153	18	0	0	NUM
ap-1263	153	19	}	}	PUNCT
ap-1263	153	20	∪	∪	X
ap-1263	153	21	{	{	PUNCT
ap-1263	153	22	cjf	cjf	PROPN
ap-1263	153	23	lhm|j	lhm|j	PROPN
ap-1263	153	24	,	,	PUNCT
ap-1263	153	25	l	l	PROPN
ap-1263	153	26	,	,	PUNCT
ap-1263	153	27	m	m	VERB
ap-1263	153	28	≥	≥	NOUN
ap-1263	153	29	0	0	NUM
ap-1263	153	30	}	}	PUNCT
ap-1263	153	31	.	.	PUNCT
ap-1263	154	1	we	we	PRON
ap-1263	154	2	now	now	ADV
ap-1263	154	3	take	take	VERB
ap-1263	154	4	the	the	DET
ap-1263	154	5	general	general	ADJ
ap-1263	154	6	element	element	NOUN
ap-1263	154	7	as	as	ADP
ap-1263	154	8	a	a	DET
ap-1263	154	9	linear	linear	ADJ
ap-1263	154	10	combination	combination	NOUN
ap-1263	154	11	x	x	X
ap-1263	155	1	=	=	PUNCT
ap-1263	155	2	n∑	n∑	PROPN
ap-1263	155	3	j	j	PROPN
ap-1263	155	4	,	,	PUNCT
ap-1263	155	5	k	k	PROPN
ap-1263	155	6	,	,	PUNCT
ap-1263	155	7	m=0	m=0	PROPN
ap-1263	155	8	βj	βj	PROPN
ap-1263	155	9	,	,	PUNCT
ap-1263	155	10	k	k	NOUN
ap-1263	155	11	,	,	PUNCT
ap-1263	155	12	mcjekhm	mcjekhm	PROPN
ap-1263	155	13	+	+	CCONJ
ap-1263	155	14	n∑	n∑	PROPN
ap-1263	155	15	j	j	PROPN
ap-1263	155	16	,	,	PUNCT
ap-1263	155	17	l	l	PROPN
ap-1263	155	18	,	,	PUNCT
ap-1263	155	19	m=0	m=0	PROPN
ap-1263	155	20	γj	γj	PROPN
ap-1263	155	21	,	,	PUNCT
ap-1263	155	22	l	l	NOUN
ap-1263	155	23	,	,	PUNCT
ap-1263	155	24	mcjf	mcjf	ADJ
ap-1263	155	25	lhm	lhm	NOUN
ap-1263	155	26	.	.	PUNCT
ap-1263	156	1	when	when	SCONJ
ap-1263	156	2	computing	compute	VERB
ap-1263	156	3	commutators	commutator	NOUN
ap-1263	157	1	[	[	X
ap-1263	157	2	x	x	X
ap-1263	157	3	,	,	PUNCT
ap-1263	157	4	e	e	NOUN
ap-1263	157	5	]	]	X
ap-1263	157	6	,	,	PUNCT
ap-1263	157	7	[	[	X
ap-1263	157	8	x	x	X
ap-1263	157	9	,	,	PUNCT
ap-1263	157	10	f	f	X
ap-1263	157	11	]	]	PUNCT
ap-1263	157	12	and	and	CCONJ
ap-1263	157	13	[	[	X
ap-1263	157	14	x	x	X
ap-1263	157	15	,	,	PUNCT
ap-1263	157	16	h	h	NOUN
ap-1263	157	17	]	]	X
ap-1263	157	18	one	one	PRON
ap-1263	157	19	can	can	AUX
ap-1263	157	20	make	make	VERB
ap-1263	157	21	use	use	NOUN
ap-1263	157	22	of	of	ADP
ap-1263	157	23	the	the	DET
ap-1263	157	24	fact	fact	NOUN
ap-1263	157	25	that	that	SCONJ
ap-1263	157	26	,	,	PUNCT
ap-1263	157	27	for	for	ADP
ap-1263	157	28	example	example	NOUN
ap-1263	157	29	[	[	X
ap-1263	157	30	cjekhm	cjekhm	NOUN
ap-1263	157	31	,	,	PUNCT
ap-1263	157	32	e	e	X
ap-1263	157	33	]	]	X
ap-1263	157	34	=	=	PUNCT
ap-1263	157	35	cj	cj	NOUN
ap-1263	158	1	[	[	X
ap-1263	158	2	ekhm	ekhm	ADJ
ap-1263	158	3	,	,	PUNCT
ap-1263	158	4	e	e	X
ap-1263	158	5	]	]	X
ap-1263	158	6	=	=	SYM
ap-1263	158	7	cjek[hm	cjek[hm	NOUN
ap-1263	158	8	,	,	PUNCT
ap-1263	158	9	e	e	X
ap-1263	158	10	]	]	X
ap-1263	158	11	etc	etc	X
ap-1263	158	12	.	.	X
ap-1263	159	1	it	it	PRON
ap-1263	159	2	is	be	AUX
ap-1263	159	3	also	also	ADV
ap-1263	159	4	clear	clear	ADJ
ap-1263	159	5	(	(	PUNCT
ap-1263	159	6	as	as	SCONJ
ap-1263	159	7	opposed	oppose	VERB
ap-1263	159	8	to	to	ADP
ap-1263	159	9	the	the	DET
ap-1263	159	10	original	original	ADJ
ap-1263	159	11	case	case	NOUN
ap-1263	159	12	)	)	PUNCT
ap-1263	159	13	what	what	PRON
ap-1263	159	14	it	it	PRON
ap-1263	159	15	is	be	AUX
ap-1263	159	16	sufficient	sufficient	ADJ
ap-1263	159	17	to	to	PART
ap-1263	159	18	show	show	VERB
ap-1263	159	19	:	:	PUNCT
ap-1263	159	20	one	one	PRON
ap-1263	159	21	must	must	AUX
ap-1263	159	22	show	show	VERB
ap-1263	159	23	that	that	SCONJ
ap-1263	159	24	coefficients	coefficient	NOUN
ap-1263	159	25	βj	βj	PRON
ap-1263	159	26	,	,	PUNCT
ap-1263	159	27	k	k	X
ap-1263	159	28	,	,	PUNCT
ap-1263	159	29	m	m	VERB
ap-1263	159	30	=	=	NOUN
ap-1263	159	31	0	0	NUM
ap-1263	159	32	for	for	ADP
ap-1263	159	33	(	(	PUNCT
ap-1263	159	34	k	k	X
ap-1263	159	35	,	,	PUNCT
ap-1263	159	36	m	m	NOUN
ap-1263	159	37	)	)	PUNCT
ap-1263	159	38	=	=	SYM
ap-1263	159	39	(	(	PUNCT
ap-1263	159	40	0	0	NUM
ap-1263	159	41	,	,	PUNCT
ap-1263	159	42	0	0	NUM
ap-1263	159	43	)	)	PUNCT
ap-1263	159	44	,	,	PUNCT
ap-1263	159	45	similarly	similarly	ADV
ap-1263	159	46	for	for	ADP
ap-1263	159	47	γ	γ	NOUN
ap-1263	159	48	’s	’s	NOUN
ap-1263	159	49	.	.	PUNCT
ap-1263	160	1	this	this	PRON
ap-1263	160	2	can	can	AUX
ap-1263	160	3	be	be	AUX
ap-1263	160	4	seen	see	VERB
ap-1263	160	5	from	from	ADP
ap-1263	160	6	(	(	PUNCT
ap-1263	160	7	10	10	NUM
ap-1263	160	8	)	)	PUNCT
ap-1263	160	9	.	.	PUNCT
ap-1263	161	1	5	5	NUM
ap-1263	161	2	center	center	NOUN
ap-1263	161	3	of	of	ADP
ap-1263	161	4	u	u	NOUN
ap-1263	161	5	′	′	NUM
ap-1263	161	6	q(so3	q(so3	ADV
ap-1263	161	7	)	)	PUNCT
ap-1263	161	8	let	let	VERB
ap-1263	161	9	us	we	PRON
ap-1263	161	10	apply	apply	VERB
ap-1263	161	11	the	the	DET
ap-1263	161	12	process	process	NOUN
ap-1263	161	13	introduced	introduce	VERB
ap-1263	161	14	above	above	ADV
ap-1263	161	15	to	to	ADP
ap-1263	161	16	the	the	DET
ap-1263	161	17	case	case	NOUN
ap-1263	161	18	of	of	ADP
ap-1263	161	19	the	the	DET
ap-1263	161	20	nonstandard	nonstandard	ADJ
ap-1263	161	21	deformation	deformation	NOUN
ap-1263	161	22	u	u	NOUN
ap-1263	161	23	′	′	NOUN
ap-1263	161	24	q(so3	q(so3	ADV
ap-1263	161	25	)	)	PUNCT
ap-1263	161	26	.	.	PUNCT
ap-1263	162	1	first	first	ADV
ap-1263	162	2	,	,	PUNCT
ap-1263	162	3	let	let	VERB
ap-1263	162	4	us	we	PRON
ap-1263	162	5	assume	assume	VERB
ap-1263	162	6	qn	qn	NOUN
ap-1263	162	7	=	=	NOUN
ap-1263	162	8	1	1	NUM
ap-1263	162	9	for	for	ADP
ap-1263	162	10	all	all	DET
ap-1263	162	11	n.	n.	NOUN
ap-1263	162	12	using	use	VERB
ap-1263	162	13	the	the	DET
ap-1263	162	14	first	first	ADJ
ap-1263	162	15	relation	relation	NOUN
ap-1263	162	16	(	(	PUNCT
