id	sid	tid	token	lemma	pos
ajema-5949	1	1	244	244	NUM
ajema-5949	1	2	journal	journal	NOUN
ajema-5949	1	3	of	of	ADP
ajema-5949	1	4	engineering	engineering	NOUN
ajema-5949	1	5	,	,	PUNCT
ajema-5949	1	6	mechanics	mechanic	NOUN
ajema-5949	1	7	and	and	CCONJ
ajema-5949	1	8	architecture	architecture	NOUN
ajema-5949	1	9	www	www	NOUN
ajema-5949	1	10	.	.	PUNCT
ajema-5949	2	1	grnjournal.us	grnjournal.us	PROPN
ajema-5949	2	2	american	american	PROPN
ajema-5949	2	3	journal	journal	PROPN
ajema-5949	2	4	of	of	ADP
ajema-5949	2	5	engineering	engineering	NOUN
ajema-5949	2	6	,	,	PUNCT
ajema-5949	2	7	mechanics	mechanic	NOUN
ajema-5949	2	8	and	and	CCONJ
ajema-5949	2	9	architecture	architecture	NOUN
ajema-5949	2	10	volume	volume	NOUN
ajema-5949	2	11	2	2	NUM
ajema-5949	2	12	,	,	PUNCT
ajema-5949	2	13	issue	issue	NOUN
ajema-5949	2	14	12	12	NUM
ajema-5949	2	15	,	,	PUNCT
ajema-5949	2	16	2024	2024	NUM
ajema-5949	2	17	issn	issn	X
ajema-5949	2	18	(	(	PUNCT
ajema-5949	2	19	e	e	NOUN
ajema-5949	2	20	):	):	PUNCT
ajema-5949	2	21	2993	2993	NUM
ajema-5949	2	22	-	-	SYM
ajema-5949	2	23	2637	2637	NUM
ajema-5949	2	24	algebraic	algebraic	ADJ
ajema-5949	2	25	structures	structure	NOUN
ajema-5949	2	26	in	in	ADP
ajema-5949	2	27	non	non	ADJ
ajema-5949	2	28	-	-	ADJ
ajema-5949	2	29	commutative	commutative	ADJ
ajema-5949	2	30	geometry	geometry	NOUN
ajema-5949	2	31	:	:	PUNCT
ajema-5949	2	32	an	an	DET
ajema-5949	2	33	exploration	exploration	NOUN
ajema-5949	2	34	of	of	ADP
ajema-5949	2	35	quantum	quantum	NOUN
ajema-5949	2	36	groups	group	NOUN
ajema-5949	2	37	aastha	aastha	PROPN
ajema-5949	2	38	(	(	PUNCT
ajema-5949	2	39	m.sc	m.sc	PROPN
ajema-5949	2	40	.	.	PUNCT
ajema-5949	2	41	net	net	PROPN
ajema-5949	2	42	)	)	PUNCT
ajema-5949	2	43	,	,	PUNCT
ajema-5949	2	44	assistant	assistant	NOUN
ajema-5949	2	45	professor	professor	NOUN
ajema-5949	2	46	in	in	ADP
ajema-5949	2	47	mathematics	mathematics	PROPN
ajema-5949	2	48	(	(	PUNCT
ajema-5949	2	49	part	part	NOUN
ajema-5949	2	50	time	time	NOUN
ajema-5949	2	51	)	)	PUNCT
ajema-5949	2	52	,	,	PUNCT
ajema-5949	2	53	ch	ch	PROPN
ajema-5949	2	54	.	.	PUNCT
ajema-5949	2	55	ranbir	ranbir	PROPN
ajema-5949	2	56	singh	singh	PROPN
ajema-5949	2	57	university	university	PROPN
ajema-5949	2	58	,	,	PUNCT
ajema-5949	2	59	jind	jind	PROPN
ajema-5949	2	60	,	,	PUNCT
ajema-5949	2	61	haryana	haryana	PROPN
ajema-5949	2	62	,	,	PUNCT
ajema-5949	2	63	mayyar	mayyar	PROPN
ajema-5949	2	64	,	,	PUNCT
ajema-5949	2	65	hisar	hisar	PROPN
ajema-5949	2	66	,	,	PUNCT
ajema-5949	2	67	haryana	haryana	PROPN
ajema-5949	2	68	abstract	abstract	PROPN
ajema-5949	2	69	:	:	PUNCT
ajema-5949	2	70	non	non	ADJ
ajema-5949	2	71	-	-	ADJ
ajema-5949	2	72	commutative	commutative	ADJ
ajema-5949	2	73	geometry	geometry	NOUN
ajema-5949	2	74	offers	offer	VERB
ajema-5949	2	75	a	a	DET
ajema-5949	2	76	framework	framework	NOUN
ajema-5949	2	77	for	for	ADP
ajema-5949	2	78	studying	study	VERB
ajema-5949	2	79	spaces	space	NOUN
ajema-5949	2	80	where	where	SCONJ
ajema-5949	2	81	the	the	DET
ajema-5949	2	82	coordinates	coordinate	NOUN
ajema-5949	2	83	do	do	AUX
ajema-5949	2	84	not	not	PART
ajema-5949	2	85	commute	commute	VERB
ajema-5949	2	86	,	,	PUNCT
ajema-5949	2	87	extending	extend	VERB
ajema-5949	2	88	classical	classical	ADJ
ajema-5949	2	89	geometric	geometric	ADJ
ajema-5949	2	90	concepts	concept	NOUN
ajema-5949	2	91	into	into	ADP
ajema-5949	2	92	quantum	quantum	ADJ
ajema-5949	2	93	mechanics	mechanic	NOUN
ajema-5949	2	94	and	and	CCONJ
ajema-5949	2	95	quantum	quantum	NOUN
ajema-5949	2	96	field	field	NOUN
ajema-5949	2	97	theory	theory	NOUN
ajema-5949	2	98	.	.	PUNCT
ajema-5949	3	1	a	a	DET
ajema-5949	3	2	key	key	ADJ
ajema-5949	3	3	algebraic	algebraic	ADJ
ajema-5949	3	4	structure	structure	NOUN
ajema-5949	3	5	within	within	ADP
ajema-5949	3	6	this	this	DET
ajema-5949	3	7	framework	framework	NOUN
ajema-5949	3	8	is	be	AUX
ajema-5949	3	9	the	the	DET
ajema-5949	3	10	quantum	quantum	ADJ
ajema-5949	3	11	group	group	NOUN
ajema-5949	3	12	,	,	PUNCT
ajema-5949	3	13	which	which	PRON
ajema-5949	3	14	serves	serve	VERB
ajema-5949	3	15	as	as	ADP
ajema-5949	3	16	a	a	DET
ajema-5949	3	17	quantum	quantum	ADJ
ajema-5949	3	18	analogue	analogue	NOUN
ajema-5949	3	19	of	of	ADP
ajema-5949	3	20	a	a	DET
ajema-5949	3	21	lie	lie	NOUN
ajema-5949	3	22	group	group	NOUN
ajema-5949	3	23	,	,	PUNCT
ajema-5949	3	24	exhibiting	exhibit	VERB
ajema-5949	3	25	distinct	distinct	ADJ
ajema-5949	3	26	properties	property	NOUN
ajema-5949	3	27	due	due	ADJ
ajema-5949	3	28	to	to	ADP
ajema-5949	3	29	the	the	DET
ajema-5949	3	30	noncommutative	noncommutative	ADJ
ajema-5949	3	31	nature	nature	NOUN
ajema-5949	3	32	of	of	ADP
ajema-5949	3	33	its	its	PRON
ajema-5949	3	34	underlying	underlie	VERB
ajema-5949	3	35	algebra	algebra	NOUN
ajema-5949	3	36	.	.	PUNCT
ajema-5949	4	1	this	this	DET
ajema-5949	4	2	paper	paper	NOUN
ajema-5949	4	3	explores	explore	VERB
ajema-5949	4	4	the	the	DET
ajema-5949	4	5	role	role	NOUN
ajema-5949	4	6	of	of	ADP
ajema-5949	4	7	quantum	quantum	ADJ
ajema-5949	4	8	groups	group	NOUN
ajema-5949	4	9	in	in	ADP
ajema-5949	4	10	non	non	ADJ
ajema-5949	4	11	-	-	ADJ
ajema-5949	4	12	commutative	commutative	ADJ
ajema-5949	4	13	geometry	geometry	NOUN
ajema-5949	4	14	,	,	PUNCT
ajema-5949	4	15	focusing	focus	VERB
ajema-5949	4	16	on	on	ADP
ajema-5949	4	17	their	their	PRON
ajema-5949	4	18	algebraic	algebraic	ADJ
ajema-5949	4	19	structure	structure	NOUN
ajema-5949	4	20	,	,	PUNCT
ajema-5949	4	21	their	their	PRON
ajema-5949	4	22	relationship	relationship	NOUN
ajema-5949	4	23	to	to	ADP
ajema-5949	4	24	deformation	deformation	NOUN
ajema-5949	4	25	theory	theory	NOUN
ajema-5949	4	26	,	,	PUNCT
ajema-5949	4	27	and	and	CCONJ
ajema-5949	4	28	their	their	PRON
ajema-5949	4	29	applications	application	NOUN
ajema-5949	4	30	in	in	ADP
ajema-5949	4	31	theoretical	theoretical	ADJ
ajema-5949	4	32	physics	physics	NOUN
ajema-5949	4	33	.	.	PUNCT
ajema-5949	5	1	in	in	ADP
ajema-5949	5	2	order	order	NOUN
ajema-5949	5	3	to	to	PART
ajema-5949	5	4	better	well	ADV
ajema-5949	5	5	understand	understand	VERB
ajema-5949	5	6	how	how	SCONJ
ajema-5949	5	7	algebraic	algebraic	ADJ
ajema-5949	5	8	structures	structure	NOUN
ajema-5949	5	9	in	in	ADP
ajema-5949	5	10	non	non	ADJ
ajema-5949	5	11	-	-	ADJ
ajema-5949	5	12	commutative	commutative	ADJ
ajema-5949	5	13	geometry	geometry	NOUN
ajema-5949	5	14	can	can	AUX
ajema-5949	5	15	aid	aid	VERB
ajema-5949	5	16	in	in	ADP
ajema-5949	5	17	the	the	DET
ajema-5949	5	18	explanation	explanation	NOUN
ajema-5949	5	19	of	of	ADP
ajema-5949	5	20	quantum	quantum	NOUN
ajema-5949	5	21	phenomena	phenomenon	NOUN
ajema-5949	5	22	,	,	PUNCT
ajema-5949	5	23	this	this	DET
ajema-5949	5	24	work	work	NOUN
ajema-5949	5	25	will	will	AUX
ajema-5949	5	26	look	look	VERB
ajema-5949	5	27	at	at	ADP
ajema-5949	5	28	both	both	CCONJ
ajema-5949	5	29	the	the	DET
ajema-5949	5	30	mathematical	mathematical	ADJ
ajema-5949	5	31	characteristics	characteristic	NOUN
ajema-5949	5	32	and	and	CCONJ
ajema-5949	5	33	physical	physical	ADJ
ajema-5949	5	34	interpretations	interpretation	NOUN
ajema-5949	5	35	of	of	ADP
ajema-5949	5	36	quantum	quantum	ADJ
ajema-5949	5	37	groups	group	NOUN
ajema-5949	5	38	.	.	PUNCT
ajema-5949	6	1	keywords	keyword	NOUN
ajema-5949	6	2	:	:	PUNCT
ajema-5949	6	3	non	non	ADJ
ajema-5949	6	4	-	-	ADJ
ajema-5949	6	5	commutative	commutative	ADJ
ajema-5949	6	6	geometry	geometry	NOUN
ajema-5949	6	7	,	,	PUNCT
ajema-5949	6	8	quantum	quantum	ADJ
ajema-5949	6	9	groups	group	NOUN
ajema-5949	6	10	,	,	PUNCT
ajema-5949	6	11	algebraic	algebraic	ADJ
ajema-5949	6	12	structures	structure	NOUN
ajema-5949	6	13	,	,	PUNCT
ajema-5949	6	14	deformation	deformation	NOUN
ajema-5949	6	15	theory	theory	NOUN
ajema-5949	6	16	,	,	PUNCT
ajema-5949	6	17	quantum	quantum	ADJ
ajema-5949	6	18	physics	physics	NOUN
ajema-5949	6	19	,	,	PUNCT
ajema-5949	6	20	lie	lie	NOUN
ajema-5949	6	21	groups	group	NOUN
ajema-5949	6	22	,	,	PUNCT
ajema-5949	6	23	hopf	hopf	PROPN
ajema-5949	6	24	algebras	algebras	X
ajema-5949	6	25	.	.	PUNCT
ajema-5949	7	1	1	1	X
ajema-5949	7	2	.	.	X
ajema-5949	7	3	introduction	introduction	NOUN
ajema-5949	7	4	a	a	DET
ajema-5949	7	5	large	large	ADJ
ajema-5949	7	6	field	field	NOUN
ajema-5949	7	7	of	of	ADP
ajema-5949	7	8	study	study	NOUN
ajema-5949	7	9	known	know	VERB
ajema-5949	7	10	as	as	ADP
ajema-5949	7	11	non	non	ADJ
ajema-5949	7	12	-	-	ADJ
ajema-5949	7	13	commutative	commutative	ADJ
ajema-5949	7	14	geometry	geometry	NOUN
ajema-5949	7	15	extends	extend	VERB
ajema-5949	7	16	classical	classical	ADJ
ajema-5949	7	17	geometry	geometry	NOUN
ajema-5949	7	18	to	to	ADP
ajema-5949	7	19	situations	situation	NOUN
ajema-5949	7	20	in	in	ADP
ajema-5949	7	21	which	which	PRON
ajema-5949	7	22	the	the	DET
ajema-5949	7	23	algebra	algebra	NOUN
ajema-5949	7	24	of	of	ADP
ajema-5949	7	25	functions	function	NOUN
ajema-5949	7	26	on	on	ADP
ajema-5949	7	27	a	a	DET
ajema-5949	7	28	space	space	NOUN
ajema-5949	7	29	does	do	AUX
ajema-5949	7	30	not	not	PART
ajema-5949	7	31	commute	commute	VERB
ajema-5949	7	32	.	.	PUNCT
ajema-5949	8	1	this	this	DET
ajema-5949	8	2	method	method	NOUN
ajema-5949	8	3	,	,	PUNCT
ajema-5949	8	4	which	which	PRON
ajema-5949	8	5	was	be	AUX
ajema-5949	8	6	developed	develop	VERB
ajema-5949	8	7	by	by	ADP
ajema-5949	8	8	alain	alain	NOUN
ajema-5949	8	9	connes	conne	NOUN
ajema-5949	8	10	in	in	ADP
ajema-5949	8	11	the	the	DET
ajema-5949	8	12	1980s	1980s	NUM
ajema-5949	8	13	,	,	PUNCT
ajema-5949	8	14	offers	offer	VERB
ajema-5949	8	15	a	a	DET
ajema-5949	8	16	mathematical	mathematical	ADJ
ajema-5949	8	17	framework	framework	NOUN
ajema-5949	8	18	for	for	ADP
ajema-5949	8	19	comprehending	comprehend	VERB
ajema-5949	8	20	quantum	quantum	ADJ
ajema-5949	8	21	mechanical	mechanical	ADJ
ajema-5949	8	22	spaces	space	NOUN
ajema-5949	8	23	,	,	PUNCT
ajema-5949	8	24	especially	especially	ADV
ajema-5949	8	25	in	in	ADP
ajema-5949	8	26	situations	situation	NOUN
ajema-5949	8	27	where	where	SCONJ
ajema-5949	8	28	traditional	traditional	ADJ
ajema-5949	8	29	geometric	geometric	ADJ
ajema-5949	8	30	structures	structure	NOUN
ajema-5949	8	31	fail	fail	VERB
ajema-5949	8	32	(	(	PUNCT
ajema-5949	8	33	connes	conne	NOUN
ajema-5949	8	34	,	,	PUNCT
ajema-5949	8	35	1994	1994	NUM
ajema-5949	8	36	)	)	PUNCT
ajema-5949	8	37	.	.	PUNCT
ajema-5949	9	1	the	the	DET
ajema-5949	9	2	quantum	quantum	PROPN
ajema-5949	9	3	group	group	NOUN
ajema-5949	9	4	,	,	PUNCT
ajema-5949	9	5	a	a	DET
ajema-5949	9	6	structure	structure	NOUN
ajema-5949	9	7	that	that	PRON
ajema-5949	9	8	generalizes	generalize	VERB
ajema-5949	9	9	the	the	DET
ajema-5949	9	10	idea	idea	NOUN
ajema-5949	9	11	of	of	ADP
ajema-5949	9	12	symmetry	symmetry	NOUN
ajema-5949	9	13	groups	group	NOUN
ajema-5949	9	14	in	in	ADP
ajema-5949	9	15	a	a	DET
ajema-5949	9	16	non	non	ADJ
ajema-5949	9	17	-	-	ADJ
ajema-5949	9	18	commutative	commutative	ADJ
ajema-5949	9	19	context	context	NOUN
ajema-5949	9	20	,	,	PUNCT
ajema-5949	9	21	is	be	AUX
ajema-5949	9	22	one	one	NUM
ajema-5949	9	23	of	of	ADP
ajema-5949	9	24	the	the	DET
ajema-5949	9	25	most	most	ADV
ajema-5949	9	26	crucial	crucial	ADJ
ajema-5949	9	27	tools	tool	NOUN
ajema-5949	9	28	in	in	ADP
ajema-5949	9	29	noncommutative	noncommutative	ADJ
ajema-5949	9	30	geometry	geometry	NOUN
ajema-5949	9	31	.	.	PUNCT
ajema-5949	10	1	quantum	quantum	ADJ
ajema-5949	10	2	groups	group	NOUN
ajema-5949	10	3	,	,	PUNCT
ajema-5949	10	4	which	which	PRON
ajema-5949	10	5	may	may	AUX
ajema-5949	10	6	be	be	AUX
ajema-5949	10	7	thought	think	VERB
ajema-5949	10	8	of	of	ADP
ajema-5949	10	9	as	as	ADP
ajema-5949	10	10	deformations	deformation	NOUN
ajema-5949	10	11	of	of	ADP
ajema-5949	10	12	classical	classical	ADJ
ajema-5949	10	13	lie	lie	NOUN
ajema-5949	10	14	groups	group	NOUN
ajema-5949	10	15	,	,	PUNCT
ajema-5949	10	16	are	be	AUX
ajema-5949	10	17	strongly	strongly	ADV
ajema-5949	10	18	connected	connect	VERB
ajema-5949	10	19	to	to	ADP
ajema-5949	10	20	the	the	DET
ajema-5949	10	21	theory	theory	NOUN
ajema-5949	10	22	of	of	ADP
ajema-5949	10	23	hopf	hopf	ADJ
ajema-5949	10	24	algebras	algebra	NOUN
ajema-5949	10	25	.	.	PUNCT
ajema-5949	11	1	this	this	DET
ajema-5949	11	2	paper	paper	NOUN
ajema-5949	11	3	aims	aim	VERB
ajema-5949	11	4	to	to	PART
ajema-5949	11	5	explore	explore	VERB
ajema-5949	11	6	the	the	DET
ajema-5949	11	7	algebraic	algebraic	ADJ
ajema-5949	11	8	structures	structure	NOUN
ajema-5949	11	9	of	of	ADP
ajema-5949	11	10	quantum	quantum	ADJ
ajema-5949	11	11	groups	group	NOUN
ajema-5949	11	12	within	within	ADP
ajema-5949	11	13	the	the	DET
ajema-5949	11	14	context	context	NOUN
ajema-5949	11	15	of	of	ADP
ajema-5949	11	16	noncommutative	noncommutative	ADJ
ajema-5949	11	17	geometry	geometry	NOUN
ajema-5949	11	18	,	,	PUNCT
ajema-5949	11	19	analyzing	analyze	VERB
ajema-5949	11	20	their	their	PRON
ajema-5949	11	21	mathematical	mathematical	ADJ
ajema-5949	11	22	properties	property	NOUN
ajema-5949	11	23	and	and	CCONJ
ajema-5949	11	24	discussing	discuss	VERB
ajema-5949	11	25	their	their	PRON
ajema-5949	11	26	relevance	relevance	NOUN
ajema-5949	11	27	to	to	ADP
ajema-5949	11	28	quantum	quantum	ADJ
ajema-5949	11	29	theory	theory	NOUN
ajema-5949	11	30	.	.	PUNCT
ajema-5949	12	1	we	we	PRON
ajema-5949	12	2	will	will	AUX
ajema-5949	12	3	examine	examine	VERB
ajema-5949	12	4	how	how	SCONJ
ajema-5949	12	5	these	these	DET
ajema-5949	12	6	groups	group	NOUN
ajema-5949	12	7	arise	arise	VERB
ajema-5949	12	8	from	from	ADP
ajema-5949	12	9	the	the	DET
ajema-5949	12	10	deformation	deformation	NOUN
ajema-5949	12	11	of	of	ADP
ajema-5949	12	12	classical	classical	ADJ
ajema-5949	12	13	symmetries	symmetry	NOUN
ajema-5949	12	14	,	,	PUNCT
ajema-5949	12	15	their	their	PRON
ajema-5949	12	16	algebraic	algebraic	ADJ
ajema-5949	12	17	properties	property	NOUN
ajema-5949	12	18	,	,	PUNCT
ajema-5949	12	19	and	and	CCONJ
ajema-5949	12	20	their	their	PRON
ajema-5949	12	21	applications	application	NOUN
ajema-5949	12	22	in	in	ADP
ajema-5949	12	23	both	both	PRON
ajema-5949	12	24	mathematics	mathematic	NOUN
ajema-5949	12	25	and	and	CCONJ
ajema-5949	12	26	theoretical	theoretical	ADJ
ajema-5949	12	27	physics	physics	NOUN
ajema-5949	12	28	.	.	PUNCT
ajema-5949	13	1	2	2	X
ajema-5949	13	2	.	.	X
ajema-5949	13	3	quantum	quantum	ADJ
ajema-5949	13	4	groups	group	NOUN
ajema-5949	13	5	and	and	CCONJ
ajema-5949	13	6	non	non	ADJ
ajema-5949	13	7	-	-	ADJ
ajema-5949	13	8	commutative	commutative	ADJ
ajema-5949	13	9	geometry	geometry	NOUN
ajema-5949	13	10	drinfeld	drinfeld	VERB
ajema-5949	13	11	(	(	PUNCT
ajema-5949	13	12	1986	1986	NUM
ajema-5949	13	13	)	)	PUNCT
ajema-5949	13	14	and	and	CCONJ
ajema-5949	13	15	jimbo	jimbo	PROPN
ajema-5949	13	16	(	(	PUNCT
ajema-5949	13	17	1985	1985	NUM
ajema-5949	13	18	)	)	PUNCT
ajema-5949	13	19	introduced	introduce	VERB
ajema-5949	13	20	quantum	quantum	ADJ
ajema-5949	13	21	groups	group	NOUN
ajema-5949	13	22	in	in	ADP
ajema-5949	13	23	their	their	PRON
ajema-5949	13	24	work	work	NOUN
ajema-5949	13	25	on	on	ADP
ajema-5949	13	26	the	the	DET
ajema-5949	13	27	deformation	deformation	NOUN
ajema-5949	13	28	of	of	ADP
ajema-5949	13	29	the	the	DET
ajema-5949	13	30	classical	classical	ADJ
ajema-5949	13	31	universal	universal	ADJ
ajema-5949	13	32	enveloping	enveloping	NOUN
ajema-5949	13	33	algebras	algebra	NOUN
ajema-5949	13	34	of	of	ADP
ajema-5949	13	35	lie	lie	NOUN
ajema-5949	13	36	algebras	algebra	NOUN
ajema-5949	13	37	.	.	PUNCT
ajema-5949	14	1	in	in	ADP
ajema-5949	14	2	the	the	DET
ajema-5949	14	3	context	context	NOUN
ajema-5949	14	4	of	of	ADP
ajema-5949	14	5	non	non	ADJ
ajema-5949	14	6	-	-	ADJ
ajema-5949	14	7	commutative	commutative	ADJ
ajema-5949	14	8	geometry	geometry	NOUN
ajema-5949	14	9	,	,	PUNCT
ajema-5949	14	10	quantum	quantum	ADJ
ajema-5949	14	11	groups	group	NOUN
ajema-5949	14	12	are	be	AUX
ajema-5949	14	13	often	often	ADV
ajema-5949	14	14	studied	study	VERB
ajema-5949	14	15	as	as	ADP
ajema-5949	14	16	deformations	deformation	NOUN
ajema-5949	14	17	of	of	ADP
ajema-5949	14	18	the	the	DET
ajema-5949	14	19	symmetry	symmetry	NOUN
ajema-5949	14	20	groups	group	NOUN
ajema-5949	14	21	associated	associate	VERB
ajema-5949	14	22	to	to	ADP
ajema-5949	14	23	spaces	space	NOUN
ajema-5949	14	24	where	where	SCONJ
ajema-5949	14	25	the	the	DET
ajema-5949	14	26	coordinates	coordinate	NOUN
ajema-5949	14	27	do	do	AUX
ajema-5949	14	28	not	not	PART
ajema-5949	14	29	commute	commute	VERB
ajema-5949	14	30	.	.	PUNCT
ajema-5949	15	1	these	these	DET
ajema-5949	15	2	deformations	deformation	NOUN
ajema-5949	15	3	arise	arise	VERB
ajema-5949	15	4	naturally	naturally	ADV
ajema-5949	15	5	in	in	ADP
ajema-5949	15	6	the	the	DET
ajema-5949	15	7	study	study	NOUN
ajema-5949	15	8	245	245	NUM
ajema-5949	15	9	journal	journal	NOUN
ajema-5949	15	10	of	of	ADP
ajema-5949	15	11	engineering	engineering	NOUN
ajema-5949	15	12	,	,	PUNCT
ajema-5949	15	13	mechanics	mechanic	NOUN
ajema-5949	15	14	and	and	CCONJ
ajema-5949	15	15	architecture	architecture	NOUN
ajema-5949	15	16	www	www	NOUN
ajema-5949	15	17	.	.	PUNCT
ajema-5949	16	1	grnjournal.us	grnjournal.us	X
ajema-5949	16	2	of	of	ADP
ajema-5949	16	3	quantum	quantum	ADJ
ajema-5949	16	4	spaces	space	NOUN
ajema-5949	16	5	,	,	PUNCT
ajema-5949	16	6	where	where	SCONJ
ajema-5949	16	7	the	the	DET
ajema-5949	16	8	classical	classical	ADJ
ajema-5949	16	9	concept	concept	NOUN
ajema-5949	16	10	of	of	ADP
ajema-5949	16	11	a	a	DET
ajema-5949	16	12	group	group	NOUN
ajema-5949	16	13	is	be	AUX
ajema-5949	16	14	replaced	replace	VERB
ajema-5949	16	15	by	by	ADP
ajema-5949	16	16	an	an	DET
ajema-5949	16	17	algebraic	algebraic	ADJ
ajema-5949	16	18	structure	structure	NOUN
ajema-5949	16	19	that	that	PRON
ajema-5949	16	20	incorporates	incorporate	VERB
ajema-5949	16	21	both	both	CCONJ
ajema-5949	16	22	the	the	DET
ajema-5949	16	23	algebraic	algebraic	ADJ
ajema-5949	16	24	and	and	CCONJ
ajema-5949	16	25	co	co	ADJ
ajema-5949	16	26	-	-	ADJ
ajema-5949	16	27	algebraic	algebraic	ADJ
ajema-5949	16	28	properties	property	NOUN
ajema-5949	16	29	of	of	ADP
ajema-5949	16	30	the	the	DET
ajema-5949	16	31	underlying	underlying	ADJ
ajema-5949	16	32	space	space	NOUN
ajema-5949	16	33	.	.	PUNCT
ajema-5949	17	1	quantum	quantum	ADJ
ajema-5949	17	2	groups	group	NOUN
ajema-5949	17	3	and	and	CCONJ
ajema-5949	17	4	non	non	ADJ
ajema-5949	17	5	-	-	ADJ
ajema-5949	17	6	commutative	commutative	ADJ
ajema-5949	17	7	geometry	geometry	NOUN
ajema-5949	17	8	represent	represent	VERB
ajema-5949	17	9	advanced	advanced	ADJ
ajema-5949	17	10	concepts	concept	NOUN
ajema-5949	17	11	in	in	ADP
ajema-5949	17	12	modern	modern	ADJ
ajema-5949	17	13	mathematics	mathematic	NOUN
ajema-5949	17	14	and	and	CCONJ
ajema-5949	17	15	theoretical	theoretical	ADJ
ajema-5949	17	16	physics	physics	NOUN
ajema-5949	17	17	,	,	PUNCT
ajema-5949	17	18	expanding	expand	VERB
ajema-5949	17	19	classical	classical	ADJ
ajema-5949	17	20	structures	structure	NOUN
ajema-5949	17	21	into	into	ADP
ajema-5949	17	22	the	the	DET
ajema-5949	17	23	quantum	quantum	ADJ
ajema-5949	17	24	realm	realm	NOUN
ajema-5949	17	25	.	.	PUNCT
ajema-5949	18	1	both	both	DET
ajema-5949	18	2	fields	field	NOUN
ajema-5949	18	3	are	be	AUX
ajema-5949	18	4	essential	essential	ADJ
ajema-5949	18	5	for	for	ADP
ajema-5949	18	6	understanding	understand	VERB
ajema-5949	18	7	the	the	DET
ajema-5949	18	8	algebraic	algebraic	ADJ
ajema-5949	18	9	and	and	CCONJ
ajema-5949	18	10	geometric	geometric	ADJ
ajema-5949	18	11	structures	structure	NOUN
ajema-5949	18	12	that	that	PRON
ajema-5949	18	13	come	come	VERB
ajema-5949	18	14	up	up	ADP
ajema-5949	18	15	in	in	ADP
ajema-5949	18	16	relation	relation	NOUN
ajema-5949	18	17	to	to	ADP
ajema-5949	18	18	quantum	quantum	ADJ
ajema-5949	18	19	gravity	gravity	NOUN
ajema-5949	18	20	,	,	PUNCT
ajema-5949	18	21	quantum	quantum	ADJ
ajema-5949	18	22	field	field	NOUN
ajema-5949	18	23	theory	theory	NOUN
ajema-5949	18	24	,	,	PUNCT
ajema-5949	18	25	and	and	CCONJ
ajema-5949	18	26	quantum	quantum	NOUN
ajema-5949	18	27	mechanics	mechanic	NOUN
ajema-5949	18	28	.	.	PUNCT
ajema-5949	19	1	non	non	ADJ
ajema-5949	19	2	-	-	ADJ
ajema-5949	19	3	commutative	commutative	ADJ
ajema-5949	19	4	geometry	geometry	NOUN
ajema-5949	19	5	is	be	AUX
ajema-5949	19	6	a	a	DET
ajema-5949	19	7	generalization	generalization	NOUN
ajema-5949	19	8	of	of	ADP
ajema-5949	19	9	classical	classical	ADJ
ajema-5949	19	10	geometry	geometry	NOUN
ajema-5949	19	11	,	,	PUNCT
ajema-5949	19	12	and	and	CCONJ
ajema-5949	19	13	quantum	quantum	ADJ
ajema-5949	19	14	groups	group	NOUN
ajema-5949	19	15	are	be	AUX
ajema-5949	19	16	deformations	deformation	NOUN
ajema-5949	19	17	of	of	ADP
ajema-5949	19	18	classical	classical	ADJ
ajema-5949	19	19	lie	lie	NOUN
ajema-5949	19	20	groups	group	NOUN
ajema-5949	19	21	,	,	PUNCT
ajema-5949	19	22	offer	offer	VERB
ajema-5949	19	23	a	a	DET
ajema-5949	19	24	rigorous	rigorous	ADJ
ajema-5949	19	25	framework	framework	NOUN
ajema-5949	19	26	for	for	ADP
ajema-5949	19	27	studying	study	VERB
ajema-5949	19	28	spaces	space	NOUN
ajema-5949	19	29	where	where	SCONJ
ajema-5949	19	30	classical	classical	ADJ
ajema-5949	19	31	assumptions	assumption	NOUN
ajema-5949	19	32	of	of	ADP
ajema-5949	19	33	commutative	commutative	ADJ
ajema-5949	19	34	operations	operation	NOUN
ajema-5949	19	35	no	no	ADV
ajema-5949	19	36	longer	long	ADV
ajema-5949	19	37	hold	hold	VERB
ajema-5949	19	38	.	.	PUNCT
ajema-5949	20	1	2.1	2.1	NUM
ajema-5949	20	2	quantum	quantum	NOUN
ajema-5949	20	3	groups	group	NOUN
ajema-5949	20	4	the	the	DET
ajema-5949	20	5	idea	idea	NOUN
ajema-5949	20	6	of	of	ADP
ajema-5949	20	7	lie	lie	NOUN
ajema-5949	20	8	groups	group	NOUN
ajema-5949	20	9	is	be	AUX
ajema-5949	20	10	extended	extend	VERB
ajema-5949	20	11	to	to	ADP
ajema-5949	20	12	the	the	DET
ajema-5949	20	13	non	non	ADJ
ajema-5949	20	14	-	-	ADJ
ajema-5949	20	15	commutative	commutative	ADJ
ajema-5949	20	16	setting	setting	NOUN
ajema-5949	20	17	by	by	ADP
ajema-5949	20	18	quantum	quantum	ADJ
ajema-5949	20	19	groups	group	NOUN
ajema-5949	20	20	,	,	PUNCT
ajema-5949	20	21	which	which	PRON
ajema-5949	20	22	are	be	AUX
ajema-5949	20	23	mathematical	mathematical	ADJ
ajema-5949	20	24	structures	structure	NOUN
ajema-5949	20	25	.	.	PUNCT
ajema-5949	21	1	they	they	PRON
ajema-5949	21	2	were	be	AUX
ajema-5949	21	3	first	first	ADV
ajema-5949	21	4	presented	present	VERB
ajema-5949	21	5	as	as	ADP
ajema-5949	21	6	"	"	PUNCT
ajema-5949	21	7	deformations	deformation	NOUN
ajema-5949	21	8	"	"	PUNCT
ajema-5949	21	9	of	of	ADP
ajema-5949	21	10	classical	classical	ADJ
ajema-5949	21	11	lie	lie	NOUN
ajema-5949	21	12	groups	group	NOUN
ajema-5949	21	13	in	in	ADP
ajema-5949	21	14	the	the	DET
ajema-5949	21	15	middle	middle	NOUN
ajema-5949	21	16	of	of	ADP
ajema-5949	21	17	the	the	DET
ajema-5949	21	18	1980s	1980s	NUM
ajema-5949	21	19	by	by	ADP
ajema-5949	21	20	jimbo	jimbo	PROPN
ajema-5949	21	21	(	(	PUNCT
ajema-5949	21	22	1985	1985	NUM
ajema-5949	21	23	)	)	PUNCT
ajema-5949	21	24	and	and	CCONJ
ajema-5949	21	25	drinfeld	drinfeld	VERB
ajema-5949	21	26	(	(	PUNCT
ajema-5949	21	27	1986	1986	NUM
ajema-5949	21	28	)	)	PUNCT
ajema-5949	21	29	,	,	PUNCT
ajema-5949	21	30	specifically	specifically	ADV
ajema-5949	21	31	by	by	ADP
ajema-5949	21	32	deforming	deform	VERB
ajema-5949	21	33	the	the	DET
ajema-5949	21	34	universal	universal	ADJ
ajema-5949	21	35	enveloping	enveloping	NOUN
ajema-5949	21	36	algebras	algebra	NOUN
ajema-5949	21	37	of	of	ADP
ajema-5949	21	38	lie	lie	NOUN
ajema-5949	21	39	algebras	algebra	NOUN
ajema-5949	21	40	.	.	PUNCT
ajema-5949	22	1	quantum	quantum	ADJ
ajema-5949	22	2	groups	group	NOUN
ajema-5949	22	3	may	may	AUX
ajema-5949	22	4	be	be	AUX
ajema-5949	22	5	thought	think	VERB
ajema-5949	22	6	of	of	ADP
ajema-5949	22	7	as	as	ADP
ajema-5949	22	8	an	an	DET
ajema-5949	22	9	extension	extension	NOUN
ajema-5949	22	10	of	of	ADP
ajema-5949	22	11	symmetry	symmetry	NOUN
ajema-5949	22	12	groups	group	NOUN
ajema-5949	22	13	by	by	ADP
ajema-5949	22	14	replacing	replace	VERB
ajema-5949	22	15	the	the	DET
ajema-5949	22	16	usual	usual	ADJ
ajema-5949	22	17	commutative	commutative	ADJ
ajema-5949	22	18	connections	connection	NOUN
ajema-5949	22	19	between	between	ADP
ajema-5949	22	20	group	group	NOUN
ajema-5949	22	21	components	component	NOUN