ap-1263	162	17	2	2	NUM
ap-1263	162	18	)	)	PUNCT
ap-1263	162	19	as	as	ADP
ap-1263	162	20	a	a	DET
ap-1263	162	21	definition	definition	NOUN
ap-1263	162	22	for	for	ADP
ap-1263	162	23	i3	i3	NOUN
ap-1263	162	24	and	and	CCONJ
ap-1263	162	25	substituting	substitute	VERB
ap-1263	162	26	into	into	ADP
ap-1263	162	27	the	the	DET
ap-1263	162	28	second	second	ADJ
ap-1263	162	29	and	and	CCONJ
ap-1263	162	30	third	third	ADJ
ap-1263	162	31	relations	relation	NOUN
ap-1263	162	32	we	we	PRON
ap-1263	162	33	get	get	VERB
ap-1263	162	34	two	two	NUM
ap-1263	162	35	cubic	cubic	ADJ
ap-1263	162	36	relations	relation	NOUN
ap-1263	162	37	i2i	i2i	NOUN
ap-1263	162	38	2	2	NUM
ap-1263	162	39	1	1	NUM
ap-1263	162	40	−	−	NOUN
ap-1263	162	41	(	(	PUNCT
ap-1263	162	42	q	q	X
ap-1263	162	43	+	+	CCONJ
ap-1263	162	44	q−1)i1i2i1	q−1)i1i2i1	ADJ
ap-1263	162	45	+	+	NUM
ap-1263	162	46	i21i2	i21i2	X
ap-1263	162	47	=	=	SYM
ap-1263	162	48	−i2	−i2	PROPN
ap-1263	162	49	,	,	PUNCT
ap-1263	162	50	i22	i22	NOUN
ap-1263	162	51	i1	i1	PROPN
ap-1263	163	1	−	−	PROPN
ap-1263	164	1	(	(	PUNCT
ap-1263	164	2	q	q	PROPN
ap-1263	164	3	+	+	NUM
ap-1263	164	4	q−1)i2i1i2	q−1)i2i1i2	NOUN
ap-1263	164	5	+	+	CCONJ
ap-1263	164	6	i1i	i1i	ADP
ap-1263	164	7	2	2	NUM
ap-1263	164	8	2	2	NUM
ap-1263	164	9	=	=	SYM
ap-1263	164	10	−i1	−i1	PROPN
ap-1263	164	11	.	.	PUNCT
ap-1263	165	1	it	it	PRON
ap-1263	165	2	can	can	AUX
ap-1263	165	3	be	be	AUX
ap-1263	165	4	shown	show	VERB
ap-1263	165	5	that	that	SCONJ
ap-1263	165	6	u	u	NOUN
ap-1263	165	7	′	′	NOUN
ap-1263	165	8	q(so3	q(so3	ADV
ap-1263	165	9	)	)	PUNCT
ap-1263	165	10	is	be	AUX
ap-1263	165	11	isomorphic	isomorphic	ADJ
ap-1263	165	12	to	to	ADP
ap-1263	165	13	the	the	DET
ap-1263	165	14	algebra	algebra	NOUN
ap-1263	165	15	with	with	ADP
ap-1263	165	16	the	the	DET
ap-1263	165	17	generators	generator	NOUN
ap-1263	165	18	i1	i1	PROPN
ap-1263	165	19	,	,	PUNCT
ap-1263	165	20	i2	i2	PROPN
ap-1263	165	21	satisfying	satisfy	VERB
ap-1263	165	22	the	the	DET
ap-1263	165	23	two	two	NUM
ap-1263	165	24	above	above	ADP
ap-1263	165	25	relations	relation	NOUN
ap-1263	165	26	.	.	PUNCT
ap-1263	166	1	the	the	DET
ap-1263	166	2	casimir	casimir	PROPN
ap-1263	166	3	element	element	NOUN
ap-1263	166	4	(	(	PUNCT
ap-1263	166	5	3	3	X
ap-1263	166	6	)	)	PUNCT
ap-1263	166	7	can	can	AUX
ap-1263	166	8	be	be	AUX
ap-1263	166	9	rewritten	rewrite	VERB
ap-1263	166	10	to	to	ADP
ap-1263	166	11	the	the	DET
ap-1263	166	12	form	form	NOUN
ap-1263	166	13	(	(	PUNCT
ap-1263	166	14	we	we	PRON
ap-1263	166	15	ommit	ommit	VERB
ap-1263	166	16	scalar	scalar	ADJ
ap-1263	166	17	factor	factor	NOUN
ap-1263	166	18	q	q	NOUN
ap-1263	166	19	)	)	PUNCT
ap-1263	166	20	c	c	NOUN
ap-1263	166	21	=	=	SYM
ap-1263	166	22	(	(	PUNCT
ap-1263	166	23	q+q−1)(i21+i21i	q+q−1)(i21+i21i	ADP
ap-1263	166	24	2	2	NUM
ap-1263	166	25	2+i22	2+i22	NUM
ap-1263	166	26	)	)	PUNCT
ap-1263	167	1	+	+	NOUN
ap-1263	167	2	i2i1i2i1−[3]qi1i2i1i2	i2i1i2i1−[3]qi1i2i1i2	X
ap-1263	167	3	.	.	PUNCT
ap-1263	168	1	we	we	PRON
ap-1263	168	2	now	now	ADV
ap-1263	168	3	construct	construct	VERB
ap-1263	168	4	a	a	DET
ap-1263	168	5	different	different	ADJ
ap-1263	168	6	basis	basis	NOUN
ap-1263	168	7	of	of	ADP
ap-1263	168	8	the	the	DET
ap-1263	168	9	algebra	algebra	NOUN
ap-1263	168	10	u	u	NOUN
ap-1263	168	11	′	′	NUM
ap-1263	168	12	q(so3	q(so3	ADV
ap-1263	168	13	)	)	PUNCT
ap-1263	168	14	.	.	PUNCT
ap-1263	169	1	we	we	PRON
ap-1263	169	2	deal	deal	VERB
ap-1263	169	3	with	with	ADP
ap-1263	169	4	the	the	DET
ap-1263	169	5	following	follow	VERB
ap-1263	169	6	rewriting	rewrite	VERB
ap-1263	169	7	rules	rule	NOUN
ap-1263	169	8	:	:	PUNCT
ap-1263	169	9	i2i	i2i	NOUN
ap-1263	169	10	2	2	NUM
ap-1263	169	11	1	1	NUM
ap-1263	169	12	→	→	SYM
ap-1263	169	13	(	(	PUNCT
ap-1263	169	14	q	q	X
ap-1263	169	15	+	+	CCONJ
ap-1263	169	16	q−1)i1i2i1	q−1)i1i2i1	ADV
ap-1263	169	17	−	−	PROPN
ap-1263	169	18	i21i2	i21i2	NOUN
ap-1263	169	19	−	−	PROPN
ap-1263	169	20	i2	i2	PROPN
ap-1263	169	21	,	,	PUNCT
ap-1263	169	22	i22i1	i22i1	ADJ
ap-1263	169	23	→	→	SYM
ap-1263	169	24	(	(	PUNCT
ap-1263	169	25	q	q	PROPN
ap-1263	169	26	+	+	NUM
ap-1263	169	27	q−1)i2i1i2	q−1)i2i1i2	NOUN
ap-1263	169	28	−	−	NOUN
ap-1263	169	29	i1i	i1i	ADP
ap-1263	169	30	2	2	NUM
ap-1263	169	31	2	2	NUM
ap-1263	169	32	−	−	PROPN
ap-1263	169	33	i1	i1	NOUN
ap-1263	169	34	,	,	PUNCT
ap-1263	169	35	i2i1i2i1	i2i1i2i1	PROPN
ap-1263	169	36	→	→	SYM
ap-1263	169	37	c	c	NOUN
ap-1263	169	38	+	+	X
ap-1263	170	1	[	[	X
ap-1263	170	2	3]qi1i2i1i2	3]qi1i2i1i2	NUM
ap-1263	170	3	−	−	PROPN
ap-1263	170	4	(	(	PUNCT
ap-1263	170	5	q	q	NOUN
ap-1263	170	6	+	+	X
ap-1263	170	7	q−1)(i21	q−1)(i21	VERB
ap-1263	170	8	+	+	CCONJ
ap-1263	170	9	i21i	i21i	PRON
ap-1263	170	10	2	2	NUM
ap-1263	170	11	2	2	NUM
ap-1263	170	12	+	+	NUM
ap-1263	170	13	i22	i22	NOUN
ap-1263	170	14	)	)	PUNCT
ap-1263	170	15	,	,	PUNCT
ap-1263	170	16	i2c	i2c	NOUN
ap-1263	170	17	→	→	SYM
ap-1263	170	18	ci2	ci2	ADJ
ap-1263	170	19	,	,	PUNCT
ap-1263	170	20	i1c	i1c	NOUN
ap-1263	170	21	→	→	SYM
ap-1263	170	22	ci1	ci1	PROPN
ap-1263	170	23	.	.	PROPN
ap-1263	170	24	43	43	NUM
ap-1263	170	25	acta	acta	PROPN
ap-1263	170	26	polytechnica	polytechnica	PROPN
ap-1263	170	27	vol	vol	NOUN
ap-1263	170	28	.	.	PROPN
ap-1263	171	1	50	50	NUM
ap-1263	171	2	no	no	NOUN
ap-1263	171	3	.	.	PUNCT
ap-1263	172	1	5/2010	5/2010	NUM
ap-1263	172	2	it	it	PRON
ap-1263	172	3	can	can	AUX
ap-1263	172	4	easily	easily	ADV
ap-1263	172	5	be	be	AUX
ap-1263	172	6	seen	see	VERB
ap-1263	172	7	that	that	SCONJ
ap-1263	172	8	precisely	precisely	ADV
ap-1263	172	9	the	the	DET
ap-1263	172	10	elements	element	NOUN
ap-1263	172	11	cγiα	cγiα	VERB
ap-1263	172	12	1	1	NUM
ap-1263	172	13	(	(	PUNCT
ap-1263	172	14	i2i1	i2i1	NOUN
ap-1263	172	15	)	)	PUNCT
ap-1263	172	16	kiβ	kiβ	NOUN
ap-1263	172	17	2	2	NUM
ap-1263	172	18	,	,	PUNCT
ap-1263	172	19	γ	γ	PROPN
ap-1263	172	20	,	,	PUNCT
ap-1263	172	21	α	α	PROPN
ap-1263	172	22	,	,	PUNCT
ap-1263	172	23	β	β	X
ap-1263	172	24	≥	≥	NOUN
ap-1263	172	25	0	0	NUM
ap-1263	172	26	,	,	PUNCT
ap-1263	172	27	k	k	PROPN
ap-1263	172	28	∈	∈	PROPN
ap-1263	172	29	{	{	PUNCT
ap-1263	172	30	0	0	NUM
ap-1263	172	31	,	,	PUNCT
ap-1263	172	32	1	1	NUM
ap-1263	172	33	}	}	PUNCT
ap-1263	172	34	are	be	AUX
ap-1263	172	35	irreducible	irreducible	ADJ
ap-1263	172	36	,	,	PUNCT
ap-1263	172	37	thus	thus	ADV
ap-1263	172	38	forming	form	VERB
ap-1263	172	39	a	a	DET
ap-1263	172	40	new	new	ADJ
ap-1263	172	41	linear	linear	ADJ
ap-1263	172	42	basis	basis	NOUN
ap-1263	172	43	of	of	ADP
ap-1263	172	44	the	the	DET
ap-1263	172	45	algebra	algebra	NOUN
ap-1263	172	46	.	.	PUNCT
ap-1263	173	1	now	now	ADV
ap-1263	173	2	it	it	PRON
ap-1263	173	3	is	be	AUX
ap-1263	173	4	sufficient	sufficient	ADJ
ap-1263	173	5	to	to	PART
ap-1263	173	6	take	take	VERB
ap-1263	173	7	arbitrary	arbitrary	ADJ
ap-1263	173	8	element	element	NOUN
ap-1263	173	9	x	x	PUNCT
ap-1263	173	10	of	of	ADP
ap-1263	173	11	the	the	DET
ap-1263	173	12	form	form	NOUN
ap-1263	173	13	x	x	PUNCT
ap-1263	173	14	=	=	SYM
ap-1263	173	15	∑	∑	PUNCT
ap-1263	173	16	α	α	X
ap-1263	173	17	,	,	PUNCT
ap-1263	173	18	β	β	X
ap-1263	173	19	,	,	PUNCT
ap-1263	173	20	k	k	PROPN
ap-1263	173	21	pα	pα	PROPN
ap-1263	173	22	,	,	PUNCT
ap-1263	173	23	β	β	X
ap-1263	173	24	,	,	PUNCT
ap-1263	173	25	k(c)iα	k(c)iα	X
ap-1263	173	26	1	1	NUM
ap-1263	173	27	(	(	PUNCT
ap-1263	173	28	i2i1	i2i1	NOUN
ap-1263	173	29	)	)	PUNCT
ap-1263	173	30	kiβ	kiβ	NOUN
ap-1263	173	31	2	2	NUM
ap-1263	173	32	where	where	SCONJ
ap-1263	173	33	pα	pα	VERB
ap-1263	173	34	,	,	PUNCT
ap-1263	173	35	β	β	X
ap-1263	173	36	,	,	PUNCT
ap-1263	173	37	k	k	PROPN
ap-1263	173	38	are	be	AUX
ap-1263	173	39	arbitrary	arbitrary	ADJ
ap-1263	173	40	complex	complex	ADJ
ap-1263	173	41	polynomials	polynomial	NOUN
ap-1263	173	42	of	of	ADP
ap-1263	173	43	one	one	NUM
ap-1263	173	44	variable	variable	NOUN
ap-1263	173	45	,	,	PUNCT
ap-1263	173	46	commute	commute	NOUN
ap-1263	173	47	x	x	PUNCT
ap-1263	173	48	with	with	ADP
ap-1263	173	49	i1	i1	PROPN
ap-1263	173	50	,	,	PUNCT
ap-1263	173	51	i2	i2	PROPN
ap-1263	173	52	and	and	CCONJ
ap-1263	173	53	by	by	ADP
ap-1263	173	54	virtue	virtue	NOUN
ap-1263	173	55	of	of	ADP
ap-1263	173	56	its	its	PRON
ap-1263	173	57	equality	equality	NOUN
ap-1263	173	58	to	to	ADP
ap-1263	173	59	zero	zero	NUM
ap-1263	173	60	to	to	PART
ap-1263	173	61	show	show	VERB
ap-1263	173	62	that	that	SCONJ
ap-1263	173	63	all	all	DET
ap-1263	173	64	polynomials	polynomial	NOUN
ap-1263	173	65	pα	pα	VERB
ap-1263	173	66	,	,	PUNCT
ap-1263	173	67	β	β	X
ap-1263	173	68	,	,	PUNCT
ap-1263	173	69	k	k	PROPN
ap-1263	173	70	=	=	PUNCT
ap-1263	173	71	0	0	NUM
ap-1263	173	72	with	with	ADP
ap-1263	173	73	the	the	DET
ap-1263	173	74	only	only	ADJ
ap-1263	173	75	exception	exception	NOUN
ap-1263	173	76	p0,0,0	p0,0,0	NOUN
ap-1263	173	77	.	.	PUNCT
ap-1263	174	1	when	when	SCONJ
ap-1263	174	2	q	q	NOUN
ap-1263	174	3	is	be	AUX
ap-1263	174	4	a	a	DET
ap-1263	174	5	primitive	primitive	ADJ
ap-1263	174	6	root	root	NOUN
ap-1263	174	7	of	of	ADP
ap-1263	174	8	unity	unity	NOUN
ap-1263	174	9	,	,	PUNCT
ap-1263	174	10	qn	qn	NOUN
ap-1263	174	11	=	=	NOUN
ap-1263	174	12	1	1	NUM
ap-1263	174	13	,	,	PUNCT
ap-1263	174	14	the	the	DET
ap-1263	174	15	center	center	NOUN
ap-1263	174	16	of	of	ADP
ap-1263	174	17	the	the	DET
ap-1263	174	18	algebra	algebra	NOUN
ap-1263	174	19	does	do	AUX
ap-1263	174	20	not	not	PART
ap-1263	174	21	only	only	ADV
ap-1263	174	22	consist	consist	VERB
ap-1263	174	23	of	of	ADP
ap-1263	174	24	the	the	DET
ap-1263	174	25	ordinary	ordinary	ADJ
ap-1263	174	26	casimir	casimir	NOUN
ap-1263	174	27	element	element	NOUN
ap-1263	174	28	(	(	PUNCT
ap-1263	174	29	3	3	NUM
ap-1263	174	30	)	)	PUNCT
ap-1263	174	31	but	but	CCONJ
ap-1263	174	32	there	there	PRON
ap-1263	174	33	are	be	VERB
ap-1263	174	34	three	three	NUM
ap-1263	174	35	more	more	ADJ
ap-1263	174	36	elements	element	NOUN
ap-1263	174	37	having	have	VERB
ap-1263	174	38	the	the	DET
ap-1263	174	39	form	form	NOUN
ap-1263	174	40	cn1	cn1	NOUN
ap-1263	175	1	=	=	PUNCT
ap-1263	176	1	[	[	X
ap-1263	176	2	n−1	n−1	PROPN
ap-1263	176	3	2	2	NUM
ap-1263	176	4	]	]	PUNCT
ap-1263	176	5	∑	∑	PUNCT
ap-1263	176	6	j=0	j=0	PROPN
ap-1263	176	7	(	(	PUNCT
ap-1263	176	8	n	n	CCONJ
ap-1263	176	9	−	−	PROPN
ap-1263	176	10	j	j	PROPN
ap-1263	176	11	j	j	PROPN
ap-1263	176	12	)	)	PUNCT
ap-1263	176	13	n	n	CCONJ
ap-1263	176	14	n	n	CCONJ
ap-1263	176	15	−	−	PROPN
ap-1263	176	16	j	j	PROPN
ap-1263	176	17	(	(	PUNCT
ap-1263	176	18	i	i	PRON
ap-1263	176	19	q	q	PROPN
ap-1263	176	20	−	−	PROPN
ap-1263	176	21	q−1	q−1	PROPN
ap-1263	176	22	)	)	PUNCT
ap-1263	176	23	2j	2j	PROPN
ap-1263	176	24	in−2j	in−2j	NUM
ap-1263	176	25	1	1	NUM
ap-1263	176	26	(	(	PUNCT
ap-1263	176	27	and	and	CCONJ
ap-1263	176	28	the	the	DET
ap-1263	176	29	same	same	ADJ
ap-1263	176	30	polynomial	polynomial	NOUN
ap-1263	176	31	in	in	ADP
ap-1263	176	32	i2	i2	PROPN
ap-1263	176	33	and	and	CCONJ
ap-1263	176	34	i3	i3	NOUN
ap-1263	176	35	denoted	denote	VERB
ap-1263	176	36	by	by	ADP
ap-1263	176	37	cn2	cn2	PROPN