ajema-5949	22	22	with	with	ADP
ajema-5949	22	23	distorted	distorted	ADJ
ajema-5949	22	24	,	,	PUNCT
ajema-5949	22	25	non	non	ADJ
ajema-5949	22	26	-	-	ADJ
ajema-5949	22	27	commutative	commutative	ADJ
ajema-5949	22	28	algebraic	algebraic	ADJ
ajema-5949	22	29	interactions	interaction	NOUN
ajema-5949	22	30	(	(	PUNCT
ajema-5949	22	31	chari	chari	PROPN
ajema-5949	22	32	&	&	CCONJ
ajema-5949	22	33	pressley	pressley	PROPN
ajema-5949	22	34	,	,	PUNCT
ajema-5949	22	35	1994	1994	NUM
ajema-5949	22	36	)	)	PUNCT
ajema-5949	22	37	.	.	PUNCT
ajema-5949	23	1	a	a	DET
ajema-5949	23	2	hopf	hopf	ADJ
ajema-5949	23	3	algebra	algebra	NOUN
ajema-5949	23	4	,	,	PUNCT
ajema-5949	23	5	which	which	PRON
ajema-5949	23	6	has	have	VERB
ajema-5949	23	7	both	both	CCONJ
ajema-5949	23	8	algebraic	algebraic	ADJ
ajema-5949	23	9	and	and	CCONJ
ajema-5949	23	10	co	co	ADJ
ajema-5949	23	11	-	-	ADJ
ajema-5949	23	12	algebraic	algebraic	ADJ
ajema-5949	23	13	properties	property	NOUN
ajema-5949	23	14	,	,	PUNCT
ajema-5949	23	15	is	be	AUX
ajema-5949	23	16	a	a	DET
ajema-5949	23	17	common	common	ADJ
ajema-5949	23	18	formal	formal	ADJ
ajema-5949	23	19	definition	definition	NOUN
ajema-5949	23	20	of	of	ADP
ajema-5949	23	21	a	a	DET
ajema-5949	23	22	quantum	quantum	NOUN
ajema-5949	23	23	group	group	NOUN
ajema-5949	23	24	.	.	PUNCT
ajema-5949	24	1	multiplication	multiplication	NOUN
ajema-5949	24	2	,	,	PUNCT
ajema-5949	24	3	unit	unit	NOUN
ajema-5949	24	4	,	,	PUNCT
ajema-5949	24	5	co	co	NOUN
ajema-5949	24	6	-	-	NOUN
ajema-5949	24	7	multiplication	multiplication	NOUN
ajema-5949	24	8	,	,	PUNCT
ajema-5949	24	9	co	co	NOUN
ajema-5949	24	10	-	-	NOUN
ajema-5949	24	11	unit	unit	NOUN
ajema-5949	24	12	,	,	PUNCT
ajema-5949	24	13	and	and	CCONJ
ajema-5949	24	14	antipode	antipode	NOUN
ajema-5949	24	15	are	be	AUX
ajema-5949	24	16	the	the	DET
ajema-5949	24	17	operations	operation	NOUN
ajema-5949	24	18	that	that	PRON
ajema-5949	24	19	make	make	VERB
ajema-5949	24	20	up	up	ADP
ajema-5949	24	21	the	the	DET
ajema-5949	24	22	hopf	hopf	ADJ
ajema-5949	24	23	algebra	algebra	NOUN
ajema-5949	24	24	structure	structure	NOUN
ajema-5949	24	25	.	.	PUNCT
ajema-5949	25	1	it	it	PRON
ajema-5949	25	2	is	be	AUX
ajema-5949	25	3	possible	possible	ADJ
ajema-5949	25	4	to	to	PART
ajema-5949	25	5	consider	consider	VERB
ajema-5949	25	6	quantum	quantum	ADJ
ajema-5949	25	7	groups	group	NOUN
ajema-5949	25	8	as	as	ADP
ajema-5949	25	9	a	a	DET
ajema-5949	25	10	logical	logical	ADJ
ajema-5949	25	11	extension	extension	NOUN
ajema-5949	25	12	of	of	ADP
ajema-5949	25	13	classical	classical	ADJ
ajema-5949	25	14	symmetry	symmetry	NOUN
ajema-5949	25	15	groups	group	NOUN
ajema-5949	25	16	into	into	ADP
ajema-5949	25	17	the	the	DET
ajema-5949	25	18	quantum	quantum	ADJ
ajema-5949	25	19	realm	realm	NOUN
ajema-5949	25	20	as	as	SCONJ
ajema-5949	25	21	these	these	DET
ajema-5949	25	22	operations	operation	NOUN
ajema-5949	25	23	are	be	AUX
ajema-5949	25	24	non	non	ADJ
ajema-5949	25	25	-	-	ADJ
ajema-5949	25	26	commutative	commutative	ADJ
ajema-5949	25	27	and	and	CCONJ
ajema-5949	25	28	compatible	compatible	ADJ
ajema-5949	25	29	with	with	ADP
ajema-5949	25	30	the	the	DET
ajema-5949	25	31	distorted	distorted	ADJ
ajema-5949	25	32	symmetries	symmetry	NOUN
ajema-5949	25	33	of	of	ADP
ajema-5949	25	34	classical	classical	ADJ
ajema-5949	25	35	groups	group	NOUN
ajema-5949	25	36	.	.	PUNCT
ajema-5949	26	1	in	in	ADP
ajema-5949	26	2	particular	particular	ADJ
ajema-5949	26	3	,	,	PUNCT
ajema-5949	26	4	quantum	quantum	ADJ
ajema-5949	26	5	groups	group	NOUN
ajema-5949	26	6	are	be	AUX
ajema-5949	26	7	described	describe	VERB
ajema-5949	26	8	by	by	ADP
ajema-5949	26	9	a	a	DET
ajema-5949	26	10	parameter	parameter	NOUN
ajema-5949	26	11	q	q	NOUN
ajema-5949	26	12	(	(	PUNCT
ajema-5949	26	13	often	often	ADV
ajema-5949	26	14	referred	refer	VERB
ajema-5949	26	15	to	to	ADP
ajema-5949	26	16	as	as	ADP
ajema-5949	26	17	the	the	DET
ajema-5949	26	18	deformation	deformation	NOUN
ajema-5949	26	19	parameter	parameter	NOUN
ajema-5949	26	20	)	)	PUNCT
ajema-5949	26	21	,	,	PUNCT
ajema-5949	26	22	which	which	PRON
ajema-5949	26	23	controls	control	VERB
ajema-5949	26	24	the	the	DET
ajema-5949	26	25	degree	degree	NOUN
ajema-5949	26	26	of	of	ADP
ajema-5949	26	27	non	non	NOUN
ajema-5949	26	28	-	-	NOUN
ajema-5949	26	29	commutativity	commutativity	NOUN
ajema-5949	26	30	.	.	PUNCT
ajema-5949	27	1	when	when	SCONJ
ajema-5949	27	2	q=1	q=1	X
ajema-5949	27	3	,	,	PUNCT
ajema-5949	27	4	the	the	DET
ajema-5949	27	5	quantum	quantum	NOUN
ajema-5949	27	6	group	group	NOUN
ajema-5949	27	7	reduces	reduce	VERB
ajema-5949	27	8	to	to	ADP
ajema-5949	27	9	its	its	PRON
ajema-5949	27	10	classical	classical	ADJ
ajema-5949	27	11	counterpart	counterpart	NOUN
ajema-5949	27	12	.	.	PUNCT
ajema-5949	28	1	for	for	ADP
ajema-5949	28	2	instance	instance	NOUN
ajema-5949	28	3	,	,	PUNCT
ajema-5949	28	4	is	be	AUX
ajema-5949	28	5	a	a	DET
ajema-5949	28	6	quantum	quantum	ADJ
ajema-5949	28	7	deformation	deformation	NOUN
ajema-5949	28	8	of	of	ADP
ajema-5949	28	9	the	the	DET
ajema-5949	28	10	universal	universal	ADJ
ajema-5949	28	11	enveloping	enveloping	NOUN
ajema-5949	28	12	algebra	algebra	NOUN
ajema-5949	28	13	of	of	ADP
ajema-5949	28	14	a	a	DET
ajema-5949	28	15	lie	lie	NOUN
ajema-5949	28	16	algebra	algebra	NOUN
ajema-5949	28	17	g	g	PROPN
ajema-5949	28	18	,	,	PUNCT
ajema-5949	28	19	where	where	SCONJ
ajema-5949	28	20	the	the	DET
ajema-5949	28	21	classical	classical	ADJ
ajema-5949	28	22	lie	lie	NOUN
ajema-5949	28	23	algebra	algebra	NOUN
ajema-5949	28	24	is	be	AUX
ajema-5949	28	25	recovered	recover	VERB
ajema-5949	28	26	as	as	ADP
ajema-5949	28	27	q→1	q→1	PUNCT
ajema-5949	28	28	(	(	PUNCT
ajema-5949	28	29	drinfeld	drinfeld	PROPN
ajema-5949	28	30	,	,	PUNCT
ajema-5949	28	31	1986	1986	NUM
ajema-5949	28	32	)	)	PUNCT
ajema-5949	28	33	.	.	PUNCT
ajema-5949	29	1	when	when	SCONJ
ajema-5949	29	2	studying	study	VERB
ajema-5949	29	3	quantum	quantum	NOUN
ajema-5949	29	4	systems	system	NOUN
ajema-5949	29	5	that	that	PRON
ajema-5949	29	6	need	need	VERB
ajema-5949	29	7	a	a	DET
ajema-5949	29	8	non	non	ADJ
ajema-5949	29	9	-	-	ADJ
ajema-5949	29	10	commutative	commutative	ADJ
ajema-5949	29	11	framework	framework	NOUN
ajema-5949	29	12	,	,	PUNCT
ajema-5949	29	13	like	like	ADP
ajema-5949	29	14	those	those	PRON
ajema-5949	29	15	in	in	ADP
ajema-5949	29	16	statistical	statistical	ADJ
ajema-5949	29	17	mechanics	mechanic	NOUN
ajema-5949	29	18	,	,	PUNCT
ajema-5949	29	19	quantum	quantum	ADJ
ajema-5949	29	20	field	field	NOUN
ajema-5949	29	21	theory	theory	NOUN
ajema-5949	29	22	,	,	PUNCT
ajema-5949	29	23	and	and	CCONJ
ajema-5949	29	24	integrable	integrable	ADJ
ajema-5949	29	25	systems	system	NOUN
ajema-5949	29	26	,	,	PUNCT
ajema-5949	29	27	quantum	quantum	NOUN
ajema-5949	29	28	groups	group	NOUN
ajema-5949	29	29	have	have	AUX
ajema-5949	29	30	emerged	emerge	VERB
ajema-5949	29	31	as	as	ADP
ajema-5949	29	32	a	a	DET
ajema-5949	29	33	crucial	crucial	ADJ
ajema-5949	29	34	tool	tool	NOUN
ajema-5949	29	35	(	(	PUNCT
ajema-5949	29	36	chari	chari	PROPN
ajema-5949	29	37	&	&	CCONJ
ajema-5949	29	38	pressley	pressley	PROPN
ajema-5949	29	39	,	,	PUNCT
ajema-5949	29	40	1994	1994	NUM
ajema-5949	29	41	)	)	PUNCT
ajema-5949	29	42	.	.	PUNCT
ajema-5949	30	1	the	the	DET
ajema-5949	30	2	symmetries	symmetry	NOUN
ajema-5949	30	3	of	of	ADP
ajema-5949	30	4	quantum	quantum	ADJ
ajema-5949	30	5	spaces	space	NOUN
ajema-5949	30	6	,	,	PUNCT
ajema-5949	30	7	which	which	PRON
ajema-5949	30	8	are	be	AUX
ajema-5949	30	9	essential	essential	ADJ
ajema-5949	30	10	to	to	ADP
ajema-5949	30	11	comprehending	comprehend	VERB
ajema-5949	30	12	spin	spin	NOUN
ajema-5949	30	13	systems	system	NOUN
ajema-5949	30	14	,	,	PUNCT
ajema-5949	30	15	particle	particle	NOUN
ajema-5949	30	16	interactions	interaction	NOUN
ajema-5949	30	17	,	,	PUNCT
ajema-5949	30	18	and	and	CCONJ
ajema-5949	30	19	quantum	quantum	NOUN
ajema-5949	30	20	gravity	gravity	NOUN
ajema-5949	30	21	,	,	PUNCT
ajema-5949	30	22	can	can	AUX
ajema-5949	30	23	be	be	AUX
ajema-5949	30	24	expressed	express	VERB
ajema-5949	30	25	algebraically	algebraically	ADV
ajema-5949	30	26	thanks	thank	NOUN
ajema-5949	30	27	to	to	ADP
ajema-5949	30	28	them	they	PRON
ajema-5949	30	29	.	.	PUNCT
ajema-5949	31	1	2.2	2.2	NUM
ajema-5949	31	2	non	non	ADJ
ajema-5949	31	3	-	-	ADJ
ajema-5949	31	4	commutative	commutative	ADJ
ajema-5949	31	5	geometry	geometry	NOUN
ajema-5949	31	6	a	a	DET
ajema-5949	31	7	mathematical	mathematical	ADJ
ajema-5949	31	8	framework	framework	NOUN
ajema-5949	31	9	known	know	VERB
ajema-5949	31	10	as	as	ADP
ajema-5949	31	11	non	non	ADJ
ajema-5949	31	12	-	-	ADJ
ajema-5949	31	13	commutative	commutative	ADJ
ajema-5949	31	14	geometry	geometry	NOUN
ajema-5949	31	15	extends	extend	VERB
ajema-5949	31	16	classical	classical	ADJ
ajema-5949	31	17	geometry	geometry	NOUN
ajema-5949	31	18	to	to	ADP
ajema-5949	31	19	situations	situation	NOUN
ajema-5949	31	20	in	in	ADP
ajema-5949	31	21	which	which	PRON
ajema-5949	31	22	the	the	DET
ajema-5949	31	23	space	space	NOUN
ajema-5949	31	24	's	's	PART
ajema-5949	31	25	coordinates	coordinate	NOUN
ajema-5949	31	26	do	do	AUX
ajema-5949	31	27	not	not	PART
ajema-5949	31	28	commute	commute	VERB
ajema-5949	31	29	.	.	PUNCT
ajema-5949	32	1	this	this	DET
ajema-5949	32	2	concept	concept	NOUN
ajema-5949	32	3	has	have	AUX
ajema-5949	32	4	been	be	AUX
ajema-5949	32	5	a	a	DET
ajema-5949	32	6	central	central	ADJ
ajema-5949	32	7	area	area	NOUN
ajema-5949	32	8	of	of	ADP
ajema-5949	32	9	study	study	NOUN
ajema-5949	32	10	in	in	ADP
ajema-5949	32	11	mathematics	mathematics	PROPN
ajema-5949	32	12	and	and	CCONJ
ajema-5949	32	13	physics	physics	NOUN
ajema-5949	32	14	since	since	SCONJ
ajema-5949	32	15	it	it	PRON
ajema-5949	32	16	was	be	AUX
ajema-5949	32	17	first	first	ADV
ajema-5949	32	18	proposed	propose	VERB
ajema-5949	32	19	by	by	ADP
ajema-5949	32	20	alain	alain	PROPN
ajema-5949	32	21	connes	conne	NOUN
ajema-5949	32	22	in	in	ADP
ajema-5949	32	23	1994	1994	NUM
ajema-5949	32	24	.	.	PUNCT
ajema-5949	33	1	noncommutative	noncommutative	ADJ
ajema-5949	33	2	geometry	geometry	NOUN
ajema-5949	33	3	generates	generate	VERB
ajema-5949	33	4	novel	novel	ADJ
ajema-5949	33	5	symmetry	symmetry	NOUN
ajema-5949	33	6	and	and	CCONJ
ajema-5949	33	7	geometric	geometric	ADJ
ajema-5949	33	8	structures	structure	NOUN
ajema-5949	33	9	that	that	PRON
ajema-5949	33	10	are	be	AUX
ajema-5949	33	11	not	not	PART
ajema-5949	33	12	able	able	ADJ
ajema-5949	33	13	to	to	PART
ajema-5949	33	14	be	be	AUX
ajema-5949	33	15	described	describe	VERB
ajema-5949	33	16	by	by	ADP
ajema-5949	33	17	conventional	conventional	ADJ
ajema-5949	33	18	geometry	geometry	NOUN
ajema-5949	33	19	by	by	ADP
ajema-5949	33	20	replacing	replace	VERB
ajema-5949	33	21	the	the	DET
ajema-5949	33	22	commutative	commutative	ADJ
ajema-5949	33	23	algebra	algebra	NOUN
ajema-5949	33	24	of	of	ADP
ajema-5949	33	25	functions	function	NOUN
ajema-5949	33	26	on	on	ADP
ajema-5949	33	27	a	a	DET
ajema-5949	33	28	space	space	NOUN
ajema-5949	33	29	with	with	ADP
ajema-5949	33	30	a	a	DET
ajema-5949	33	31	non	non	ADJ
ajema-5949	33	32	-	-	ADJ
ajema-5949	33	33	commutative	commutative	ADJ
ajema-5949	33	34	algebra	algebra	NOUN
ajema-5949	33	35	.	.	PUNCT
ajema-5949	34	1	points	point	NOUN
ajema-5949	34	2	in	in	ADP
ajema-5949	34	3	space	space	NOUN
ajema-5949	34	4	are	be	AUX
ajema-5949	34	5	linked	link	VERB
ajema-5949	34	6	to	to	ADP
ajema-5949	34	7	commutative	commutative	ADJ
ajema-5949	34	8	coordinates	coordinate	NOUN
ajema-5949	34	9	in	in	ADP
ajema-5949	34	10	classical	classical	ADJ
ajema-5949	34	11	geometry	geometry	NOUN
ajema-5949	34	12	,	,	PUNCT
ajema-5949	34	13	which	which	PRON
ajema-5949	34	14	means	mean	VERB
ajema-5949	34	15	that	that	SCONJ
ajema-5949	34	16	the	the	DET
ajema-5949	34	17	order	order	NOUN
ajema-5949	34	18	in	in	ADP
ajema-5949	34	19	which	which	PRON
ajema-5949	34	20	two	two	NUM
ajema-5949	34	21	coordinates	coordinate	NOUN
ajema-5949	34	22	are	be	AUX
ajema-5949	34	23	multiplied	multiply	VERB
ajema-5949	34	24	does	do	AUX
ajema-5949	34	25	not	not	PART