ap-1263	176	38	,	,	PUNCT
ap-1263	176	39	cn3	cn3	PROPN
ap-1263	176	40	)	)	PUNCT
ap-1263	176	41	.	.	PUNCT
ap-1263	177	1	it	it	PRON
ap-1263	177	2	is	be	AUX
ap-1263	177	3	not	not	PART
ap-1263	177	4	an	an	DET
ap-1263	177	5	easy	easy	ADJ
ap-1263	177	6	task	task	NOUN
ap-1263	177	7	to	to	PART
ap-1263	177	8	show	show	VERB
ap-1263	177	9	that	that	SCONJ
ap-1263	177	10	these	these	DET
ap-1263	177	11	elements	element	NOUN
ap-1263	177	12	really	really	ADV
ap-1263	177	13	belong	belong	VERB
ap-1263	177	14	to	to	ADP
ap-1263	177	15	the	the	DET
ap-1263	177	16	center	center	NOUN
ap-1263	177	17	of	of	ADP
ap-1263	177	18	the	the	DET
ap-1263	177	19	algebra	algebra	NOUN
ap-1263	177	20	(	(	PUNCT
ap-1263	177	21	see	see	VERB
ap-1263	177	22	[	[	X
ap-1263	177	23	4	4	NUM
ap-1263	177	24	]	]	NUM
ap-1263	177	25	)	)	PUNCT
ap-1263	177	26	.	.	PUNCT
ap-1263	178	1	after	after	SCONJ
ap-1263	178	2	some	some	DET
ap-1263	178	3	transformation	transformation	NOUN
ap-1263	178	4	one	one	PRON
ap-1263	178	5	can	can	AUX
ap-1263	178	6	see	see	VERB
ap-1263	178	7	that	that	DET
ap-1263	178	8	cnj	cnj	PROPN
ap-1263	178	9	,	,	PUNCT
ap-1263	178	10	j	j	PROPN
ap-1263	178	11	=	=	SYM
ap-1263	178	12	1	1	NUM
ap-1263	178	13	,	,	PUNCT
ap-1263	178	14	2	2	NUM
ap-1263	178	15	,	,	PUNCT
ap-1263	178	16	3	3	NUM
ap-1263	178	17	are	be	AUX
ap-1263	178	18	actually	actually	ADV
ap-1263	178	19	chebyshev	chebyshev	NOUN
ap-1263	178	20	polynomials	polynomial	NOUN
ap-1263	178	21	.	.	PUNCT
ap-1263	179	1	it	it	PRON
ap-1263	179	2	turns	turn	VERB
ap-1263	179	3	out	out	ADP
ap-1263	179	4	that	that	SCONJ
ap-1263	179	5	these	these	DET
ap-1263	179	6	four	four	NUM
ap-1263	179	7	casimir	casimir	NOUN
ap-1263	179	8	elements	element	NOUN
ap-1263	179	9	are	be	AUX
ap-1263	179	10	no	no	ADV
ap-1263	179	11	longer	long	ADV
ap-1263	179	12	polynomial	polynomial	ADJ
ap-1263	179	13	independent	independent	NOUN
ap-1263	179	14	.	.	PUNCT
ap-1263	180	1	when	when	SCONJ
ap-1263	180	2	one	one	PRON
ap-1263	180	3	wants	want	VERB
ap-1263	180	4	to	to	PART
ap-1263	180	5	prove	prove	VERB
ap-1263	180	6	this	this	DET
ap-1263	180	7	fact	fact	NOUN
ap-1263	180	8	it	it	PRON
ap-1263	180	9	may	may	AUX
ap-1263	180	10	come	come	VERB
ap-1263	180	11	in	in	ADP
ap-1263	180	12	handy	handy	ADJ
ap-1263	180	13	to	to	PART
ap-1263	180	14	have	have	VERB
ap-1263	180	15	explicit	explicit	ADJ
ap-1263	180	16	polynomial	polynomial	ADJ
ap-1263	180	17	dependence	dependence	NOUN
ap-1263	180	18	for	for	ADP
ap-1263	180	19	small	small	ADJ
ap-1263	180	20	values	value	NOUN
ap-1263	180	21	of	of	ADP
ap-1263	180	22	n.	n.	NOUN
ap-1263	180	23	however	however	ADV
ap-1263	180	24	,	,	PUNCT
ap-1263	180	25	it	it	PRON
ap-1263	180	26	turns	turn	VERB
ap-1263	180	27	out	out	ADP
ap-1263	180	28	that	that	SCONJ
ap-1263	180	29	it	it	PRON
ap-1263	180	30	is	be	AUX
ap-1263	180	31	practically	practically	ADV
ap-1263	180	32	impossible	impossible	ADJ
ap-1263	180	33	to	to	PART
ap-1263	180	34	obtain	obtain	VERB
ap-1263	180	35	the	the	DET
ap-1263	180	36	relation	relation	NOUN
ap-1263	180	37	between	between	ADP
ap-1263	180	38	casimir	casimir	NOUN
ap-1263	180	39	elements	element	NOUN
ap-1263	180	40	by	by	ADP
ap-1263	180	41	“	"	PUNCT
ap-1263	180	42	brute	brute	ADJ
ap-1263	180	43	force	force	NOUN
ap-1263	180	44	”	"	PUNCT
ap-1263	180	45	,	,	PUNCT
ap-1263	180	46	even	even	ADV
ap-1263	180	47	for	for	ADP
ap-1263	180	48	the	the	DET
ap-1263	180	49	simplest	simple	ADJ
ap-1263	180	50	cases	case	NOUN
ap-1263	180	51	.	.	PUNCT
ap-1263	181	1	for	for	ADP
ap-1263	181	2	example	example	NOUN
ap-1263	181	3	,	,	PUNCT
ap-1263	181	4	for	for	ADP
ap-1263	181	5	n	n	NOUN
ap-1263	181	6	=	=	SYM
ap-1263	181	7	3	3	NUM
ap-1263	181	8	one	one	NOUN
ap-1263	181	9	can	can	AUX
ap-1263	181	10	show	show	VERB
ap-1263	181	11	that	that	SCONJ
ap-1263	181	12	c3	c3	PROPN
ap-1263	181	13	−	−	PROPN
ap-1263	181	14	qc2	qc2	NOUN
ap-1263	181	15	−	−	NOUN
ap-1263	181	16	c231	c231	PROPN
ap-1263	181	17	−	−	PROPN
ap-1263	181	18	c232−	c232−	NOUN
ap-1263	181	19	(	(	PUNCT
ap-1263	181	20	11	11	NUM
ap-1263	181	21	)	)	PUNCT
ap-1263	181	22	c233	c233	PROPN
ap-1263	182	1	+	+	CCONJ
ap-1263	183	1	3(q	3(q	NUM
ap-1263	183	2	+	+	CCONJ
ap-1263	183	3	q	q	PROPN
ap-1263	183	4	1	1	NUM
ap-1263	183	5	2	2	NUM
ap-1263	183	6	)	)	PUNCT
ap-1263	183	7	c31c32c33	c31c32c33	X
ap-1263	183	8	=	=	SYM
ap-1263	183	9	0	0	X
ap-1263	183	10	.	.	PUNCT
ap-1263	184	1	note	note	VERB
ap-1263	184	2	that	that	SCONJ
ap-1263	184	3	c3	c3	PROPN
ap-1263	184	4	is	be	AUX
ap-1263	184	5	of	of	ADP
ap-1263	184	6	degree	degree	NOUN
ap-1263	184	7	nine	nine	NUM
ap-1263	184	8	,	,	PUNCT
ap-1263	184	9	so	so	SCONJ
ap-1263	184	10	it	it	PRON
ap-1263	184	11	is	be	AUX
ap-1263	184	12	quite	quite	ADV
ap-1263	184	13	complicated	complicated	ADJ
ap-1263	184	14	even	even	ADV
ap-1263	184	15	to	to	PART
ap-1263	184	16	prove	prove	VERB
ap-1263	184	17	the	the	DET
ap-1263	184	18	given	give	VERB
ap-1263	184	19	explicit	explicit	ADJ
ap-1263	184	20	relation	relation	NOUN
ap-1263	184	21	.	.	PUNCT
ap-1263	185	1	the	the	DET
ap-1263	185	2	diamond	diamond	NOUN
ap-1263	185	3	lemma	lemma	PROPN
ap-1263	185	4	can	can	AUX
ap-1263	185	5	be	be	AUX
ap-1263	185	6	quite	quite	ADV
ap-1263	185	7	useful	useful	ADJ
ap-1263	185	8	for	for	ADP
ap-1263	185	9	obtaining	obtain	VERB
ap-1263	185	10	relations	relation	NOUN
ap-1263	185	11	of	of	ADP
ap-1263	185	12	type	type	NOUN
ap-1263	185	13	(	(	PUNCT
ap-1263	185	14	11	11	NUM
ap-1263	185	15	)	)	PUNCT
ap-1263	185	16	directly	directly	ADV
ap-1263	185	17	.	.	PUNCT
ap-1263	186	1	we	we	PRON
ap-1263	186	2	must	must	AUX
ap-1263	186	3	only	only	ADV
ap-1263	186	4	construct	construct	VERB
ap-1263	186	5	a	a	DET
ap-1263	186	6	suitable	suitable	ADJ
ap-1263	186	7	set	set	NOUN
ap-1263	186	8	of	of	ADP
ap-1263	186	9	rewriting	rewrite	VERB
ap-1263	186	10	rules	rule	NOUN
ap-1263	186	11	and	and	CCONJ
ap-1263	186	12	with	with	ADP
ap-1263	186	13	the	the	DET
ap-1263	186	14	help	help	NOUN
ap-1263	186	15	of	of	ADP
ap-1263	186	16	it	it	PRON
ap-1263	186	17	new	new	ADJ
ap-1263	186	18	advantageous	advantageous	ADJ
ap-1263	186	19	basis	basis	NOUN
ap-1263	186	20	of	of	ADP
ap-1263	186	21	the	the	DET
ap-1263	186	22	algebra	algebra	NOUN
ap-1263	186	23	.	.	PUNCT
ap-1263	187	1	first	first	ADV
ap-1263	187	2	we	we	PRON
ap-1263	187	3	start	start	VERB
ap-1263	187	4	with	with	ADP
ap-1263	187	5	ordinary	ordinary	ADJ
ap-1263	187	6	rewriting	rewrite	VERB
ap-1263	187	7	rules	rule	NOUN
ap-1263	187	8	coming	come	VERB
ap-1263	187	9	from	from	ADP
ap-1263	187	10	the	the	DET
ap-1263	187	11	commutation	commutation	NOUN
ap-1263	187	12	relations	relation	NOUN
ap-1263	187	13	,	,	PUNCT
ap-1263	187	14	namely	namely	ADV
ap-1263	187	15	i2i1	i2i1	ADP
ap-1263	187	16	→	→	SYM
ap-1263	187	17	qi1i2	qi1i2	ADJ
ap-1263	187	18	−	−	PROPN
ap-1263	187	19	q	q	NOUN
ap-1263	187	20	1	1	NUM
ap-1263	187	21	2	2	NUM
ap-1263	187	22	i3	i3	NOUN
ap-1263	187	23	,	,	PUNCT
ap-1263	187	24	i3i2	i3i2	ADP
ap-1263	187	25	→	→	PUNCT
ap-1263	187	26	qi2i3	qi2i3	NOUN
ap-1263	187	27	−	−	NOUN
ap-1263	187	28	q	q	NOUN
ap-1263	187	29	1	1	NUM
ap-1263	187	30	2	2	NUM
ap-1263	187	31	i1	i1	NOUN
ap-1263	187	32	,	,	PUNCT
ap-1263	187	33	i3i1	i3i1	NOUN
ap-1263	187	34	→	→	SYM
ap-1263	187	35	q−1i1i3	q−1i1i3	NOUN
ap-1263	188	1	+	+	CCONJ
ap-1263	188	2	q−	q−	PROPN
ap-1263	188	3	1	1	NUM
ap-1263	188	4	2	2	NUM
ap-1263	188	5	i2	i2	NOUN
ap-1263	188	6	,	,	PUNCT
ap-1263	188	7	i1c	i1c	NOUN
ap-1263	188	8	→	→	SYM
ap-1263	188	9	ci1	ci1	PROPN
ap-1263	188	10	,	,	PUNCT
ap-1263	188	11	i2c	i2c	NOUN
ap-1263	188	12	→	→	SYM
ap-1263	188	13	ci2	ci2	ADJ
ap-1263	188	14	,	,	PUNCT
ap-1263	188	15	i3c	i3c	NOUN
ap-1263	188	16	→	→	SYM
ap-1263	188	17	ci3	ci3	PROPN
ap-1263	188	18	.	.	PUNCT
ap-1263	189	1	the	the	DET
ap-1263	189	2	powers	power	NOUN
ap-1263	189	3	of	of	ADP
ap-1263	189	4	the	the	DET
ap-1263	189	5	generators	generator	NOUN
ap-1263	189	6	can	can	AUX
ap-1263	189	7	be	be	AUX
ap-1263	189	8	reduced	reduce	VERB
ap-1263	189	9	using	use	VERB
ap-1263	189	10	casimir	casimir	NOUN
ap-1263	189	11	elements	element	NOUN
ap-1263	189	12	cnk	cnk	ADV
ap-1263	189	13	,	,	PUNCT
ap-1263	189	14	therefore	therefore	ADV
ap-1263	189	15	we	we	PRON
ap-1263	189	16	add	add	VERB
ap-1263	189	17	the	the	DET
ap-1263	189	18	relations	relation	NOUN
ap-1263	189	19	in	in	ADP
ap-1263	189	20	k	k	PROPN
ap-1263	189	21	→	→	SYM
ap-1263	189	22	cnk	cnk	ADJ
ap-1263	190	1	−	−	PROPN
ap-1263	191	1	[	[	X
ap-1263	191	2	n−1	n−1	PROPN
ap-1263	191	3	2	2	NUM
ap-1263	191	4	]	]	PUNCT
ap-1263	191	5	∑	∑	PUNCT
ap-1263	191	6	j=1	j=1	NOUN
ap-1263	191	7	(	(	PUNCT
ap-1263	191	8	n	n	ADV
ap-1263	191	9	−	−	PROPN
ap-1263	191	10	j	j	PROPN
ap-1263	191	11	j	j	PROPN
ap-1263	191	12	)	)	PUNCT
ap-1263	191	13	n	n	CCONJ
ap-1263	191	14	n	n	CCONJ
ap-1263	191	15	−	−	PROPN
ap-1263	191	16	j	j	PROPN
ap-1263	191	17	(	(	PUNCT
ap-1263	191	18	i	i	PRON
ap-1263	191	19	q	q	PROPN
ap-1263	191	20	−	−	PROPN
ap-1263	191	21	q−1	q−1	PROPN
ap-1263	191	22	)	)	PUNCT
ap-1263	191	23	2j	2j	PROPN
ap-1263	191	24	in−2j	in−2j	PROPN
ap-1263	191	25	k	k	NOUN
ap-1263	191	26	,	,	PUNCT
ap-1263	191	27	k	k	PROPN
ap-1263	191	28	=	=	SYM
ap-1263	191	29	1	1	NUM
ap-1263	191	30	,	,	PUNCT
ap-1263	191	31	2	2	NUM
ap-1263	191	32	,	,	PUNCT
ap-1263	191	33	3	3	NUM
ap-1263	191	34	.	.	PUNCT
ap-1263	192	1	next	next	ADV
ap-1263	192	2	we	we	PRON
ap-1263	192	3	must	must	AUX
ap-1263	192	4	ensure	ensure	VERB
ap-1263	192	5	that	that	SCONJ
ap-1263	192	6	casimir	casimir	NOUN
ap-1263	192	7	element	element	NOUN
ap-1263	192	8	c	c	PROPN
ap-1263	192	9	does	do	AUX
ap-1263	192	10	not	not	PART
ap-1263	192	11	appear	appear	VERB
ap-1263	192	12	too	too	ADV
ap-1263	192	13	many	many	ADJ
ap-1263	192	14	times	time	NOUN
ap-1263	192	15	.	.	PUNCT
ap-1263	193	1	this	this	PRON
ap-1263	193	2	is	be	AUX
ap-1263	193	3	ensured	ensure	VERB
ap-1263	193	4	by	by	ADP
ap-1263	193	5	the	the	DET
ap-1263	193	6	relation	relation	NOUN
ap-1263	193	7	acb	acb	PROPN
ap-1263	193	8	→	→	SYM
ap-1263	193	9	a(q2i21	a(q2i21	NOUN
ap-1263	193	10	+	+	NUM
ap-1263	193	11	i22	i22	NOUN
ap-1263	193	12	+	+	CCONJ
ap-1263	193	13	q2i23	q2i23	ADJ
ap-1263	193	14	−	−	PROPN
ap-1263	193	15	(	(	PUNCT
ap-1263	193	16	q	q	PROPN
ap-1263	193	17	52	52	NUM
ap-1263	193	18	−	−	NOUN
ap-1263	193	19	q	q	NOUN
ap-1263	193	20	1	1	NUM
ap-1263	193	21	2	2	NUM
ap-1263	193	22	)	)	PUNCT
ap-1263	193	23	i1i2i3)b	i1i2i3)b	PROPN
ap-1263	193	24	,	,	PUNCT
ap-1263	193	25	where	where	SCONJ
ap-1263	193	26	a	a	X
ap-1263	193	27	,	,	PUNCT
ap-1263	193	28	b	b	NOUN
ap-1263	193	29	are	be	AUX
ap-1263	193	30	arbitrary	arbitrary	ADJ
ap-1263	193	31	monomials	monomial	NOUN
ap-1263	193	32	,	,	PUNCT
ap-1263	193	33	and	and	CCONJ
ap-1263	193	34	it	it	PRON
ap-1263	193	35	comes	come	VERB
ap-1263	193	36	into	into	ADP
ap-1263	193	37	play	play	NOUN
ap-1263	193	38	only	only	ADV
ap-1263	193	39	if	if	SCONJ
ap-1263	193	40	the	the	DET
ap-1263	193	41	count	count	NOUN
ap-1263	193	42	of	of	ADP
ap-1263	193	43	letters	letter	NOUN
ap-1263	193	44	ik	ik	PROPN