ajema-5949	34	26	affect	affect	VERB
ajema-5949	34	27	the	the	DET
ajema-5949	34	28	result	result	NOUN
ajema-5949	34	29	.	.	PUNCT
ajema-5949	35	1	this	this	DET
ajema-5949	35	2	commutativity	commutativity	NOUN
ajema-5949	35	3	assumption	assumption	NOUN
ajema-5949	35	4	,	,	PUNCT
ajema-5949	35	5	however	however	ADV
ajema-5949	35	6	,	,	PUNCT
ajema-5949	35	7	is	be	AUX
ajema-5949	35	8	violated	violate	VERB
ajema-5949	35	9	in	in	ADP
ajema-5949	35	10	quantum	quantum	ADJ
ajema-5949	35	11	field	field	NOUN
ajema-5949	35	12	theory	theory	NOUN
ajema-5949	35	13	and	and	CCONJ
ajema-5949	35	14	quantum	quantum	NOUN
ajema-5949	35	15	mechanics	mechanic	NOUN
ajema-5949	35	16	,	,	PUNCT
ajema-5949	35	17	especially	especially	ADV
ajema-5949	35	18	at	at	ADP
ajema-5949	35	19	the	the	DET
ajema-5949	35	20	planck	planck	NOUN
ajema-5949	35	21	scale	scale	NOUN
ajema-5949	35	22	where	where	SCONJ
ajema-5949	35	23	quantum	quantum	NOUN
ajema-5949	35	24	effects	effect	NOUN
ajema-5949	35	25	predominate	predominate	ADJ
ajema-5949	35	26	.	.	PUNCT
ajema-5949	36	1	these	these	DET
ajema-5949	36	2	quantum	quantum	ADJ
ajema-5949	36	3	spaces	space	NOUN
ajema-5949	36	4	can	can	AUX
ajema-5949	36	5	be	be	AUX
ajema-5949	36	6	modeled	model	VERB
ajema-5949	36	7	using	use	VERB
ajema-5949	36	8	non	non	ADJ
ajema-5949	36	9	-	-	ADJ
ajema-5949	36	10	commutative	commutative	ADJ
ajema-5949	36	11	geometry	geometry	NOUN
ajema-5949	36	12	,	,	PUNCT
ajema-5949	36	13	in	in	ADP
ajema-5949	36	14	which	which	PRON
ajema-5949	36	15	a	a	DET
ajema-5949	36	16	c	c	NOUN
ajema-5949	36	17	-	-	PUNCT
ajema-5949	36	18	algebra	algebra	NOUN
ajema-5949	36	19	—	—	PUNCT
ajema-5949	36	20	a	a	DET
ajema-5949	36	21	mathematical	mathematical	ADJ
ajema-5949	36	22	entity	entity	NOUN
ajema-5949	36	23	that	that	PRON
ajema-5949	36	24	expresses	express	VERB
ajema-5949	36	25	the	the	DET
ajema-5949	36	26	space	space	NOUN
ajema-5949	36	27	's	's	PART
ajema-5949	36	28	non	non	ADJ
ajema-5949	36	29	-	-	ADJ
ajema-5949	36	30	commutative	commutative	ADJ
ajema-5949	36	31	character	character	NOUN
ajema-5949	36	32	—	—	PUNCT
ajema-5949	36	33	replaces	replace	VERB
ajema-5949	36	34	the	the	DET
ajema-5949	36	35	algebra	algebra	NOUN
ajema-5949	36	36	of	of	ADP
ajema-5949	36	37	functions	function	NOUN
ajema-5949	36	38	.	.	PUNCT
ajema-5949	37	1	connes	conne	NOUN
ajema-5949	37	2	(	(	PUNCT
ajema-5949	37	3	1994	1994	NUM
ajema-5949	37	4	)	)	PUNCT
ajema-5949	37	5	showed	show	VERB
ajema-5949	37	6	that	that	SCONJ
ajema-5949	37	7	non	non	ADJ
ajema-5949	37	8	-	-	ADJ
ajema-5949	37	9	commutative	commutative	ADJ
ajema-5949	37	10	geometry	geometry	NOUN
ajema-5949	37	11	could	could	AUX
ajema-5949	37	12	be	be	AUX
ajema-5949	37	13	used	use	VERB
ajema-5949	37	14	to	to	PART
ajema-5949	37	15	extend	extend	VERB
ajema-5949	37	16	classical	classical	ADJ
ajema-5949	37	17	geometric	geometric	ADJ
ajema-5949	37	18	concepts	concept	NOUN
ajema-5949	37	19	,	,	PUNCT
ajema-5949	37	20	such	such	ADJ
ajema-5949	37	21	as	as	ADP
ajema-5949	37	22	the	the	DET
ajema-5949	37	23	notion	notion	NOUN
ajema-5949	37	24	of	of	ADP
ajema-5949	37	25	distance	distance	NOUN
ajema-5949	37	26	,	,	PUNCT
ajema-5949	37	27	curvature	curvature	NOUN
ajema-5949	37	28	,	,	PUNCT
ajema-5949	37	29	and	and	CCONJ
ajema-5949	37	30	topology	topology	NOUN
ajema-5949	37	31	,	,	PUNCT
ajema-5949	37	32	to	to	ADP
ajema-5949	37	33	quantum	quantum	ADJ
ajema-5949	37	34	spaces	space	NOUN
ajema-5949	37	35	.	.	PUNCT
ajema-5949	38	1	one	one	NUM
ajema-5949	38	2	of	of	ADP
ajema-5949	38	3	the	the	DET
ajema-5949	38	4	most	most	ADV
ajema-5949	38	5	significant	significant	ADJ
ajema-5949	38	6	contributions	contribution	NOUN
ajema-5949	38	7	of	of	ADP
ajema-5949	38	8	non	non	ADJ
ajema-5949	38	9	-	-	ADJ
ajema-5949	38	10	commutative	commutative	ADJ
ajema-5949	38	11	geometry	geometry	NOUN
ajema-5949	38	12	is	be	AUX
ajema-5949	38	13	the	the	DET
ajema-5949	38	14	interpretation	interpretation	NOUN
ajema-5949	38	15	of	of	ADP
ajema-5949	38	16	space	space	NOUN
ajema-5949	38	17	-	-	PUNCT
ajema-5949	38	18	time	time	NOUN
ajema-5949	38	19	as	as	ADP
ajema-5949	38	20	a	a	DET
ajema-5949	38	21	non	non	ADJ
ajema-5949	38	22	-	-	ADJ
ajema-5949	38	23	commutative	commutative	ADJ
ajema-5949	38	24	algebra	algebra	NOUN
ajema-5949	38	25	.	.	PUNCT
ajema-5949	39	1	this	this	DET
ajema-5949	39	2	viewpoint	viewpoint	NOUN
ajema-5949	39	3	is	be	AUX
ajema-5949	39	4	especially	especially	ADV
ajema-5949	39	5	pertinent	pertinent	ADJ
ajema-5949	39	6	to	to	ADP
ajema-5949	39	7	the	the	DET
ajema-5949	39	8	study	study	NOUN
ajema-5949	39	9	of	of	ADP
ajema-5949	39	10	246	246	NUM
ajema-5949	39	11	journal	journal	NOUN
ajema-5949	39	12	of	of	ADP
ajema-5949	39	13	engineering	engineering	NOUN
ajema-5949	39	14	,	,	PUNCT
ajema-5949	39	15	mechanics	mechanic	NOUN
ajema-5949	39	16	and	and	CCONJ
ajema-5949	39	17	architecture	architecture	NOUN
ajema-5949	39	18	www	www	NOUN
ajema-5949	39	19	.	.	PUNCT
ajema-5949	40	1	grnjournal.us	grnjournal.us	X
ajema-5949	40	2	quantum	quantum	NOUN
ajema-5949	40	3	gravity	gravity	NOUN
ajema-5949	40	4	as	as	ADP
ajema-5949	40	5	theories	theory	NOUN
ajema-5949	40	6	such	such	ADJ
ajema-5949	40	7	as	as	ADP
ajema-5949	40	8	loop	loop	NOUN
ajema-5949	40	9	quantum	quantum	NOUN
ajema-5949	40	10	gravity	gravity	NOUN
ajema-5949	40	11	imply	imply	VERB
ajema-5949	40	12	that	that	SCONJ
ajema-5949	40	13	the	the	DET
ajema-5949	40	14	structure	structure	NOUN
ajema-5949	40	15	of	of	ADP
ajema-5949	40	16	spacetime	spacetime	NOUN
ajema-5949	40	17	may	may	AUX
ajema-5949	40	18	be	be	AUX
ajema-5949	40	19	essentially	essentially	ADV
ajema-5949	40	20	non	non	ADJ
ajema-5949	40	21	-	-	ADJ
ajema-5949	40	22	commutative	commutative	ADJ
ajema-5949	40	23	at	at	ADP
ajema-5949	40	24	microscopic	microscopic	ADJ
ajema-5949	40	25	scales	scale	NOUN
ajema-5949	40	26	.	.	PUNCT
ajema-5949	41	1	furthermore	furthermore	ADV
ajema-5949	41	2	,	,	PUNCT
ajema-5949	41	3	the	the	DET
ajema-5949	41	4	study	study	NOUN
ajema-5949	41	5	of	of	ADP
ajema-5949	41	6	quantum	quantum	ADJ
ajema-5949	41	7	spaces	space	NOUN
ajema-5949	41	8	—	—	PUNCT
ajema-5949	41	9	spaces	space	NOUN
ajema-5949	41	10	in	in	ADP
ajema-5949	41	11	which	which	PRON
ajema-5949	41	12	the	the	DET
ajema-5949	41	13	coordinates	coordinate	NOUN
ajema-5949	41	14	are	be	AUX
ajema-5949	41	15	controlled	control	VERB
ajema-5949	41	16	by	by	ADP
ajema-5949	41	17	quantum	quantum	ADJ
ajema-5949	41	18	group	group	NOUN
ajema-5949	41	19	symmetries	symmetry	NOUN
ajema-5949	41	20	—	—	PUNCT
ajema-5949	41	21	has	have	VERB
ajema-5949	41	22	a	a	DET
ajema-5949	41	23	close	close	ADJ
ajema-5949	41	24	relationship	relationship	NOUN
ajema-5949	41	25	with	with	ADP
ajema-5949	41	26	non	non	ADJ
ajema-5949	41	27	-	-	ADJ
ajema-5949	41	28	commutative	commutative	ADJ
ajema-5949	41	29	geometry	geometry	NOUN
ajema-5949	41	30	(	(	PUNCT
ajema-5949	41	31	connes	conne	NOUN
ajema-5949	41	32	,	,	PUNCT
ajema-5949	41	33	1994	1994	NUM
ajema-5949	41	34	)	)	PUNCT
ajema-5949	41	35	.	.	PUNCT
ajema-5949	42	1	these	these	DET
ajema-5949	42	2	non	non	ADJ
ajema-5949	42	3	-	-	ADJ
ajema-5949	42	4	commutative	commutative	ADJ
ajema-5949	42	5	spaces	space	NOUN
ajema-5949	42	6	'	'	PART
ajema-5949	42	7	symmetries	symmetry	NOUN
ajema-5949	42	8	are	be	AUX
ajema-5949	42	9	described	describe	VERB
ajema-5949	42	10	by	by	ADP
ajema-5949	42	11	quantum	quantum	ADJ
ajema-5949	42	12	groups	group	NOUN
ajema-5949	42	13	,	,	PUNCT
ajema-5949	42	14	which	which	PRON
ajema-5949	42	15	makes	make	VERB
ajema-5949	42	16	them	they	PRON
ajema-5949	42	17	a	a	DET
ajema-5949	42	18	crucial	crucial	ADJ
ajema-5949	42	19	tool	tool	NOUN
ajema-5949	42	20	for	for	ADP
ajema-5949	42	21	comprehending	comprehend	VERB
ajema-5949	42	22	the	the	DET
ajema-5949	42	23	algebraic	algebraic	ADJ
ajema-5949	42	24	structures	structure	NOUN
ajema-5949	42	25	that	that	PRON
ajema-5949	42	26	underlie	underlie	ADJ
ajema-5949	42	27	quantum	quantum	ADJ
ajema-5949	42	28	spaces	space	NOUN
ajema-5949	42	29	.	.	PUNCT
ajema-5949	43	1	2.3	2.3	NUM
ajema-5949	43	2	relationship	relationship	NOUN
ajema-5949	43	3	between	between	ADP
ajema-5949	43	4	quantum	quantum	ADJ
ajema-5949	43	5	groups	group	NOUN
ajema-5949	43	6	and	and	CCONJ
ajema-5949	43	7	non	non	ADJ
ajema-5949	43	8	-	-	ADJ
ajema-5949	43	9	commutative	commutative	ADJ
ajema-5949	43	10	geometry	geometry	NOUN
ajema-5949	43	11	quantum	quantum	NOUN
ajema-5949	43	12	groups	group	NOUN
ajema-5949	43	13	and	and	CCONJ
ajema-5949	43	14	non	non	ADJ
ajema-5949	43	15	-	-	ADJ
ajema-5949	43	16	commutative	commutative	ADJ
ajema-5949	43	17	geometry	geometry	NOUN
ajema-5949	43	18	are	be	AUX
ajema-5949	43	19	closely	closely	ADV
ajema-5949	43	20	connected	connect	VERB
ajema-5949	43	21	areas	area	NOUN
ajema-5949	43	22	since	since	SCONJ
ajema-5949	43	23	they	they	PRON
ajema-5949	43	24	both	both	PRON
ajema-5949	43	25	focus	focus	VERB
ajema-5949	43	26	on	on	ADP
ajema-5949	43	27	non	non	ADJ
ajema-5949	43	28	-	-	ADJ
ajema-5949	43	29	commutative	commutative	ADJ
ajema-5949	43	30	structures	structure	NOUN
ajema-5949	43	31	.	.	PUNCT
ajema-5949	44	1	quantum	quantum	ADJ
ajema-5949	44	2	groups	group	NOUN
ajema-5949	44	3	give	give	VERB
ajema-5949	44	4	a	a	DET
ajema-5949	44	5	way	way	NOUN
ajema-5949	44	6	to	to	PART
ajema-5949	44	7	describe	describe	VERB
ajema-5949	44	8	the	the	DET
ajema-5949	44	9	symmetries	symmetry	NOUN
ajema-5949	44	10	of	of	ADP
ajema-5949	44	11	non	non	ADJ
ajema-5949	44	12	-	-	ADJ
ajema-5949	44	13	commutative	commutative	ADJ
ajema-5949	44	14	spaces	space	NOUN
ajema-5949	44	15	,	,	PUNCT
ajema-5949	44	16	whereas	whereas	SCONJ
ajema-5949	44	17	non	non	ADJ
ajema-5949	44	18	-	-	ADJ
ajema-5949	44	19	commutative	commutative	ADJ
ajema-5949	44	20	geometry	geometry	NOUN
ajema-5949	44	21	offers	offer	VERB
ajema-5949	44	22	a	a	DET
ajema-5949	44	23	more	more	ADV
ajema-5949	44	24	broad	broad	ADJ
ajema-5949	44	25	framework	framework	NOUN
ajema-5949	44	26	for	for	ADP
ajema-5949	44	27	using	use	VERB
ajema-5949	44	28	quantum	quantum	ADJ
ajema-5949	44	29	groups	group	NOUN
ajema-5949	44	30	.	.	PUNCT
ajema-5949	45	1	in	in	ADP
ajema-5949	45	2	fact	fact	NOUN
ajema-5949	45	3	,	,	PUNCT
ajema-5949	45	4	non	non	ADJ
ajema-5949	45	5	-	-	ADJ
ajema-5949	45	6	commutative	commutative	ADJ
ajema-5949	45	7	geometry	geometry	NOUN
ajema-5949	45	8	provides	provide	VERB
ajema-5949	45	9	the	the	DET
ajema-5949	45	10	setting	setting	NOUN
ajema-5949	45	11	for	for	SCONJ
ajema-5949	45	12	quantum	quantum	ADJ
ajema-5949	45	13	groups	group	NOUN
ajema-5949	45	14	to	to	PART
ajema-5949	45	15	act	act	VERB
ajema-5949	45	16	as	as	ADP
ajema-5949	45	17	symmetries	symmetry	NOUN
ajema-5949	45	18	of	of	ADP
ajema-5949	45	19	quantum	quantum	ADJ
ajema-5949	45	20	spaces	space	NOUN
ajema-5949	45	21	,	,	PUNCT
ajema-5949	45	22	while	while	SCONJ
ajema-5949	45	23	the	the	DET
ajema-5949	45	24	algebraic	algebraic	ADJ
ajema-5949	45	25	structure	structure	NOUN
ajema-5949	45	26	of	of	ADP
ajema-5949	45	27	quantum	quantum	ADJ
ajema-5949	45	28	groups	group	NOUN
ajema-5949	45	29	helps	help	VERB
ajema-5949	45	30	define	define	VERB
ajema-5949	45	31	the	the	DET
ajema-5949	45	32	transformations	transformation	NOUN
ajema-5949	45	33	that	that	PRON
ajema-5949	45	34	preserve	preserve	VERB
ajema-5949	45	35	the	the	DET
ajema-5949	45	36	non	non	ADJ
ajema-5949	45	37	-	-	ADJ
ajema-5949	45	38	commutative	commutative	ADJ
ajema-5949	45	39	structure	structure	NOUN
ajema-5949	45	40	of	of	ADP
ajema-5949	45	41	these	these	DET
ajema-5949	45	42	spaces	space	NOUN
ajema-5949	45	43	.	.	PUNCT
ajema-5949	46	1	one	one	NUM
ajema-5949	46	2	key	key	ADJ
ajema-5949	46	3	area	area	NOUN
ajema-5949	46	4	where	where	SCONJ
ajema-5949	46	5	quantum	quantum	NOUN
ajema-5949	46	6	groups	group	NOUN
ajema-5949	46	7	and	and	CCONJ
ajema-5949	46	8	non	non	ADJ
ajema-5949	46	9	-	-	ADJ
ajema-5949	46	10	commutative	commutative	ADJ
ajema-5949	46	11	geometry	geometry	NOUN
ajema-5949	46	12	intersect	intersect	NOUN
ajema-5949	46	13	is	be	AUX
ajema-5949	46	14	in	in	ADP
ajema-5949	46	15	the	the	DET
ajema-5949	46	16	study	study	NOUN
ajema-5949	46	17	of	of	ADP
ajema-5949	46	18	quantum	quantum	ADJ
ajema-5949	46	19	spaces	space	NOUN
ajema-5949	46	20	,	,	PUNCT
ajema-5949	46	21	which	which	PRON
ajema-5949	46	22	are	be	AUX
ajema-5949	46	23	modeled	model	VERB
ajema-5949	46	24	using	use	VERB
ajema-5949	46	25	non	non	ADJ
ajema-5949	46	26	-	-	ADJ
ajema-5949	46	27	commutative	commutative	ADJ
ajema-5949	46	28	algebras	algebra	NOUN
ajema-5949	46	29	.	.	PUNCT
ajema-5949	47	1	the	the	DET
ajema-5949	47	2	quantum	quantum	ADJ
ajema-5949	47	3	symmetries	symmetry	NOUN
ajema-5949	47	4	of	of	ADP
ajema-5949	47	5	these	these	DET
ajema-5949	47	6	spaces	space	NOUN
ajema-5949	47	7	are	be	AUX
ajema-5949	47	8	described	describe	VERB
ajema-5949	47	9	by	by	ADP
ajema-5949	47	10	quantum	quantum	ADJ
ajema-5949	47	11	groups	group	NOUN
ajema-5949	47	12	,	,	PUNCT
ajema-5949	47	13	and	and	CCONJ
ajema-5949	47	14	these	these	DET
ajema-5949	47	15	groups	group	NOUN
ajema-5949	47	16	act	act	VERB
ajema-5949	47	17	as	as	ADP
ajema-5949	47	18	deformations	deformation	NOUN
ajema-5949	47	19	of	of	ADP
ajema-5949	47	20	classical	classical	ADJ
ajema-5949	47	21	symmetries	symmetry	NOUN
ajema-5949	47	22	that	that	PRON
ajema-5949	47	23	become	become	VERB
ajema-5949	47	24	relevant	relevant	ADJ
ajema-5949	47	25	at	at	ADP
ajema-5949	47	26	the	the	DET
ajema-5949	47	27	quantum	quantum	ADJ
ajema-5949	47	28	level	level	NOUN
ajema-5949	47	29	(	(	PUNCT
ajema-5949	47	30	chari	chari	PROPN
ajema-5949	47	31	&	&	CCONJ
ajema-5949	47	32	pressley	pressley	PROPN
ajema-5949	47	33	,	,	PUNCT
ajema-5949	47	34	1994	1994	NUM
ajema-5949	47	35	)	)	PUNCT
ajema-5949	47	36	.	.	PUNCT
ajema-5949	48	1	noncommutative	noncommutative	ADJ
ajema-5949	48	2	geometry	geometry	NOUN
ajema-5949	48	3	can	can	AUX
ajema-5949	48	4	provide	provide	VERB
ajema-5949	48	5	profound	profound	ADJ
ajema-5949	48	6	insights	insight	NOUN
ajema-5949	48	7	into	into	ADP
ajema-5949	48	8	the	the	DET
ajema-5949	48	9	characteristics	characteristic	NOUN
ajema-5949	48	10	of	of	ADP
ajema-5949	48	11	quantum	quantum	ADJ
ajema-5949	48	12	spacetime	spacetime	NOUN
ajema-5949	48	13	and	and	CCONJ
ajema-5949	48	14	the	the	DET
ajema-5949	48	15	symmetries	symmetry	NOUN
ajema-5949	48	16	governing	govern	VERB
ajema-5949	48	17	it	it	PRON
ajema-5949	48	18	through	through	ADP
ajema-5949	48	19	this	this	DET
ajema-5949	48	20	interaction	interaction	NOUN
ajema-5949	48	21	.	.	PUNCT
ajema-5949	49	1	quantum	quantum	ADJ
ajema-5949	49	2	groups	group	NOUN
ajema-5949	49	3	and	and	CCONJ
ajema-5949	49	4	non	non	ADJ
ajema-5949	49	5	-	-	ADJ
ajema-5949	49	6	commutative	commutative	ADJ
ajema-5949	49	7	geometry	geometry	NOUN
ajema-5949	49	8	in	in	ADP
ajema-5949	49	9	theoretical	theoretical	ADJ
ajema-5949	49	10	physics	physics	NOUN
ajema-5949	49	11	offer	offer	VERB
ajema-5949	49	12	a	a	DET
ajema-5949	49	13	framework	framework	NOUN
ajema-5949	49	14	for	for	ADP
ajema-5949	49	15	investigating	investigate	VERB
ajema-5949	49	16	quantum	quantum	ADJ
ajema-5949	49	17	gravity	gravity	NOUN
ajema-5949	49	18	and	and	CCONJ
ajema-5949	49	19	the	the	DET
ajema-5949	49	20	possible	possible	ADJ
ajema-5949	49	21	non	non	ADJ
ajema-5949	49	22	-	-	ADJ
ajema-5949	49	23	commutative	commutative	ADJ
ajema-5949	49	24	structure	structure	NOUN
ajema-5949	49	25	of	of	ADP
ajema-5949	49	26	spacetime	spacetime	NOUN
ajema-5949	49	27	at	at	ADP
ajema-5949	49	28	the	the	DET
ajema-5949	49	29	planck	planck	NOUN
ajema-5949	49	30	scale	scale	NOUN
ajema-5949	49	31	.	.	PUNCT
ajema-5949	50	1	in	in	ADP
ajema-5949	50	2	the	the	DET
ajema-5949	50	3	study	study	NOUN
ajema-5949	50	4	of	of	ADP
ajema-5949	50	5	quantum	quantum	ADJ
ajema-5949	50	6	field	field	NOUN
ajema-5949	50	7	theory	theory	NOUN
ajema-5949	50	8	and	and	CCONJ
ajema-5949	50	9	integrable	integrable	ADJ
ajema-5949	50	10	systems	system	NOUN
ajema-5949	50	11	,	,	PUNCT
ajema-5949	50	12	the	the	DET
ajema-5949	50	13	deformed	deformed	ADJ
ajema-5949	50	14	symmetries	symmetry	NOUN
ajema-5949	50	15	of	of	ADP
ajema-5949	50	16	quantum	quantum	ADJ
ajema-5949	50	17	spacetime	spacetime	NOUN
ajema-5949	50	18	are	be	AUX
ajema-5949	50	19	best	well	ADV
ajema-5949	50	20	described	describe	VERB
ajema-5949	50	21	by	by	ADP
ajema-5949	50	22	the	the	DET
ajema-5949	50	23	algebraic	algebraic	ADJ
ajema-5949	50	24	structure	structure	NOUN
ajema-5949	50	25	of	of	ADP
ajema-5949	50	26	quantum	quantum	ADJ
ajema-5949	50	27	groups	group	NOUN
ajema-5949	50	28	.	.	PUNCT
ajema-5949	51	1	quantum	quantum	ADJ
ajema-5949	51	2	groups	group	NOUN
ajema-5949	51	3	and	and	CCONJ
ajema-5949	51	4	non	non	ADJ
ajema-5949	51	5	-	-	ADJ
ajema-5949	51	6	commutative	commutative	ADJ
ajema-5949	51	7	geometry	geometry	NOUN
ajema-5949	51	8	provide	provide	VERB
ajema-5949	51	9	a	a	DET
ajema-5949	51	10	unified	unified	ADJ
ajema-5949	51	11	framework	framework	NOUN
ajema-5949	51	12	for	for	ADP
ajema-5949	51	13	studying	study	VERB
ajema-5949	51	14	quantum	quantum	ADJ
ajema-5949	51	15	spaces	space	NOUN
ajema-5949	51	16	and	and	CCONJ
ajema-5949	51	17	their	their	PRON
ajema-5949	51	18	symmetries	symmetry	NOUN
ajema-5949	51	19	.	.	PUNCT
ajema-5949	52	1	quantum	quantum	ADJ
ajema-5949	52	2	groups	group	NOUN
ajema-5949	52	3	,	,	PUNCT
ajema-5949	52	4	as	as	ADP
ajema-5949	52	5	deformations	deformation	NOUN
ajema-5949	52	6	of	of	ADP
ajema-5949	52	7	classical	classical	ADJ
ajema-5949	52	8	lie	lie	NOUN
ajema-5949	52	9	groups	group	NOUN
ajema-5949	52	10	,	,	PUNCT
ajema-5949	52	11	offer	offer	VERB
ajema-5949	52	12	a	a	DET
ajema-5949	52	13	way	way	NOUN
ajema-5949	52	14	to	to	PART
ajema-5949	52	15	generalize	generalize	VERB
ajema-5949	52	16	symmetries	symmetry	NOUN
ajema-5949	52	17	into	into	ADP
ajema-5949	52	18	the	the	DET
ajema-5949	52	19	non	non	ADJ
ajema-5949	52	20	-	-	ADJ
ajema-5949	52	21	commutative	commutative	ADJ
ajema-5949	52	22	realm	realm	NOUN
ajema-5949	52	23	,	,	PUNCT
ajema-5949	52	24	while	while	SCONJ
ajema-5949	52	25	non	non	ADJ
ajema-5949	52	26	-	-	ADJ
ajema-5949	52	27	commutative	commutative	ADJ
ajema-5949	52	28	geometry	geometry	NOUN
ajema-5949	52	29	extends	extend	VERB
ajema-5949	52	30	classical	classical	ADJ
ajema-5949	52	31	geometric	geometric	ADJ
ajema-5949	52	32	concepts	concept	NOUN
ajema-5949	52	33	into	into	ADP
ajema-5949	52	34	a	a	DET
ajema-5949	52	35	quantum	quantum	ADJ
ajema-5949	52	36	context	context	NOUN
ajema-5949	52	37	.	.	PUNCT
ajema-5949	53	1	together	together	ADV
ajema-5949	53	2	,	,	PUNCT
ajema-5949	53	3	these	these	DET
ajema-5949	53	4	concepts	concept	NOUN
ajema-5949	53	5	have	have	VERB
ajema-5949	53	6	profound	profound	ADJ
ajema-5949	53	7	implications	implication	NOUN
ajema-5949	53	8	for	for	ADP
ajema-5949	53	9	understanding	understand	VERB
ajema-5949	53	10	quantum	quantum	ADJ
ajema-5949	53	11	phenomena	phenomenon	NOUN
ajema-5949	53	12	,	,	PUNCT
ajema-5949	53	13	particularly	particularly	ADV
ajema-5949	53	14	in	in	ADP
ajema-5949	53	15	the	the	DET
ajema-5949	53	16	fields	field	NOUN
ajema-5949	53	17	of	of	ADP
ajema-5949	53	18	quantum	quantum	ADJ
ajema-5949	53	19	field	field	NOUN
ajema-5949	53	20	theory	theory	NOUN
ajema-5949	53	21	,	,	PUNCT
ajema-5949	53	22	quantum	quantum	NOUN
ajema-5949	53	23	gravity	gravity	NOUN
ajema-5949	53	24	,	,	PUNCT
ajema-5949	53	25	and	and	CCONJ
ajema-5949	53	26	integrable	integrable	ADJ
ajema-5949	53	27	systems	system	NOUN
ajema-5949	53	28	.	.	PUNCT
ajema-5949	54	1	as	as	SCONJ
ajema-5949	54	2	quantum	quantum	NOUN
ajema-5949	54	3	theory	theory	NOUN
ajema-5949	54	4	continues	continue	VERB
ajema-5949	54	5	to	to	PART
ajema-5949	54	6	evolve	evolve	VERB
ajema-5949	54	7	,	,	PUNCT
ajema-5949	54	8	the	the	DET
ajema-5949	54	9	study	study	NOUN
ajema-5949	54	10	of	of	ADP
ajema-5949	54	11	quantum	quantum	ADJ
ajema-5949	54	12	groups	group	NOUN
ajema-5949	54	13	and	and	CCONJ
ajema-5949	54	14	non	non	ADJ
ajema-5949	54	15	-	-	ADJ
ajema-5949	54	16	commutative	commutative	ADJ
ajema-5949	54	17	geometry	geometry	NOUN
ajema-5949	54	18	will	will	AUX
ajema-5949	54	19	remain	remain	VERB
ajema-5949	54	20	crucial	crucial	ADJ
ajema-5949	54	21	for	for	ADP
ajema-5949	54	22	unraveling	unravel	VERB
ajema-5949	54	23	the	the	DET
ajema-5949	54	24	algebraic	algebraic	ADJ
ajema-5949	54	25	and	and	CCONJ
ajema-5949	54	26	geometric	geometric	ADJ
ajema-5949	54	27	structure	structure	NOUN
ajema-5949	54	28	of	of	ADP
ajema-5949	54	29	the	the	DET
ajema-5949	54	30	quantum	quantum	ADJ
ajema-5949	54	31	world	world	NOUN
ajema-5949	54	32	.	.	PUNCT
ajema-5949	55	1	3	3	X
ajema-5949	55	2	.	.	NOUN
ajema-5949	55	3	mathematical	mathematical	ADJ
ajema-5949	55	4	properties	property	NOUN
ajema-5949	55	5	of	of	ADP
ajema-5949	55	6	quantum	quantum	ADJ
ajema-5949	55	7	groups	group	NOUN
ajema-5949	55	8	quantum	quantum	NOUN
ajema-5949	55	9	groups	group	NOUN
ajema-5949	55	10	are	be	AUX
ajema-5949	55	11	algebraic	algebraic	ADJ
ajema-5949	55	12	structures	structure	NOUN
ajema-5949	55	13	that	that	PRON
ajema-5949	55	14	generalize	generalize	VERB
ajema-5949	55	15	classical	classical	ADJ
ajema-5949	55	16	lie	lie	NOUN
ajema-5949	55	17	groups	group	NOUN
ajema-5949	55	18	and	and	CCONJ
ajema-5949	55	19	lie	lie	VERB
ajema-5949	55	20	algebras	algebra	NOUN
ajema-5949	55	21	to	to	ADP
ajema-5949	55	22	the	the	DET
ajema-5949	55	23	non	non	ADJ
ajema-5949	55	24	-	-	ADJ
ajema-5949	55	25	commutative	commutative	ADJ
ajema-5949	55	26	setting	setting	NOUN
ajema-5949	55	27	.	.	PUNCT
ajema-5949	56	1	these	these	DET
ajema-5949	56	2	objects	object	NOUN
ajema-5949	56	3	exhibit	exhibit	VERB
ajema-5949	56	4	several	several	ADJ
ajema-5949	56	5	mathematical	mathematical	ADJ
ajema-5949	56	6	properties	property	NOUN
ajema-5949	56	7	that	that	PRON
ajema-5949	56	8	distinguish	distinguish	VERB
ajema-5949	56	9	them	they	PRON
ajema-5949	56	10	from	from	ADP
ajema-5949	56	11	traditional	traditional	ADJ
ajema-5949	56	12	structures	structure	NOUN
ajema-5949	56	13	,	,	PUNCT
ajema-5949	56	14	with	with	ADP
ajema-5949	56	15	a	a	DET
ajema-5949	56	16	significant	significant	ADJ
ajema-5949	56	17	emphasis	emphasis	NOUN
ajema-5949	56	18	on	on	ADP
ajema-5949	56	19	their	their	PRON
ajema-5949	56	20	noncommutative	noncommutative	ADJ
ajema-5949	56	21	nature	nature	NOUN
ajema-5949	56	22	and	and	CCONJ
ajema-5949	56	23	their	their	PRON
ajema-5949	56	24	relationship	relationship	NOUN
ajema-5949	56	25	to	to	ADP
ajema-5949	56	26	hopf	hopf	ADJ
ajema-5949	56	27	algebras	algebra	NOUN
ajema-5949	56	28	.	.	PUNCT
ajema-5949	57	1	understanding	understand	VERB
ajema-5949	57	2	the	the	DET
ajema-5949	57	3	mathematical	mathematical	ADJ
ajema-5949	57	4	properties	property	NOUN
ajema-5949	57	5	of	of	ADP
ajema-5949	57	6	quantum	quantum	ADJ
ajema-5949	57	7	groups	group	NOUN
ajema-5949	57	8	is	be	AUX
ajema-5949	57	9	essential	essential	ADJ
ajema-5949	57	10	for	for	ADP
ajema-5949	57	11	their	their	PRON
ajema-5949	57	12	application	application	NOUN
ajema-5949	57	13	in	in	ADP
ajema-5949	57	14	both	both	CCONJ
ajema-5949	57	15	pure	pure	ADJ
ajema-5949	57	16	mathematics	mathematic	NOUN
ajema-5949	57	17	and	and	CCONJ
ajema-5949	57	18	theoretical	theoretical	ADJ
ajema-5949	57	19	physics	physics	NOUN
ajema-5949	57	20	.	.	PUNCT
ajema-5949	58	1	below	below	ADV
ajema-5949	58	2	,	,	PUNCT
ajema-5949	58	3	we	we	PRON
ajema-5949	58	4	explore	explore	VERB
ajema-5949	58	5	the	the	DET
ajema-5949	58	6	key	key	ADJ
ajema-5949	58	7	properties	property	NOUN
ajema-5949	58	8	that	that	PRON
ajema-5949	58	9	define	define	VERB
ajema-5949	58	10	quantum	quantum	ADJ
ajema-5949	58	11	groups	group	NOUN
ajema-5949	58	12	,	,	PUNCT
ajema-5949	58	13	including	include	VERB
ajema-5949	58	14	their	their	PRON
ajema-5949	58	15	algebraic	algebraic	ADJ
ajema-5949	58	16	structure	structure	NOUN
ajema-5949	58	17	,	,	PUNCT
ajema-5949	58	18	the	the	DET
ajema-5949	58	19	hopf	hopf	ADJ
ajema-5949	58	20	algebra	algebra	NOUN
ajema-5949	58	21	framework	framework	NOUN
ajema-5949	58	22	,	,	PUNCT
ajema-5949	58	23	their	their	PRON
ajema-5949	58	24	representations	representation	NOUN
ajema-5949	58	25	,	,	PUNCT
ajema-5949	58	26	and	and	CCONJ
ajema-5949	58	27	the	the	DET
ajema-5949	58	28	deformation	deformation	NOUN