ap-1263	193	45	(	(	PUNCT
ap-1263	193	46	k	k	NOUN
ap-1263	193	47	=	=	SYM
ap-1263	193	48	1	1	NUM
ap-1263	193	49	,	,	PUNCT
ap-1263	193	50	2	2	NUM
ap-1263	193	51	,	,	PUNCT
ap-1263	193	52	3	3	NUM
ap-1263	193	53	)	)	PUNCT
ap-1263	193	54	and	and	CCONJ
ap-1263	193	55	c	c	PROPN
ap-1263	193	56	in	in	ADP
ap-1263	193	57	monomial	monomial	ADJ
ap-1263	193	58	acb	acb	PROPN
ap-1263	193	59	is	be	AUX
ap-1263	193	60	greater	great	ADJ
ap-1263	193	61	or	or	CCONJ
ap-1263	193	62	equal	equal	ADJ
ap-1263	193	63	to	to	PART
ap-1263	193	64	n.	n.	VERB
ap-1263	193	65	the	the	DET
ap-1263	193	66	last	last	ADJ
ap-1263	193	67	rule	rule	NOUN
ap-1263	193	68	(	(	PUNCT
ap-1263	193	69	or	or	CCONJ
ap-1263	193	70	,	,	PUNCT
ap-1263	193	71	better	well	ADV
ap-1263	193	72	to	to	PART
ap-1263	193	73	say	say	VERB
ap-1263	193	74	,	,	PUNCT
ap-1263	193	75	set	set	NOUN
ap-1263	193	76	of	of	ADP
ap-1263	193	77	rules	rule	NOUN
ap-1263	193	78	)	)	PUNCT
ap-1263	193	79	which	which	PRON
ap-1263	193	80	we	we	PRON
ap-1263	193	81	do	do	AUX
ap-1263	193	82	not	not	PART
ap-1263	193	83	present	present	VERB
ap-1263	193	84	explicitly	explicitly	ADV
ap-1263	193	85	transforms	transform	VERB
ap-1263	193	86	cjw	cjw	PROPN
ap-1263	193	87	→	→	SYM
ap-1263	193	88	cj+1w̃	cj+1w̃	NOUN
ap-1263	193	89	,	,	PUNCT
ap-1263	193	90	where	where	SCONJ
ap-1263	193	91	w	w	NOUN
ap-1263	193	92	is	be	AUX
ap-1263	193	93	any	any	DET
ap-1263	193	94	product	product	NOUN
ap-1263	193	95	of	of	ADP
ap-1263	193	96	generators	generator	NOUN
ap-1263	193	97	ik	ik	PROPN
ap-1263	193	98	,	,	PUNCT
ap-1263	193	99	k	k	NOUN
ap-1263	193	100	=	=	SYM
ap-1263	193	101	1	1	NUM
ap-1263	193	102	,	,	PUNCT
ap-1263	193	103	2	2	NUM
ap-1263	193	104	,	,	PUNCT
ap-1263	193	105	3	3	NUM
ap-1263	193	106	with	with	ADP
ap-1263	193	107	the	the	DET
ap-1263	193	108	property	property	NOUN
ap-1263	193	109	that	that	PRON
ap-1263	193	110	every	every	DET
ap-1263	193	111	generator	generator	NOUN
ap-1263	193	112	i1	i1	PROPN
ap-1263	193	113	,	,	PUNCT
ap-1263	193	114	i2	i2	PROPN
ap-1263	193	115	,	,	PUNCT
ap-1263	193	116	i3	i3	NOUN
ap-1263	193	117	is	be	AUX
ap-1263	193	118	present	present	ADJ
ap-1263	193	119	in	in	ADP
ap-1263	193	120	the	the	DET
ap-1263	193	121	product	product	NOUN
ap-1263	193	122	.	.	PUNCT
ap-1263	194	1	using	use	VERB
ap-1263	194	2	the	the	DET
ap-1263	194	3	commutation	commutation	NOUN
ap-1263	194	4	relations	relation	NOUN
ap-1263	194	5	,	,	PUNCT
ap-1263	194	6	w	w	PROPN
ap-1263	194	7	is	be	AUX
ap-1263	194	8	transformed	transform	VERB
ap-1263	194	9	to	to	ADP
ap-1263	194	10	the	the	DET
ap-1263	194	11	form	form	NOUN
ap-1263	194	12	i1i2i3w1	i1i2i3w1	ADJ
ap-1263	194	13	and	and	CCONJ
ap-1263	194	14	the	the	DET
ap-1263	194	15	product	product	NOUN
ap-1263	194	16	i1i2i3	i1i2i3	PROPN
ap-1263	194	17	is	be	AUX
ap-1263	194	18	then	then	ADV
ap-1263	194	19	converted	convert	VERB
ap-1263	194	20	to	to	ADP
ap-1263	194	21	c	c	NOUN
ap-1263	194	22	using	use	VERB
ap-1263	194	23	the	the	DET
ap-1263	194	24	rule	rule	NOUN
ap-1263	194	25	i1i2i3	i1i2i3	PROPN
ap-1263	194	26	→	→	PUNCT
ap-1263	194	27	(	(	PUNCT
ap-1263	194	28	q	q	NOUN
ap-1263	194	29	5	5	NUM
ap-1263	194	30	2	2	NUM
ap-1263	194	31	−	−	NOUN
ap-1263	194	32	q	q	NOUN
ap-1263	194	33	1	1	NUM
ap-1263	194	34	2	2	NUM
ap-1263	194	35	)	)	PUNCT
ap-1263	194	36	−1(q2i21	−1(q2i21	NOUN
ap-1263	194	37	+	+	CCONJ
ap-1263	194	38	i22	i22	NOUN
ap-1263	195	1	+	+	X
ap-1263	195	2	q2i23	q2i23	ADJ
ap-1263	195	3	−	−	PROPN
ap-1263	195	4	c	c	NOUN
ap-1263	195	5	)	)	PUNCT
ap-1263	195	6	.	.	PUNCT
ap-1263	196	1	these	these	DET
ap-1263	196	2	transformation	transformation	NOUN
ap-1263	196	3	rules	rule	NOUN
ap-1263	196	4	now	now	ADV
ap-1263	196	5	lead	lead	VERB
ap-1263	196	6	to	to	ADP
ap-1263	196	7	the	the	DET
ap-1263	196	8	basis	basis	NOUN
ap-1263	196	9	containing	contain	VERB
ap-1263	196	10	the	the	DET
ap-1263	196	11	following	follow	VERB
ap-1263	196	12	elements	element	NOUN
ap-1263	196	13	:	:	PUNCT
ap-1263	196	14	cα	cα	PART
ap-1263	196	15	n1c	n1c	ADV
ap-1263	196	16	β	β	X
ap-1263	196	17	n2c	n2c	PROPN
ap-1263	196	18	γ	γ	PROPN
ap-1263	196	19	n3c	n3c	PROPN
ap-1263	196	20	δik	δik	PROPN
ap-1263	196	21	1	1	NUM
ap-1263	197	1	i	i	NOUN
ap-1263	197	2	l	l	PROPN
ap-1263	197	3	2i	2i	NUM
ap-1263	197	4	m	m	PROPN
ap-1263	197	5	3	3	NUM
ap-1263	197	6	,	,	PUNCT
ap-1263	197	7	α	α	PROPN
ap-1263	197	8	,	,	PUNCT
ap-1263	197	9	β	β	X
ap-1263	197	10	,	,	PUNCT
ap-1263	197	11	γ	γ	X
ap-1263	197	12	≥	≥	NUM
ap-1263	197	13	0	0	NUM
ap-1263	197	14	,	,	PUNCT
ap-1263	197	15	0	0	NUM
ap-1263	197	16	≤	≤	NUM
ap-1263	197	17	δ	δ	PROPN
ap-1263	197	18	≤	≤	PROPN
ap-1263	197	19	n	n	CCONJ
ap-1263	197	20	−	−	PROPN
ap-1263	197	21	1	1	NUM
ap-1263	197	22	,	,	PUNCT
ap-1263	197	23	0	0	NUM
ap-1263	197	24	≤	≤	NUM
ap-1263	197	25	k	k	NOUN
ap-1263	197	26	,	,	PUNCT
ap-1263	197	27	l	l	NOUN
ap-1263	197	28	,	,	PUNCT
ap-1263	197	29	m	m	VERB
ap-1263	197	30	≤	≤	NOUN
ap-1263	197	31	n	n	CCONJ
ap-1263	197	32	−	−	PROPN
ap-1263	197	33	1−	1−	NUM
ap-1263	197	34	δ	δ	PROPN
ap-1263	197	35	,	,	PUNCT
ap-1263	197	36	klm	klm	PROPN
ap-1263	197	37	=	=	PUNCT
ap-1263	197	38	0	0	PROPN
ap-1263	197	39	.	.	PUNCT
ap-1263	198	1	if	if	SCONJ
ap-1263	198	2	we	we	PRON
ap-1263	198	3	want	want	VERB
ap-1263	198	4	to	to	PART
ap-1263	198	5	find	find	VERB
ap-1263	198	6	the	the	DET
ap-1263	198	7	explicit	explicit	ADJ
ap-1263	198	8	relation	relation	NOUN
ap-1263	198	9	between	between	ADP
ap-1263	198	10	casimir	casimir	NOUN
ap-1263	198	11	elements	element	NOUN
ap-1263	198	12	,	,	PUNCT