ajema-5949	58	29	parameter	parameter	NOUN
ajema-5949	58	30	that	that	PRON
ajema-5949	58	31	characterizes	characterize	VERB
ajema-5949	58	32	their	their	PRON
ajema-5949	58	33	behavior	behavior	NOUN
ajema-5949	58	34	.	.	PUNCT
ajema-5949	59	1	3.1	3.1	NUM
ajema-5949	59	2	.	.	PUNCT
ajema-5949	60	1	non	non	ADJ
ajema-5949	60	2	-	-	NOUN
ajema-5949	60	3	commutativity	commutativity	ADJ
ajema-5949	60	4	a	a	DET
ajema-5949	60	5	defining	define	VERB
ajema-5949	60	6	characteristic	characteristic	NOUN
ajema-5949	60	7	of	of	ADP
ajema-5949	60	8	quantum	quantum	ADJ
ajema-5949	60	9	groups	group	NOUN
ajema-5949	60	10	is	be	AUX
ajema-5949	60	11	their	their	PRON
ajema-5949	60	12	non	non	ADJ
ajema-5949	60	13	-	-	ADJ
ajema-5949	60	14	commutative	commutative	ADJ
ajema-5949	60	15	nature	nature	NOUN
ajema-5949	60	16	.	.	PUNCT
ajema-5949	61	1	unlike	unlike	ADP
ajema-5949	61	2	classical	classical	ADJ
ajema-5949	61	3	lie	lie	NOUN
ajema-5949	61	4	groups	group	NOUN
ajema-5949	61	5	,	,	PUNCT
ajema-5949	61	6	where	where	SCONJ
ajema-5949	61	7	the	the	DET
ajema-5949	61	8	group	group	NOUN
ajema-5949	61	9	operations	operation	NOUN
ajema-5949	61	10	(	(	PUNCT
ajema-5949	61	11	such	such	ADJ
ajema-5949	61	12	as	as	ADP
ajema-5949	61	13	multiplication	multiplication	NOUN
ajema-5949	61	14	)	)	PUNCT
ajema-5949	61	15	commute	commute	NOUN
ajema-5949	61	16	,	,	PUNCT
ajema-5949	61	17	quantum	quantum	ADJ
ajema-5949	61	18	groups	group	NOUN
ajema-5949	61	19	are	be	AUX
ajema-5949	61	20	defined	define	VERB
ajema-5949	61	21	by	by	ADP
ajema-5949	61	22	deformed	deform	VERB
ajema-5949	61	23	commutation	commutation	NOUN
ajema-5949	61	24	relations	relation	NOUN
ajema-5949	61	25	.	.	PUNCT
ajema-5949	62	1	these	these	DET
ajema-5949	62	2	relations	relation	NOUN
ajema-5949	62	3	are	be	AUX
ajema-5949	62	4	controlled	control	VERB
ajema-5949	62	5	by	by	ADP
ajema-5949	62	6	a	a	DET
ajema-5949	62	7	deformation	deformation	NOUN
ajema-5949	62	8	parameter	parameter	NOUN
ajema-5949	62	9	q	q	NOUN
ajema-5949	62	10	,	,	PUNCT
ajema-5949	62	11	which	which	PRON
ajema-5949	62	12	introduces	introduce	VERB
ajema-5949	62	13	a	a	DET
ajema-5949	62	14	degree	degree	NOUN
ajema-5949	62	15	of	of	ADP
ajema-5949	62	16	non	non	NOUN
ajema-5949	62	17	-	-	NOUN
ajema-5949	62	18	commutativity	commutativity	NOUN
ajema-5949	62	19	.	.	PUNCT
ajema-5949	63	1	for	for	ADP
ajema-5949	63	2	example	example	NOUN
ajema-5949	63	3	,	,	PUNCT
ajema-5949	63	4	in	in	ADP
ajema-5949	63	5	the	the	DET
ajema-5949	63	6	quantum	quantum	ADJ
ajema-5949	63	7	247	247	NUM
ajema-5949	63	8	journal	journal	NOUN
ajema-5949	63	9	of	of	ADP
ajema-5949	63	10	engineering	engineering	NOUN
ajema-5949	63	11	,	,	PUNCT
ajema-5949	63	12	mechanics	mechanic	NOUN
ajema-5949	63	13	and	and	CCONJ
ajema-5949	63	14	architecture	architecture	NOUN
ajema-5949	63	15	www	www	NOUN
ajema-5949	63	16	.	.	PUNCT
ajema-5949	63	17	grnjournal.us	grnjournal.us	X
ajema-5949	63	18	group	group	NOUN
ajema-5949	63	19	uq(g	uq(g	ADV
ajema-5949	63	20	)	)	PUNCT
ajema-5949	63	21	,	,	PUNCT
ajema-5949	63	22	where	where	SCONJ
ajema-5949	63	23	g	g	PROPN
ajema-5949	63	24	is	be	AUX
ajema-5949	63	25	a	a	DET
ajema-5949	63	26	lie	lie	NOUN
ajema-5949	63	27	algebra	algebra	NOUN
ajema-5949	63	28	,	,	PUNCT
ajema-5949	63	29	the	the	DET
ajema-5949	63	30	commutation	commutation	NOUN
ajema-5949	63	31	relations	relation	NOUN
ajema-5949	63	32	are	be	AUX
ajema-5949	63	33	deformed	deform	VERB
ajema-5949	63	34	by	by	ADP
ajema-5949	63	35	powers	power	NOUN
ajema-5949	63	36	of	of	ADP
ajema-5949	63	37	qqq	qqq	NOUN
ajema-5949	63	38	,	,	PUNCT
ajema-5949	63	39	leading	lead	VERB
ajema-5949	63	40	to	to	ADP
ajema-5949	63	41	the	the	DET
ajema-5949	63	42	following	follow	VERB
ajema-5949	63	43	general	general	ADJ
ajema-5949	63	44	form	form	NOUN
ajema-5949	63	45	:	:	PUNCT
ajema-5949	63	46	here	here	ADV
ajema-5949	63	47	,	,	PUNCT
ajema-5949	63	48	x	x	X
ajema-5949	63	49	,	,	PUNCT
ajema-5949	63	50	y	y	PROPN
ajema-5949	63	51	,	,	PUNCT
ajema-5949	63	52	and	and	CCONJ
ajema-5949	63	53	z	z	AUX
ajema-5949	63	54	represent	represent	VERB
ajema-5949	63	55	elements	element	NOUN
ajema-5949	63	56	of	of	ADP
ajema-5949	63	57	the	the	DET
ajema-5949	63	58	lie	lie	NOUN
ajema-5949	63	59	algebra	algebra	NOUN
ajema-5949	63	60	,	,	PUNCT
ajema-5949	63	61	and	and	CCONJ
ajema-5949	63	62	q	q	NOUN
ajema-5949	63	63	is	be	AUX
ajema-5949	63	64	the	the	DET
ajema-5949	63	65	deformation	deformation	NOUN
ajema-5949	63	66	parameter	parameter	NOUN
ajema-5949	63	67	.	.	PUNCT
ajema-5949	64	1	when	when	SCONJ
ajema-5949	64	2	q=1	q=1	X
ajema-5949	64	3	,	,	PUNCT
ajema-5949	64	4	these	these	DET
ajema-5949	64	5	relations	relation	NOUN
ajema-5949	64	6	reduce	reduce	VERB
ajema-5949	64	7	to	to	ADP
ajema-5949	64	8	the	the	DET
ajema-5949	64	9	classical	classical	ADJ
ajema-5949	64	10	commutative	commutative	ADJ
ajema-5949	64	11	relations	relation	NOUN
ajema-5949	64	12	of	of	ADP
ajema-5949	64	13	a	a	DET
ajema-5949	64	14	lie	lie	NOUN
ajema-5949	64	15	algebra	algebra	NOUN
ajema-5949	64	16	(	(	PUNCT
ajema-5949	64	17	chari	chari	PROPN
ajema-5949	64	18	&	&	CCONJ
ajema-5949	64	19	pressley	pressley	PROPN
ajema-5949	64	20	,	,	PUNCT
ajema-5949	64	21	1994	1994	NUM
ajema-5949	64	22	)	)	PUNCT
ajema-5949	64	23	.	.	PUNCT
ajema-5949	65	1	this	this	DET
ajema-5949	65	2	non	non	ADJ
ajema-5949	65	3	-	-	ADJ
ajema-5949	65	4	commutative	commutative	ADJ
ajema-5949	65	5	structure	structure	NOUN
ajema-5949	65	6	is	be	AUX
ajema-5949	65	7	one	one	NUM
ajema-5949	65	8	of	of	ADP
ajema-5949	65	9	the	the	DET
ajema-5949	65	10	hallmarks	hallmark	NOUN
ajema-5949	65	11	of	of	ADP
ajema-5949	65	12	quantum	quantum	NOUN
ajema-5949	65	13	groups	group	NOUN
ajema-5949	65	14	and	and	CCONJ
ajema-5949	65	15	is	be	AUX
ajema-5949	65	16	central	central	ADJ
ajema-5949	65	17	to	to	ADP
ajema-5949	65	18	their	their	PRON
ajema-5949	65	19	role	role	NOUN
ajema-5949	65	20	in	in	ADP
ajema-5949	65	21	quantum	quantum	ADJ
ajema-5949	65	22	mechanics	mechanic	NOUN
ajema-5949	65	23	and	and	CCONJ
ajema-5949	65	24	quantum	quantum	NOUN
ajema-5949	65	25	field	field	NOUN
ajema-5949	65	26	theory	theory	NOUN
ajema-5949	65	27	.	.	PUNCT
ajema-5949	66	1	3.2	3.2	NUM
ajema-5949	66	2	.	.	PUNCT
ajema-5949	67	1	hopf	hopf	ADJ
ajema-5949	67	2	algebra	algebra	NOUN
ajema-5949	67	3	structure	structure	NOUN
ajema-5949	67	4	quantum	quantum	NOUN
ajema-5949	67	5	groups	group	NOUN
ajema-5949	67	6	are	be	AUX
ajema-5949	67	7	typically	typically	ADV
ajema-5949	67	8	studied	study	VERB
ajema-5949	67	9	as	as	ADP
ajema-5949	67	10	hopf	hopf	ADJ
ajema-5949	67	11	algebras	algebra	NOUN
ajema-5949	67	12	,	,	PUNCT
ajema-5949	67	13	which	which	PRON
ajema-5949	67	14	are	be	AUX
ajema-5949	67	15	algebraic	algebraic	ADJ
ajema-5949	67	16	structures	structure	NOUN
ajema-5949	67	17	equipped	equip	VERB
ajema-5949	67	18	with	with	ADP
ajema-5949	67	19	both	both	CCONJ
ajema-5949	67	20	algebraic	algebraic	ADJ
ajema-5949	67	21	and	and	CCONJ
ajema-5949	67	22	co	co	ADJ
ajema-5949	67	23	-	-	ADJ
ajema-5949	67	24	algebraic	algebraic	ADJ
ajema-5949	67	25	operations	operation	NOUN
ajema-5949	67	26	.	.	PUNCT
ajema-5949	68	1	a	a	DET
ajema-5949	68	2	hopf	hopf	ADJ
ajema-5949	68	3	algebra	algebra	NOUN
ajema-5949	68	4	consists	consist	VERB
ajema-5949	68	5	of	of	ADP
ajema-5949	68	6	several	several	ADJ
ajema-5949	68	7	operations	operation	NOUN
ajema-5949	68	8	that	that	PRON
ajema-5949	68	9	generalize	generalize	VERB
ajema-5949	68	10	the	the	DET
ajema-5949	68	11	structure	structure	NOUN
ajema-5949	68	12	of	of	ADP
ajema-5949	68	13	a	a	DET
ajema-5949	68	14	group	group	NOUN
ajema-5949	68	15	to	to	ADP
ajema-5949	68	16	the	the	DET
ajema-5949	68	17	non	non	ADJ
ajema-5949	68	18	-	-	ADJ
ajema-5949	68	19	commutative	commutative	ADJ
ajema-5949	68	20	setting	setting	NOUN
ajema-5949	68	21	:	:	PUNCT
ajema-5949	68	22	➢	➢	VERB
ajema-5949	68	23	multiplication	multiplication	NOUN
ajema-5949	68	24	and	and	CCONJ
ajema-5949	68	25	unit	unit	NOUN
ajema-5949	68	26	:	:	PUNCT
ajema-5949	68	27	the	the	DET
ajema-5949	68	28	algebraic	algebraic	ADJ
ajema-5949	68	29	operations	operation	NOUN
ajema-5949	68	30	of	of	ADP
ajema-5949	68	31	multiplication	multiplication	NOUN
ajema-5949	68	32	and	and	CCONJ
ajema-5949	68	33	unit	unit	NOUN
ajema-5949	68	34	are	be	AUX
ajema-5949	68	35	standard	standard	ADJ
ajema-5949	68	36	operations	operation	NOUN
ajema-5949	68	37	in	in	ADP
ajema-5949	68	38	any	any	DET
ajema-5949	68	39	algebra	algebra	NOUN
ajema-5949	68	40	.	.	PUNCT
ajema-5949	69	1	➢	➢	VERB
ajema-5949	69	2	co	co	NOUN
ajema-5949	69	3	-	-	NOUN
ajema-5949	69	4	multiplication	multiplication	NOUN
ajema-5949	69	5	and	and	CCONJ
ajema-5949	69	6	co	co	NOUN
ajema-5949	69	7	-	-	NOUN
ajema-5949	69	8	unit	unit	NOUN
ajema-5949	69	9	:	:	PUNCT
ajema-5949	69	10	these	these	DET
ajema-5949	69	11	operations	operation	NOUN
ajema-5949	69	12	provide	provide	VERB
ajema-5949	69	13	the	the	DET
ajema-5949	69	14	co	co	ADJ
ajema-5949	69	15	-	-	ADJ
ajema-5949	69	16	algebraic	algebraic	ADJ
ajema-5949	69	17	structure	structure	NOUN
ajema-5949	69	18	that	that	PRON
ajema-5949	69	19	allows	allow	VERB
ajema-5949	69	20	for	for	ADP
ajema-5949	69	21	a	a	DET
ajema-5949	69	22	duality	duality	NOUN
ajema-5949	69	23	between	between	ADP
ajema-5949	69	24	the	the	DET
ajema-5949	69	25	algebra	algebra	NOUN
ajema-5949	69	26	and	and	CCONJ
ajema-5949	69	27	the	the	DET
ajema-5949	69	28	co	co	NOUN
ajema-5949	69	29	-	-	NOUN
ajema-5949	69	30	algebra	algebra	NOUN
ajema-5949	69	31	.	.	PUNCT
ajema-5949	70	1	the	the	DET
ajema-5949	70	2	co	co	NOUN
ajema-5949	70	3	-	-	ADJ
ajema-5949	70	4	multiplication	multiplication	ADJ
ajema-5949	70	5	map	map	NOUN
ajema-5949	70	6	δ	δ	PROPN
ajema-5949	70	7	satisfies	satisfy	VERB
ajema-5949	70	8	the	the	DET
ajema-5949	70	9	co	co	NOUN
ajema-5949	70	10	-	-	ADJ
ajema-5949	70	11	associativity	associativity	ADJ
ajema-5949	70	12	property	property	NOUN
ajema-5949	70	13	:	:	PUNCT
ajema-5949	70	14	where	where	SCONJ
ajema-5949	70	15	a	a	PRON
ajema-5949	70	16	and	and	CCONJ
ajema-5949	70	17	b	b	NOUN
ajema-5949	70	18	are	be	AUX
ajema-5949	70	19	elements	element	NOUN
ajema-5949	70	20	of	of	ADP
ajema-5949	70	21	the	the	DET
ajema-5949	70	22	quantum	quantum	NOUN
ajema-5949	70	23	group	group	NOUN
ajema-5949	70	24	.	.	PUNCT
ajema-5949	71	1	the	the	DET
ajema-5949	71	2	co	co	NOUN
ajema-5949	71	3	-	-	NOUN
ajema-5949	71	4	unit	unit	NOUN
ajema-5949	71	5	map	map	NOUN
ajema-5949	71	6	ϵ	ϵ	AUX
ajema-5949	71	7	provides	provide	VERB
ajema-5949	71	8	a	a	DET
ajema-5949	71	9	counit	counit	VERB
ajema-5949	71	10	for	for	ADP
ajema-5949	71	11	the	the	DET
ajema-5949	71	12	co	co	NOUN
ajema-5949	71	13	-	-	ADJ
ajema-5949	71	14	algebra	algebra	ADJ
ajema-5949	71	15	structure	structure	NOUN
ajema-5949	71	16	,	,	PUNCT
ajema-5949	71	17	satisfying	satisfy	VERB
ajema-5949	71	18	:	:	PUNCT
ajema-5949	71	19	➢	➢	NOUN
ajema-5949	71	20	antipode	antipode	NOUN
ajema-5949	71	21	:	:	PUNCT
ajema-5949	71	22	the	the	DET
ajema-5949	71	23	antipode	antipode	NOUN
ajema-5949	71	24	s	s	VERB
ajema-5949	71	25	is	be	AUX
ajema-5949	71	26	a	a	DET
ajema-5949	71	27	map	map	NOUN
ajema-5949	71	28	that	that	PRON
ajema-5949	71	29	acts	act	VERB
ajema-5949	71	30	as	as	ADP
ajema-5949	71	31	a	a	DET
ajema-5949	71	32	"	"	PUNCT
ajema-5949	71	33	quantum	quantum	ADJ
ajema-5949	71	34	inverse	inverse	NOUN
ajema-5949	71	35	"	"	PUNCT
ajema-5949	71	36	for	for	ADP
ajema-5949	71	37	elements	element	NOUN
ajema-5949	71	38	in	in	ADP
ajema-5949	71	39	the	the	DET
ajema-5949	71	40	quantum	quantum	NOUN
ajema-5949	71	41	group	group	NOUN
ajema-5949	71	42	.	.	PUNCT
ajema-5949	72	1	the	the	DET
ajema-5949	72	2	antipode	antipode	NOUN
ajema-5949	72	3	satisfies	satisfy	VERB
ajema-5949	72	4	the	the	DET
ajema-5949	72	5	relation	relation	NOUN
ajema-5949	72	6	:	:	PUNCT
ajema-5949	72	7	where	where	SCONJ
ajema-5949	72	8	t	t	PROPN
ajema-5949	72	9	is	be	AUX
ajema-5949	72	10	a	a	DET
ajema-5949	72	11	specific	specific	ADJ
ajema-5949	72	12	twist	twist	NOUN
ajema-5949	72	13	operator	operator	NOUN
ajema-5949	72	14	.	.	PUNCT
ajema-5949	73	1	this	this	DET
ajema-5949	73	2	operation	operation	NOUN
ajema-5949	73	3	is	be	AUX
ajema-5949	73	4	key	key	ADJ
ajema-5949	73	5	to	to	ADP
ajema-5949	73	6	the	the	DET
ajema-5949	73	7	algebraic	algebraic	ADJ
ajema-5949	73	8	structure	structure	NOUN
ajema-5949	73	9	of	of	ADP
ajema-5949	73	10	quantum	quantum	ADJ
ajema-5949	73	11	groups	group	NOUN
ajema-5949	73	12	(	(	PUNCT
ajema-5949	73	13	drinfeld	drinfeld	PROPN
ajema-5949	73	14	,	,	PUNCT
ajema-5949	73	15	1986	1986	NUM
ajema-5949	73	16	;	;	PUNCT
ajema-5949	73	17	chari	chari	PROPN
ajema-5949	73	18	&	&	CCONJ
ajema-5949	73	19	pressley	pressley	PROPN
ajema-5949	73	20	,	,	PUNCT
ajema-5949	73	21	1994	1994	NUM
ajema-5949	73	22	)	)	PUNCT
ajema-5949	73	23	.	.	PUNCT
ajema-5949	74	1	the	the	DET
ajema-5949	74	2	hopf	hopf	ADJ
ajema-5949	74	3	algebra	algebra	NOUN
ajema-5949	74	4	structure	structure	NOUN
ajema-5949	74	5	encapsulates	encapsulate	VERB
ajema-5949	74	6	both	both	CCONJ
ajema-5949	74	7	the	the	DET
ajema-5949	74	8	algebraic	algebraic	ADJ
ajema-5949	74	9	and	and	CCONJ
ajema-5949	74	10	co	co	ADJ
ajema-5949	74	11	-	-	ADJ
ajema-5949	74	12	algebraic	algebraic	ADJ
ajema-5949	74	13	properties	property	NOUN
ajema-5949	74	14	of	of	ADP
ajema-5949	74	15	quantum	quantum	ADJ
ajema-5949	74	16	groups	group	NOUN
ajema-5949	74	17	and	and	CCONJ
ajema-5949	74	18	is	be	AUX
ajema-5949	74	19	essential	essential	ADJ
ajema-5949	74	20	for	for	ADP
ajema-5949	74	21	their	their	PRON
ajema-5949	74	22	application	application	NOUN
ajema-5949	74	23	in	in	ADP
ajema-5949	74	24	various	various	ADJ
ajema-5949	74	25	fields	field	NOUN
ajema-5949	74	26	such	such	ADJ
ajema-5949	74	27	as	as	ADP
ajema-5949	74	28	statistical	statistical	ADJ
ajema-5949	74	29	mechanics	mechanic	NOUN
ajema-5949	74	30	&	&	CCONJ
ajema-5949	74	31	quantum	quantum	ADJ
ajema-5949	74	32	field	field	NOUN
ajema-5949	74	33	theory	theory	NOUN
ajema-5949	74	34	.	.	PUNCT
ajema-5949	75	1	3.3	3.3	NUM
ajema-5949	75	2	.	.	PUNCT
ajema-5949	76	1	deformation	deformation	NOUN
ajema-5949	76	2	of	of	ADP
ajema-5949	76	3	lie	lie	NOUN
ajema-5949	76	4	algebras	algebras	PROPN
ajema-5949	76	5	quantum	quantum	NOUN
ajema-5949	76	6	groups	group	NOUN
ajema-5949	76	7	arise	arise	VERB
ajema-5949	76	8	as	as	ADP
ajema-5949	76	9	deformations	deformation	NOUN
ajema-5949	76	10	of	of	ADP
ajema-5949	76	11	classical	classical	ADJ
ajema-5949	76	12	lie	lie	NOUN
ajema-5949	76	13	algebras	algebra	NOUN
ajema-5949	76	14	.	.	PUNCT
ajema-5949	77	1	the	the	DET
ajema-5949	77	2	deformation	deformation	NOUN
ajema-5949	77	3	is	be	AUX
ajema-5949	77	4	controlled	control	VERB
ajema-5949	77	5	by	by	ADP
ajema-5949	77	6	the	the	DET
ajema-5949	77	7	parameter	parameter	NOUN
ajema-5949	77	8	q	q	PROPN
ajema-5949	77	9	,	,	PUNCT
ajema-5949	77	10	which	which	PRON
ajema-5949	77	11	modifies	modify	VERB
ajema-5949	77	12	the	the	DET
ajema-5949	77	13	lie	lie	NOUN
ajema-5949	77	14	algebra	algebra	NOUN
ajema-5949	77	15	's	's	PART
ajema-5949	77	16	classical	classical	ADJ
ajema-5949	77	17	commutation	commutation	NOUN
ajema-5949	77	18	relations	relation	NOUN
ajema-5949	77	19	.	.	PUNCT
ajema-5949	78	1	the	the	DET
ajema-5949	78	2	quantum	quantum	ADJ
ajema-5949	78	3	group	group	NOUN
ajema-5949	78	4	uq(g	uq(g	ADV
ajema-5949	78	5	)	)	PUNCT
ajema-5949	78	6	is	be	AUX
ajema-5949	78	7	a	a	DET
ajema-5949	78	8	deformed	deform	VERB
ajema-5949	78	9	version	version	NOUN
ajema-5949	78	10	of	of	ADP
ajema-5949	78	11	the	the	DET
ajema-5949	78	12	universal	universal	ADJ
ajema-5949	78	13	enveloping	enveloping	NOUN
ajema-5949	78	14	algebra	algebra	NOUN
ajema-5949	78	15	u(g	u(g	PROPN
ajema-5949	78	16	)	)	PUNCT
ajema-5949	78	17	of	of	ADP
ajema-5949	78	18	a	a	DET
ajema-5949	78	19	lie	lie	NOUN
ajema-5949	78	20	algebra	algebra	NOUN
ajema-5949	78	21	g.	g.	PROPN
ajema-5949	78	22	when	when	SCONJ
ajema-5949	78	23	q=1	q=1	X
ajema-5949	78	24	,	,	PUNCT
ajema-5949	78	25	the	the	DET
ajema-5949	78	26	quantum	quantum	NOUN
ajema-5949	78	27	group	group	NOUN
ajema-5949	78	28	reduces	reduce	VERB
ajema-5949	78	29	to	to	ADP
ajema-5949	78	30	the	the	DET
ajema-5949	78	31	classical	classical	ADJ
ajema-5949	78	32	lie	lie	NOUN
ajema-5949	78	33	group	group	NOUN
ajema-5949	78	34	or	or	CCONJ
ajema-5949	78	35	lie	lie	VERB
ajema-5949	78	36	algebra	algebra	NOUN
ajema-5949	78	37	,	,	PUNCT
ajema-5949	78	38	and	and	CCONJ
ajema-5949	78	39	the	the	DET
ajema-5949	78	40	commutation	commutation	NOUN
ajema-5949	78	41	relations	relation	NOUN
ajema-5949	78	42	are	be	AUX
ajema-5949	78	43	restored	restore	VERB
ajema-5949	78	44	to	to	ADP
ajema-5949	78	45	their	their	PRON
ajema-5949	78	46	classical	classical	ADJ
ajema-5949	78	47	form	form	NOUN
ajema-5949	78	48	.	.	PUNCT
ajema-5949	79	1	this	this	DET
ajema-5949	79	2	deformation	deformation	NOUN
ajema-5949	79	3	can	can	AUX
ajema-5949	79	4	be	be	AUX
ajema-5949	79	5	understood	understand	VERB
ajema-5949	79	6	in	in	ADP
ajema-5949	79	7	terms	term	NOUN
ajema-5949	79	8	of	of	ADP
ajema-5949	79	9	deformation	deformation	NOUN
ajema-5949	79	10	theory	theory	NOUN
ajema-5949	79	11	,	,	PUNCT
ajema-5949	79	12	where	where	SCONJ
ajema-5949	79	13	one	one	NUM
ajema-5949	79	14	systematically	systematically	ADV
ajema-5949	79	15	studies	study	VERB
ajema-5949	79	16	how	how	SCONJ
ajema-5949	79	17	algebraic	algebraic	ADJ
ajema-5949	79	18	structures	structure	NOUN
ajema-5949	79	19	can	can	AUX
ajema-5949	79	20	change	change	VERB
ajema-5949	79	21	when	when	SCONJ
ajema-5949	79	22	a	a	DET
ajema-5949	79	23	parameter	parameter	NOUN
ajema-5949	79	24	(	(	PUNCT
ajema-5949	79	25	such	such	ADJ
ajema-5949	79	26	as	as	ADP
ajema-5949	79	27	q	q	NOUN
ajema-5949	79	28	)	)	PUNCT
ajema-5949	79	29	is	be	AUX
ajema-5949	79	30	introduced	introduce	VERB
ajema-5949	79	31	.	.	PUNCT
ajema-5949	80	1	the	the	DET
ajema-5949	80	2	deformation	deformation	NOUN
ajema-5949	80	3	of	of	ADP
ajema-5949	80	4	the	the	DET
ajema-5949	80	5	lie	lie	NOUN
ajema-5949	80	6	algebra	algebra	NOUN
ajema-5949	80	7	into	into	ADP
ajema-5949	80	8	a	a	DET
ajema-5949	80	9	quantum	quantum	NOUN
ajema-5949	80	10	group	group	NOUN
ajema-5949	80	11	is	be	AUX
ajema-5949	80	12	significant	significant	ADJ
ajema-5949	80	13	because	because	SCONJ
ajema-5949	80	14	it	it	PRON
ajema-5949	80	15	allows	allow	VERB
ajema-5949	80	16	the	the	DET
ajema-5949	80	17	formulation	formulation	NOUN
ajema-5949	80	18	of	of	ADP
ajema-5949	80	19	quantum	quantum	ADJ
ajema-5949	80	20	symmetries	symmetry	NOUN
ajema-5949	80	21	that	that	PRON
ajema-5949	80	22	do	do	AUX
ajema-5949	80	23	not	not	PART
ajema-5949	80	24	commute	commute	VERB
ajema-5949	80	25	,	,	PUNCT
ajema-5949	80	26	which	which	PRON
ajema-5949	80	27	is	be	AUX
ajema-5949	80	28	an	an	DET
ajema-5949	80	29	essential	essential	ADJ
ajema-5949	80	30	property	property	NOUN
ajema-5949	80	31	for	for	ADP
ajema-5949	80	32	describing	describe	VERB
ajema-5949	80	33	quantum	quantum	NOUN
ajema-5949	80	34	systems	system	NOUN
ajema-5949	80	35	(	(	PUNCT
ajema-5949	80	36	drinfeld	drinfeld	PROPN
ajema-5949	80	37	,	,	PUNCT
ajema-5949	80	38	1986	1986	NUM
ajema-5949	80	39	;	;	PUNCT
ajema-5949	80	40	jimbo	jimbo	PROPN
ajema-5949	80	41	,	,	PUNCT
ajema-5949	80	42	1985	1985	NUM
ajema-5949	80	43	)	)	PUNCT
ajema-5949	80	44	.	.	PUNCT
ajema-5949	81	1	3.4	3.4	NUM
ajema-5949	81	2	.	.	PUNCT
ajema-5949	81	3	representation	representation	NOUN
ajema-5949	81	4	theory	theory	NOUN
ajema-5949	81	5	one	one	NUM
ajema-5949	81	6	of	of	ADP
ajema-5949	81	7	its	its	PRON
ajema-5949	81	8	main	main	ADJ
ajema-5949	81	9	features	feature	NOUN
ajema-5949	81	10	is	be	AUX
ajema-5949	81	11	the	the	DET
ajema-5949	81	12	representation	representation	NOUN
ajema-5949	81	13	theory	theory	NOUN
ajema-5949	81	14	of	of	ADP
ajema-5949	81	15	quantum	quantum	ADJ
ajema-5949	81	16	groups	group	NOUN
ajema-5949	81	17	,	,	PUNCT
ajema-5949	81	18	which	which	PRON
ajema-5949	81	19	studies	study	VERB
ajema-5949	81	20	their	their	PRON
ajema-5949	81	21	behavior	behavior	NOUN
ajema-5949	81	22	on	on	ADP
ajema-5949	81	23	vector	vector	NOUN
ajema-5949	81	24	spaces	space	NOUN
ajema-5949	81	25	.	.	PUNCT
ajema-5949	82	1	the	the	DET
ajema-5949	82	2	representation	representation	NOUN
ajema-5949	82	3	theory	theory	NOUN
ajema-5949	82	4	of	of	ADP
ajema-5949	82	5	quantum	quantum	NOUN
ajema-5949	82	6	groups	group	NOUN
ajema-5949	82	7	is	be	AUX
ajema-5949	82	8	a	a	DET
ajema-5949	82	9	generalization	generalization	NOUN
ajema-5949	82	10	of	of	ADP
ajema-5949	82	11	the	the	DET
ajema-5949	82	12	classical	classical	ADJ
ajema-5949	82	13	representation	representation	NOUN
ajema-5949	82	14	theory	theory	NOUN
ajema-5949	82	15	of	of	ADP
ajema-5949	82	16	lie	lie	NOUN
ajema-5949	82	17	groups	group	NOUN
ajema-5949	82	18	and	and	CCONJ
ajema-5949	82	19	lie	lie	VERB
ajema-5949	82	20	algebras	algebra	NOUN
ajema-5949	82	21	to	to	ADP
ajema-5949	82	22	the	the	DET
ajema-5949	82	23	non	non	ADJ
ajema-5949	82	24	-	-	ADJ
ajema-5949	82	25	commutative	commutative	ADJ
ajema-5949	82	26	248	248	NUM
ajema-5949	82	27	journal	journal	NOUN
ajema-5949	82	28	of	of	ADP
ajema-5949	82	29	engineering	engineering	NOUN
ajema-5949	82	30	,	,	PUNCT
ajema-5949	82	31	mechanics	mechanic	NOUN
ajema-5949	82	32	and	and	CCONJ
ajema-5949	82	33	architecture	architecture	NOUN
ajema-5949	82	34	www	www	NOUN
ajema-5949	82	35	.	.	PUNCT
ajema-5949	83	1	grnjournal.us	grnjournal.us	X
ajema-5949	83	2	context	context	NOUN
ajema-5949	83	3	.	.	PUNCT
ajema-5949	84	1	the	the	DET
ajema-5949	84	2	representations	representation	NOUN
ajema-5949	84	3	of	of	ADP
ajema-5949	84	4	quantum	quantum	ADJ
ajema-5949	84	5	groups	group	NOUN
ajema-5949	84	6	are	be	AUX
ajema-5949	84	7	built	build	VERB
ajema-5949	84	8	using	use	VERB
ajema-5949	84	9	the	the	DET
ajema-5949	84	10	same	same	ADJ
ajema-5949	84	11	algebraic	algebraic	ADJ
ajema-5949	84	12	techniques	technique	NOUN
ajema-5949	84	13	as	as	ADP
ajema-5949	84	14	classical	classical	ADJ
ajema-5949	84	15	lie	lie	NOUN
ajema-5949	84	16	groups	group	NOUN
ajema-5949	84	17	,	,	PUNCT
ajema-5949	84	18	but	but	CCONJ
ajema-5949	84	19	the	the	DET
ajema-5949	84	20	deformed	deform	VERB
ajema-5949	84	21	commutation	commutation	NOUN
ajema-5949	84	22	connections	connection	NOUN
ajema-5949	84	23	lead	lead	VERB
ajema-5949	84	24	to	to	ADP
ajema-5949	84	25	novel	novel	ADJ
ajema-5949	84	26	events	event	NOUN
ajema-5949	84	27	and	and	CCONJ
ajema-5949	84	28	special	special	ADJ
ajema-5949	84	29	mathematical	mathematical	ADJ
ajema-5949	84	30	structures	structure	NOUN
ajema-5949	84	31	.	.	PUNCT
ajema-5949	85	1	in	in	ADP
ajema-5949	85	2	the	the	DET
ajema-5949	85	3	case	case	NOUN
ajema-5949	85	4	of	of	ADP
ajema-5949	85	5	a	a	DET
ajema-5949	85	6	quantum	quantum	ADJ
ajema-5949	85	7	group	group	NOUN
ajema-5949	85	8	uq(g	uq(g	ADV
ajema-5949	85	9	)	)	PUNCT
ajema-5949	85	10	,	,	PUNCT
ajema-5949	85	11	the	the	DET
ajema-5949	85	12	representations	representation	NOUN
ajema-5949	85	13	can	can	AUX
ajema-5949	85	14	be	be	AUX
ajema-5949	85	15	classified	classify	VERB
ajema-5949	85	16	in	in	ADP
ajema-5949	85	17	terms	term	NOUN
ajema-5949	85	18	of	of	ADP
ajema-5949	85	19	modules	module	NOUN
ajema-5949	85	20	over	over	ADP
ajema-5949	85	21	the	the	DET
ajema-5949	85	22	hopf	hopf	ADJ
ajema-5949	85	23	algebra	algebra	NOUN
ajema-5949	85	24	,	,	PUNCT
ajema-5949	85	25	with	with	ADP
ajema-5949	85	26	certain	certain	ADJ
ajema-5949	85	27	representations	representation	NOUN
ajema-5949	85	28	corresponding	correspond	VERB
ajema-5949	85	29	to	to	ADP
ajema-5949	85	30	finite	finite	ADJ
ajema-5949	85	31	-	-	ADJ
ajema-5949	85	32	dimensional	dimensional	ADJ
ajema-5949	85	33	irreducible	irreducible	ADJ
ajema-5949	85	34	representations	representation	NOUN
ajema-5949	85	35	,	,	PUNCT
ajema-5949	85	36	analogous	analogous	ADJ
ajema-5949	85	37	to	to	ADP
ajema-5949	85	38	the	the	DET
ajema-5949	85	39	classical	classical	ADJ
ajema-5949	85	40	case	case	NOUN
ajema-5949	85	41	(	(	PUNCT
ajema-5949	85	42	chari	chari	PROPN
ajema-5949	85	43	&	&	CCONJ
ajema-5949	85	44	pressley	pressley	PROPN
ajema-5949	85	45	,	,	PUNCT
ajema-5949	85	46	1994	1994	NUM
ajema-5949	85	47	)	)	PUNCT
ajema-5949	85	48	.	.	PUNCT