ap-1263	198	13	we	we	PRON
ap-1263	198	14	simply	simply	ADV
ap-1263	198	15	express	express	VERB
ap-1263	198	16	cn	cn	PROPN
ap-1263	198	17	in	in	ADP
ap-1263	198	18	the	the	DET
ap-1263	198	19	basis	basis	NOUN
ap-1263	198	20	specified	specify	VERB
ap-1263	198	21	(	(	PUNCT
ap-1263	198	22	using	use	VERB
ap-1263	198	23	a	a	DET
ap-1263	198	24	finite	finite	ADJ
ap-1263	198	25	number	number	NOUN
ap-1263	198	26	of	of	ADP
ap-1263	198	27	rewriting	rewrite	VERB
ap-1263	198	28	rules	rule	NOUN
ap-1263	198	29	reducing	reduce	VERB
ap-1263	198	30	cn	cn	PROPN
ap-1263	198	31	to	to	ADP
ap-1263	198	32	canonical	canonical	ADJ
ap-1263	198	33	form	form	NOUN
ap-1263	198	34	)	)	PUNCT
ap-1263	198	35	.	.	PUNCT
ap-1263	199	1	in	in	ADP
ap-1263	199	2	general	general	ADJ
ap-1263	199	3	,	,	PUNCT
ap-1263	199	4	one	one	PRON
ap-1263	199	5	can	can	AUX
ap-1263	199	6	show	show	VERB
ap-1263	199	7	that	that	SCONJ
ap-1263	199	8	for	for	ADP
ap-1263	199	9	odd	odd	ADJ
ap-1263	199	10	n	n	NOUN
ap-1263	199	11	the	the	DET
ap-1263	199	12	elements	element	NOUN
ap-1263	199	13	c	c	X
ap-1263	199	14	,	,	PUNCT
ap-1263	199	15	cn1	cn1	PROPN
ap-1263	199	16	,	,	PUNCT
ap-1263	199	17	cn2	cn2	PROPN
ap-1263	199	18	,	,	PUNCT
ap-1263	199	19	cn3	cn3	PROPN
ap-1263	199	20	fulfil	fulfil	VERB
ap-1263	199	21	the	the	DET
ap-1263	199	22	relation	relation	NOUN
ap-1263	199	23	c2n1	c2n1	PROPN
ap-1263	200	1	+	+	CCONJ
ap-1263	200	2	c2n2	c2n2	NOUN
ap-1263	200	3	+	+	CCONJ
ap-1263	200	4	c2n3	c2n3	X
ap-1263	200	5	+	+	CCONJ
ap-1263	200	6	(	(	PUNCT
ap-1263	200	7	q	q	X
ap-1263	200	8	−	−	PROPN
ap-1263	200	9	q−1)ncn1cn2cn3	q−1)ncn1cn2cn3	PROPN
ap-1263	200	10	=	=	SYM
ap-1263	201	1	n−1∏	n−1∏	PROPN
ap-1263	201	2	k=0	k=0	PROPN
ap-1263	201	3	(	(	PUNCT
ap-1263	201	4	c	c	X
ap-1263	201	5	+	+	NOUN
ap-1263	201	6	q	q	X
ap-1263	202	1	[	[	X
ap-1263	202	2	k]q	k]q	X
ap-1263	203	1	[	[	X
ap-1263	203	2	k	k	X
ap-1263	203	3	+	+	PROPN
ap-1263	203	4	1]q	1]q	NUM
ap-1263	203	5	)	)	PUNCT
ap-1263	203	6	.	.	PUNCT
ap-1263	204	1	the	the	DET
ap-1263	204	2	relation	relation	NOUN
ap-1263	204	3	for	for	ADP
ap-1263	204	4	even	even	ADV
ap-1263	204	5	n	n	ADV
ap-1263	204	6	as	as	ADV
ap-1263	204	7	well	well	ADV
ap-1263	204	8	as	as	ADP
ap-1263	204	9	the	the	DET
ap-1263	204	10	proof	proof	NOUN
ap-1263	204	11	of	of	ADP
ap-1263	204	12	this	this	PRON
ap-1263	204	13	can	can	AUX
ap-1263	204	14	be	be	AUX
ap-1263	204	15	found	find	VERB
ap-1263	204	16	in	in	ADP
ap-1263	204	17	[	[	X
ap-1263	204	18	7	7	NUM
ap-1263	204	19	]	]	PUNCT
ap-1263	204	20	.	.	PUNCT
ap-1263	205	1	acknowledgement	acknowledgement	NOUN
ap-1263	205	2	we	we	PRON
ap-1263	205	3	acknowledge	acknowledge	VERB
ap-1263	205	4	financial	financial	ADJ
ap-1263	205	5	support	support	NOUN
ap-1263	205	6	from	from	ADP
ap-1263	205	7	grant	grant	PROPN
ap-1263	205	8	201/10/1509	201/10/1509	NUM
ap-1263	205	9	of	of	ADP
ap-1263	205	10	the	the	DET
ap-1263	205	11	czech	czech	PROPN
ap-1263	205	12	science	science	NOUN
ap-1263	205	13	foundation	foundation	PROPN
ap-1263	205	14	and	and	CCONJ
ap-1263	205	15	msm6840770039	msm6840770039	NOUN
ap-1263	205	16	of	of	ADP
ap-1263	205	17	the	the	DET
ap-1263	205	18	ministry	ministry	PROPN
ap-1263	205	19	of	of	ADP
ap-1263	205	20	education	education	PROPN
ap-1263	205	21	,	,	PUNCT
ap-1263	205	22	youth	youth	NOUN
ap-1263	205	23	,	,	PUNCT
ap-1263	205	24	and	and	CCONJ
ap-1263	205	25	sports	sport	NOUN
ap-1263	205	26	of	of	ADP
ap-1263	205	27	the	the	DET
ap-1263	205	28	czech	czech	PROPN
ap-1263	205	29	republic	republic	NOUN
ap-1263	205	30	.	.	PUNCT
ap-1263	206	1	44	44	NUM
ap-1263	206	2	acta	acta	PROPN
ap-1263	206	3	polytechnica	polytechnica	PROPN
ap-1263	206	4	vol	vol	NOUN
ap-1263	206	5	.	.	PROPN
ap-1263	207	1	50	50	NUM
ap-1263	207	2	no	no	NOUN
ap-1263	207	3	.	.	PUNCT
ap-1263	208	1	5/2010	5/2010	NUM
ap-1263	208	2	references	reference	NOUN
ap-1263	208	3	[	[	X
ap-1263	208	4	1	1	NUM
ap-1263	208	5	]	]	X
ap-1263	208	6	lusztig	lusztig	ADJ
ap-1263	208	7	,	,	PUNCT
ap-1263	208	8	g	g	NOUN
ap-1263	208	9	:	:	PUNCT
ap-1263	208	10	introduction	introduction	NOUN
ap-1263	208	11	to	to	ADP
ap-1263	208	12	quantum	quantum	ADJ
ap-1263	208	13	groups	group	NOUN
ap-1263	208	14	,	,	PUNCT
ap-1263	208	15	birkhäuser	birkhäuser	NOUN
ap-1263	208	16	,	,	PUNCT
ap-1263	208	17	boston	boston	PROPN
ap-1263	208	18	,	,	PUNCT
ap-1263	208	19	1993	1993	NUM
ap-1263	208	20	.	.	PUNCT
ap-1263	209	1	[	[	X
ap-1263	209	2	2	2	NUM
ap-1263	209	3	]	]	X
ap-1263	209	4	klimyk	klimyk	NOUN
ap-1263	209	5	,	,	PUNCT
ap-1263	209	6	a.	a.	NOUN
ap-1263	209	7	u.	u.	PROPN
ap-1263	209	8	,	,	PUNCT
ap-1263	209	9	schmüdgen	schmüdgen	PROPN
ap-1263	209	10	,	,	PUNCT
ap-1263	209	11	k.	k.	NOUN
ap-1263	209	12	:	:	PUNCT
ap-1263	209	13	quantum	quantum	ADJ
ap-1263	209	14	groups	group	NOUN
ap-1263	209	15	and	and	CCONJ
ap-1263	209	16	their	their	PRON
ap-1263	209	17	representations	representation	NOUN
ap-1263	209	18	,	,	PUNCT
ap-1263	209	19	springer	springer	NOUN
ap-1263	209	20	,	,	PUNCT
ap-1263	209	21	berlin	berlin	PROPN
ap-1263	209	22	,	,	PUNCT
ap-1263	209	23	1997	1997	NUM
ap-1263	209	24	.	.	PUNCT
ap-1263	210	1	[	[	X
ap-1263	210	2	3	3	NUM
ap-1263	210	3	]	]	X
ap-1263	210	4	tange	tange	NOUN
ap-1263	210	5	,	,	PUNCT
ap-1263	210	6	r.	r.	PROPN
ap-1263	210	7	:	:	PUNCT
ap-1263	210	8	the	the	DET
ap-1263	210	9	centre	centre	NOUN
ap-1263	210	10	of	of	ADP
ap-1263	210	11	quantum	quantum	PROPN
ap-1263	210	12	sln	sln	NOUN
ap-1263	210	13	at	at	ADP
ap-1263	210	14	root	root	NOUN
ap-1263	210	15	of	of	ADP
ap-1263	210	16	unity	unity	NOUN
ap-1263	210	17	,	,	PUNCT
ap-1263	210	18	j.	j.	PROPN
ap-1263	210	19	algebra	algebra	PROPN
ap-1263	210	20	301	301	NUM
ap-1263	210	21	(	(	PUNCT
ap-1263	210	22	2006	2006	NUM
ap-1263	210	23	)	)	PUNCT
ap-1263	210	24	425–445	425–445	NUM
ap-1263	210	25	.	.	PUNCT
ap-1263	211	1	[	[	X
ap-1263	211	2	4	4	NUM
ap-1263	211	3	]	]	X
ap-1263	211	4	havlíček	havlíček	NOUN
ap-1263	211	5	,	,	PUNCT
ap-1263	211	6	m.	m.	NOUN
ap-1263	211	7	,	,	PUNCT
ap-1263	211	8	pošta	pošta	PROPN
ap-1263	211	9	,	,	PUNCT
ap-1263	211	10	s.	s.	PROPN
ap-1263	211	11	:	:	PUNCT
ap-1263	211	12	on	on	ADP
ap-1263	211	13	the	the	DET
ap-1263	211	14	classification	classification	NOUN
ap-1263	211	15	of	of	ADP
ap-1263	211	16	irreducible	irreducible	ADJ
ap-1263	211	17	finite	finite	ADJ
ap-1263	211	18	-	-	ADJ
ap-1263	211	19	dimensional	dimensional	ADJ
ap-1263	211	20	representations	representation	NOUN
ap-1263	211	21	of	of	ADP
ap-1263	211	22	u	u	NOUN
ap-1263	211	23	′	′	NUM
ap-1263	211	24	q(so3	q(so3	ADV
ap-1263	211	25	)	)	PUNCT
ap-1263	211	26	algebra	algebra	NOUN
ap-1263	211	27	,	,	PUNCT
ap-1263	211	28	j.	j.	PROPN
ap-1263	211	29	math	math	PROPN
ap-1263	211	30	.	.	PUNCT
ap-1263	212	1	phys	phy	NOUN
ap-1263	212	2	.	.	PUNCT
ap-1263	213	1	42	42	NUM
ap-1263	213	2	(	(	PUNCT
ap-1263	213	3	2001	2001	NUM
ap-1263	213	4	)	)	PUNCT
ap-1263	213	5	,	,	PUNCT
ap-1263	213	6	472–500	472–500	NUM
ap-1263	213	7	.	.	PUNCT
ap-1263	214	1	[	[	X
ap-1263	214	2	5	5	NUM
ap-1263	214	3	]	]	X
ap-1263	214	4	havlíček	havlíček	NOUN
ap-1263	214	5	,	,	PUNCT
ap-1263	214	6	m.	m.	NOUN
ap-1263	214	7	,	,	PUNCT
ap-1263	214	8	klimyk	klimyk	PROPN
ap-1263	214	9	,	,	PUNCT
ap-1263	214	10	a.	a.	NOUN
ap-1263	214	11	u.	u.	PROPN
ap-1263	214	12	,	,	PUNCT
ap-1263	214	13	pošta	pošta	PROPN
ap-1263	214	14	,	,	PUNCT
ap-1263	214	15	s.	s.	PROPN
ap-1263	214	16	:	:	PUNCT
ap-1263	214	17	representations	representation	NOUN
ap-1263	214	18	of	of	ADP
ap-1263	214	19	the	the	DET
ap-1263	214	20	cyclically	cyclically	ADV
ap-1263	214	21	symmetric	symmetric	ADJ
ap-1263	214	22	q	q	ADJ
ap-1263	214	23	-	-	PUNCT
ap-1263	214	24	deformed	deform	VERB
ap-1263	214	25	algebra	algebra	NOUN
ap-1263	214	26	soq(3	soq(3	NOUN
ap-1263	214	27	)	)	PUNCT
ap-1263	214	28	,	,	PUNCT
ap-1263	214	29	j.	j.	PROPN
ap-1263	214	30	math	math	PROPN
ap-1263	214	31	.	.	PUNCT
ap-1263	215	1	phys	phy	NOUN
ap-1263	215	2	.	.	PUNCT
ap-1263	216	1	40	40	NUM
ap-1263	216	2	(	(	PUNCT
ap-1263	216	3	1999	1999	NUM
ap-1263	216	4	)	)	PUNCT
ap-1263	216	5	,	,	PUNCT
ap-1263	216	6	2	2	NUM
ap-1263	216	7	135–2	135–2	NUM
ap-1263	216	8	161	161	NUM
ap-1263	216	9	.	.	PUNCT
ap-1263	217	1	[	[	X
ap-1263	217	2	6	6	NUM
ap-1263	217	3	]	]	X
ap-1263	217	4	bergmann	bergmann	PROPN
ap-1263	217	5	,	,	PUNCT
ap-1263	217	6	g.	g.	PROPN
ap-1263	217	7	m.	m.	PROPN
ap-1263	217	8	:	:	PUNCT
ap-1263	217	9	diamond	diamond	PROPN
ap-1263	217	10	lemma	lemma	PROPN
ap-1263	217	11	for	for	ADP
ap-1263	217	12	ring	ring	NOUN
ap-1263	217	13	theory	theory	NOUN
ap-1263	217	14	,	,	PUNCT
ap-1263	217	15	adv	adv	PROPN
ap-1263	217	16	.	.	PUNCT
ap-1263	217	17	math	math	PROPN
ap-1263	217	18	.	.	PUNCT
ap-1263	218	1	29	29	NUM
ap-1263	218	2	(	(	PUNCT
ap-1263	218	3	1978	1978	NUM
ap-1263	218	4	)	)	PUNCT
ap-1263	218	5	,	,	PUNCT
ap-1263	218	6	178–218	178–218	NUM
ap-1263	218	7	.	.	PUNCT
ap-1263	219	1	[	[	X
ap-1263	219	2	7	7	NUM
ap-1263	219	3	]	]	X
ap-1263	219	4	havlíček	havlíček	NOUN
ap-1263	219	5	,	,	PUNCT
ap-1263	219	6	m.	m.	NOUN
ap-1263	219	7	,	,	PUNCT
ap-1263	219	8	pošta	pošta	PROPN
ap-1263	219	9	,	,	PUNCT
ap-1263	219	10	s.	s.	PROPN
ap-1263	219	11	:	:	PUNCT
ap-1263	219	12	center	center	NOUN
ap-1263	219	13	of	of	ADP
ap-1263	219	14	algebra	algebra	NOUN
ap-1263	219	15	u	u	NOUN
ap-1263	219	16	′	′	NUM
ap-1263	219	17	q(so3	q(so3	ADV
ap-1263	219	18	)	)	PUNCT
ap-1263	219	19	,	,	PUNCT
ap-1263	219	20	submitted	submit	VERB
ap-1263	219	21	to	to	ADP
ap-1263	219	22	j.	j.	PROPN
ap-1263	219	23	math	math	PROPN
ap-1263	219	24	.	.	PUNCT
ap-1263	220	1	phys	phy	NOUN
ap-1263	220	2	.	.	PUNCT
ap-1263	221	1	prof	prof	PROPN
ap-1263	221	2	.	.	PUNCT
ap-1263	222	1	ing	ing	PROPN
ap-1263	222	2	.	.	PUNCT
ap-1263	223	1	miloslav	miloslav	PROPN
ap-1263	223	2	havlíček	havlíček	PROPN
ap-1263	223	3	,	,	PUNCT
ap-1263	223	4	drsc	drsc	PROPN
ap-1263	223	5	.	.	PUNCT
ap-1263	224	1	e	e	X
ap-1263	224	2	-	-	NOUN
ap-1263	224	3	mail	mail	NOUN
ap-1263	224	4	:	:	PUNCT
ap-1263	224	5	miloslav.havlicek@fjfi.cvut.cz	miloslav.havlicek@fjfi.cvut.cz	PROPN
ap-1263	224	6	doc	doc	PROPN
ap-1263	224	7	.	.	PROPN
ap-1263	225	1	ing	ing	PROPN
ap-1263	225	2	.	.	PUNCT
ap-1263	226	1	severin	severin	PROPN
ap-1263	226	2	pošta	pošta	PROPN
ap-1263	226	3	,	,	PUNCT
ap-1263	226	4	ph.d	ph.d	PROPN
ap-1263	226	5	.	.	PUNCT
ap-1263	227	1	e	e	X
ap-1263	227	2	-	-	NOUN
ap-1263	227	3	mail	mail	NOUN
ap-1263	227	4	:	:	PUNCT
ap-1263	227	5	severin.posta@fjfi.cvut.cz	severin.posta@fjfi.cvut.cz	NOUN
ap-1263	227	6	department	department	PROPN
ap-1263	227	7	of	of	ADP
ap-1263	227	8	mathematics	mathematics	PROPN
ap-1263	227	9	fnspe	fnspe	PROPN
ap-1263	227	10	,	,	PUNCT
ap-1263	227	11	czech	czech	PROPN
ap-1263	227	12	technical	technical	PROPN
ap-1263	227	13	university	university	PROPN
ap-1263	227	14	in	in	ADP
ap-1263	227	15	prague	prague	PROPN
ap-1263	227	16	trojanova	trojanova	X
ap-1263	227	17	13	13	NUM
ap-1263	227	18	,	,	PUNCT
ap-1263	227	19	cz-120	cz-120	PROPN
ap-1263	227	20	00	00	PUNCT
ap-1263	228	1	prague	prague	PROPN
ap-1263	228	2	45	45	NUM