ajema-5949	86	1	these	these	DET
ajema-5949	86	2	representations	representation	NOUN
ajema-5949	86	3	are	be	AUX
ajema-5949	86	4	crucial	crucial	ADJ
ajema-5949	86	5	for	for	ADP
ajema-5949	86	6	understanding	understand	VERB
ajema-5949	86	7	how	how	SCONJ
ajema-5949	86	8	quantum	quantum	ADJ
ajema-5949	86	9	symmetries	symmetry	NOUN
ajema-5949	86	10	act	act	VERB
ajema-5949	86	11	on	on	ADP
ajema-5949	86	12	quantum	quantum	NOUN
ajema-5949	86	13	systems	system	NOUN
ajema-5949	86	14	,	,	PUNCT
ajema-5949	86	15	and	and	CCONJ
ajema-5949	86	16	they	they	PRON
ajema-5949	86	17	have	have	VERB
ajema-5949	86	18	applications	application	NOUN
ajema-5949	86	19	in	in	ADP
ajema-5949	86	20	fields	field	NOUN
ajema-5949	86	21	like	like	ADP
ajema-5949	86	22	statistical	statistical	ADJ
ajema-5949	86	23	mechanics	mechanic	NOUN
ajema-5949	86	24	,	,	PUNCT
ajema-5949	86	25	integrable	integrable	ADJ
ajema-5949	86	26	systems	system	NOUN
ajema-5949	86	27	,	,	PUNCT
ajema-5949	86	28	and	and	CCONJ
ajema-5949	86	29	quantum	quantum	ADJ
ajema-5949	86	30	field	field	NOUN
ajema-5949	86	31	theory	theory	NOUN
ajema-5949	86	32	.	.	PUNCT
ajema-5949	87	1	3.5	3.5	NUM
ajema-5949	87	2	.	.	PUNCT
ajema-5949	87	3	quantum	quantum	PROPN
ajema-5949	87	4	group	group	NOUN
ajema-5949	87	5	symmetries	symmetry	NOUN
ajema-5949	87	6	quantum	quantum	NOUN
ajema-5949	87	7	groups	group	NOUN
ajema-5949	87	8	describe	describe	VERB
ajema-5949	87	9	the	the	DET
ajema-5949	87	10	symmetries	symmetry	NOUN
ajema-5949	87	11	of	of	ADP
ajema-5949	87	12	quantum	quantum	ADJ
ajema-5949	87	13	spaces	space	NOUN
ajema-5949	87	14	,	,	PUNCT
ajema-5949	87	15	which	which	PRON
ajema-5949	87	16	are	be	AUX
ajema-5949	87	17	typically	typically	ADV
ajema-5949	87	18	noncommutative	noncommutative	ADJ
ajema-5949	87	19	spaces	space	NOUN
ajema-5949	87	20	.	.	PUNCT
ajema-5949	88	1	in	in	ADP
ajema-5949	88	2	these	these	DET
ajema-5949	88	3	settings	setting	NOUN
ajema-5949	88	4	,	,	PUNCT
ajema-5949	88	5	the	the	DET
ajema-5949	88	6	quantum	quantum	NOUN
ajema-5949	88	7	group	group	NOUN
ajema-5949	88	8	acts	act	VERB
ajema-5949	88	9	as	as	ADP
ajema-5949	88	10	a	a	DET
ajema-5949	88	11	generalized	generalized	ADJ
ajema-5949	88	12	symmetry	symmetry	NOUN
ajema-5949	88	13	group	group	NOUN
ajema-5949	88	14	,	,	PUNCT
ajema-5949	88	15	preserving	preserve	VERB
ajema-5949	88	16	the	the	DET
ajema-5949	88	17	structure	structure	NOUN
ajema-5949	88	18	of	of	ADP
ajema-5949	88	19	the	the	DET
ajema-5949	88	20	space	space	NOUN
ajema-5949	88	21	despite	despite	SCONJ
ajema-5949	88	22	its	its	PRON
ajema-5949	88	23	non	non	ADJ
ajema-5949	88	24	-	-	ADJ
ajema-5949	88	25	commutative	commutative	ADJ
ajema-5949	88	26	nature	nature	NOUN
ajema-5949	88	27	.	.	PUNCT
ajema-5949	89	1	quantum	quantum	ADJ
ajema-5949	89	2	groups	group	NOUN
ajema-5949	89	3	are	be	AUX
ajema-5949	89	4	particularly	particularly	ADV
ajema-5949	89	5	important	important	ADJ
ajema-5949	89	6	in	in	ADP
ajema-5949	89	7	the	the	DET
ajema-5949	89	8	study	study	NOUN
ajema-5949	89	9	of	of	ADP
ajema-5949	89	10	quantum	quantum	ADJ
ajema-5949	89	11	field	field	NOUN
ajema-5949	89	12	theory	theory	NOUN
ajema-5949	89	13	and	and	CCONJ
ajema-5949	89	14	integrable	integrable	ADJ
ajema-5949	89	15	systems	system	NOUN
ajema-5949	89	16	,	,	PUNCT
ajema-5949	89	17	where	where	SCONJ
ajema-5949	89	18	they	they	PRON
ajema-5949	89	19	describe	describe	VERB
ajema-5949	89	20	symmetries	symmetry	NOUN
ajema-5949	89	21	that	that	PRON
ajema-5949	89	22	go	go	VERB
ajema-5949	89	23	beyond	beyond	ADP
ajema-5949	89	24	classical	classical	ADJ
ajema-5949	89	25	lie	lie	NOUN
ajema-5949	89	26	groups	group	NOUN
ajema-5949	89	27	and	and	CCONJ
ajema-5949	89	28	provide	provide	VERB
ajema-5949	89	29	a	a	DET
ajema-5949	89	30	more	more	ADV
ajema-5949	89	31	accurate	accurate	ADJ
ajema-5949	89	32	description	description	NOUN
ajema-5949	89	33	of	of	ADP
ajema-5949	89	34	quantum	quantum	ADJ
ajema-5949	89	35	phenomena	phenomenon	NOUN
ajema-5949	89	36	.	.	PUNCT
ajema-5949	90	1	for	for	ADP
ajema-5949	90	2	instance	instance	NOUN
ajema-5949	90	3	,	,	PUNCT
ajema-5949	90	4	quantum	quantum	ADJ
ajema-5949	90	5	groups	group	NOUN
ajema-5949	90	6	are	be	AUX
ajema-5949	90	7	used	use	VERB
ajema-5949	90	8	to	to	PART
ajema-5949	90	9	model	model	VERB
ajema-5949	90	10	symmetries	symmetry	NOUN
ajema-5949	90	11	in	in	ADP
ajema-5949	90	12	quantum	quantum	NOUN
ajema-5949	90	13	spin	spin	NOUN
ajema-5949	90	14	systems	system	NOUN
ajema-5949	90	15	and	and	CCONJ
ajema-5949	90	16	lattice	lattice	NOUN
ajema-5949	90	17	models	model	NOUN
ajema-5949	90	18	.	.	PUNCT
ajema-5949	91	1	the	the	DET
ajema-5949	91	2	non	non	ADJ
ajema-5949	91	3	-	-	ADJ
ajema-5949	91	4	commutative	commutative	ADJ
ajema-5949	91	5	structure	structure	NOUN
ajema-5949	91	6	of	of	ADP
ajema-5949	91	7	the	the	DET
ajema-5949	91	8	quantum	quantum	NOUN
ajema-5949	91	9	group	group	NOUN
ajema-5949	91	10	is	be	AUX
ajema-5949	91	11	essential	essential	ADJ
ajema-5949	91	12	for	for	ADP
ajema-5949	91	13	capturing	capture	VERB
ajema-5949	91	14	the	the	DET
ajema-5949	91	15	quantum	quantum	ADJ
ajema-5949	91	16	nature	nature	NOUN
ajema-5949	91	17	of	of	ADP
ajema-5949	91	18	these	these	DET
ajema-5949	91	19	systems	system	NOUN
ajema-5949	91	20	,	,	PUNCT
ajema-5949	91	21	which	which	PRON
ajema-5949	91	22	can	can	AUX
ajema-5949	91	23	not	not	PART
ajema-5949	91	24	be	be	AUX
ajema-5949	91	25	adequately	adequately	ADV
ajema-5949	91	26	described	describe	VERB
ajema-5949	91	27	by	by	ADP
ajema-5949	91	28	classical	classical	ADJ
ajema-5949	91	29	symmetry	symmetry	NOUN
ajema-5949	91	30	groups	group	NOUN
ajema-5949	91	31	(	(	PUNCT
ajema-5949	91	32	chari	chari	PROPN
ajema-5949	91	33	&	&	CCONJ
ajema-5949	91	34	pressley	pressley	PROPN
ajema-5949	91	35	,	,	PUNCT
ajema-5949	91	36	1994	1994	NUM
ajema-5949	91	37	)	)	PUNCT
ajema-5949	91	38	.	.	PUNCT
ajema-5949	92	1	3.6	3.6	NUM
ajema-5949	92	2	.	.	PUNCT
ajema-5949	93	1	co	co	NOUN
ajema-5949	93	2	-	-	NOUN
ajema-5949	93	3	structure	structure	NOUN
ajema-5949	93	4	and	and	CCONJ
ajema-5949	93	5	duality	duality	NOUN
ajema-5949	93	6	another	another	DET
ajema-5949	93	7	important	important	ADJ
ajema-5949	93	8	factor	factor	NOUN
ajema-5949	93	9	influencing	influence	VERB
ajema-5949	93	10	the	the	DET
ajema-5949	93	11	mathematical	mathematical	ADJ
ajema-5949	93	12	characteristics	characteristic	NOUN
ajema-5949	93	13	of	of	ADP
ajema-5949	93	14	quantum	quantum	ADJ
ajema-5949	93	15	groups	group	NOUN
ajema-5949	93	16	is	be	AUX
ajema-5949	93	17	their	their	PRON
ajema-5949	93	18	co	co	NOUN
ajema-5949	93	19	-	-	NOUN
ajema-5949	93	20	structure	structure	NOUN
ajema-5949	93	21	.	.	PUNCT
ajema-5949	94	1	quantum	quantum	ADJ
ajema-5949	94	2	groups	group	NOUN
ajema-5949	94	3	frequently	frequently	ADV
ajema-5949	94	4	have	have	VERB
ajema-5949	94	5	duality	duality	NOUN
ajema-5949	94	6	properties	property	NOUN
ajema-5949	94	7	,	,	PUNCT
ajema-5949	94	8	where	where	SCONJ
ajema-5949	94	9	the	the	DET
ajema-5949	94	10	algebra	algebra	NOUN
ajema-5949	94	11	of	of	ADP
ajema-5949	94	12	functions	function	NOUN
ajema-5949	94	13	on	on	ADP
ajema-5949	94	14	a	a	DET
ajema-5949	94	15	quantum	quantum	NOUN
ajema-5949	94	16	group	group	NOUN
ajema-5949	94	17	is	be	AUX
ajema-5949	94	18	dual	dual	ADJ
ajema-5949	94	19	to	to	ADP
ajema-5949	94	20	the	the	DET
ajema-5949	94	21	algebra	algebra	NOUN
ajema-5949	94	22	of	of	ADP
ajema-5949	94	23	co	co	NOUN
ajema-5949	94	24	-	-	NOUN
ajema-5949	94	25	functions	function	NOUN
ajema-5949	94	26	,	,	PUNCT
ajema-5949	94	27	in	in	ADP
ajema-5949	94	28	addition	addition	NOUN
ajema-5949	94	29	to	to	ADP
ajema-5949	94	30	their	their	PRON
ajema-5949	94	31	algebraic	algebraic	ADJ
ajema-5949	94	32	and	and	CCONJ
ajema-5949	94	33	coalgebraic	coalgebraic	ADJ
ajema-5949	94	34	structure	structure	NOUN
ajema-5949	94	35	.	.	PUNCT
ajema-5949	95	1	similar	similar	ADJ
ajema-5949	95	2	to	to	ADP
ajema-5949	95	3	the	the	DET
ajema-5949	95	4	classical	classical	ADJ
ajema-5949	95	5	duality	duality	NOUN
ajema-5949	95	6	between	between	ADP
ajema-5949	95	7	a	a	DET
ajema-5949	95	8	lie	lie	NOUN
ajema-5949	95	9	group	group	NOUN
ajema-5949	95	10	and	and	CCONJ
ajema-5949	95	11	its	its	PRON
ajema-5949	95	12	lie	lie	NOUN
ajema-5949	95	13	algebra	algebra	NOUN
ajema-5949	95	14	,	,	PUNCT
ajema-5949	95	15	this	this	DET
ajema-5949	95	16	duality	duality	NOUN
ajema-5949	95	17	offers	offer	VERB
ajema-5949	95	18	a	a	DET
ajema-5949	95	19	natural	natural	ADJ
ajema-5949	95	20	context	context	NOUN
ajema-5949	95	21	for	for	ADP
ajema-5949	95	22	studying	study	VERB
ajema-5949	95	23	quantum	quantum	ADJ
ajema-5949	95	24	symmetries	symmetry	NOUN
ajema-5949	95	25	and	and	CCONJ
ajema-5949	95	26	transformations	transformation	NOUN
ajema-5949	95	27	.	.	PUNCT
ajema-5949	96	1	this	this	DET
ajema-5949	96	2	interplay	interplay	NOUN
ajema-5949	96	3	between	between	ADP
ajema-5949	96	4	the	the	DET
ajema-5949	96	5	algebraic	algebraic	ADJ
ajema-5949	96	6	and	and	CCONJ
ajema-5949	96	7	co	co	ADJ
ajema-5949	96	8	-	-	ADJ
ajema-5949	96	9	algebraic	algebraic	ADJ
ajema-5949	96	10	structures	structure	NOUN
ajema-5949	96	11	allows	allow	VERB
ajema-5949	96	12	quantum	quantum	ADJ
ajema-5949	96	13	groups	group	NOUN
ajema-5949	96	14	to	to	PART
ajema-5949	96	15	serve	serve	VERB
ajema-5949	96	16	as	as	ADP
ajema-5949	96	17	powerful	powerful	ADJ
ajema-5949	96	18	tools	tool	NOUN
ajema-5949	96	19	in	in	ADP
ajema-5949	96	20	understanding	understand	VERB
ajema-5949	96	21	both	both	CCONJ
ajema-5949	96	22	classical	classical	ADJ
ajema-5949	96	23	and	and	CCONJ
ajema-5949	96	24	quantum	quantum	ADJ
ajema-5949	96	25	symmetries	symmetry	NOUN
ajema-5949	96	26	(	(	PUNCT
ajema-5949	96	27	chari	chari	PROPN
ajema-5949	96	28	&	&	CCONJ
ajema-5949	96	29	pressley	pressley	PROPN
ajema-5949	96	30	,	,	PUNCT
ajema-5949	96	31	1994	1994	NUM
ajema-5949	96	32	)	)	PUNCT
ajema-5949	96	33	.	.	PUNCT
ajema-5949	97	1	the	the	DET
ajema-5949	97	2	mathematical	mathematical	ADJ
ajema-5949	97	3	properties	property	NOUN
ajema-5949	97	4	of	of	ADP
ajema-5949	97	5	quantum	quantum	ADJ
ajema-5949	97	6	groups	group	NOUN
ajema-5949	97	7	,	,	PUNCT
ajema-5949	97	8	including	include	VERB
ajema-5949	97	9	their	their	PRON
ajema-5949	97	10	non	non	ADJ
ajema-5949	97	11	-	-	ADJ
ajema-5949	97	12	commutative	commutative	ADJ
ajema-5949	97	13	nature	nature	NOUN
ajema-5949	97	14	,	,	PUNCT
ajema-5949	97	15	hopf	hopf	ADJ
ajema-5949	97	16	algebra	algebra	NOUN
ajema-5949	97	17	structure	structure	NOUN
ajema-5949	97	18	,	,	PUNCT
ajema-5949	97	19	representation	representation	NOUN
ajema-5949	97	20	theory	theory	NOUN
ajema-5949	97	21	,	,	PUNCT
ajema-5949	97	22	and	and	CCONJ
ajema-5949	97	23	connection	connection	NOUN
ajema-5949	97	24	to	to	ADP
ajema-5949	97	25	classical	classical	ADJ
ajema-5949	97	26	lie	lie	NOUN
ajema-5949	97	27	algebras	algebra	NOUN
ajema-5949	97	28	,	,	PUNCT
ajema-5949	97	29	make	make	VERB
ajema-5949	97	30	them	they	PRON
ajema-5949	97	31	a	a	DET
ajema-5949	97	32	powerful	powerful	ADJ
ajema-5949	97	33	tool	tool	NOUN
ajema-5949	97	34	for	for	ADP
ajema-5949	97	35	studying	study	VERB
ajema-5949	97	36	quantum	quantum	ADJ
ajema-5949	97	37	symmetries	symmetry	NOUN
ajema-5949	97	38	.	.	PUNCT
ajema-5949	98	1	as	as	ADP
ajema-5949	98	2	deformations	deformation	NOUN
ajema-5949	98	3	of	of	ADP
ajema-5949	98	4	classical	classical	ADJ
ajema-5949	98	5	lie	lie	NOUN
ajema-5949	98	6	groups	group	NOUN
ajema-5949	98	7	,	,	PUNCT
ajema-5949	98	8	quantum	quantum	ADJ
ajema-5949	98	9	groups	group	NOUN
ajema-5949	98	10	provide	provide	VERB
ajema-5949	98	11	a	a	DET
ajema-5949	98	12	rigorous	rigorous	ADJ
ajema-5949	98	13	algebraic	algebraic	ADJ
ajema-5949	98	14	framework	framework	NOUN
ajema-5949	98	15	for	for	ADP
ajema-5949	98	16	understanding	understand	VERB
ajema-5949	98	17	non	non	ADJ
ajema-5949	98	18	-	-	ADJ
ajema-5949	98	19	commutative	commutative	ADJ
ajema-5949	98	20	spaces	space	NOUN
ajema-5949	98	21	and	and	CCONJ
ajema-5949	98	22	symmetries	symmetry	NOUN
ajema-5949	98	23	that	that	PRON
ajema-5949	98	24	arise	arise	VERB
ajema-5949	98	25	in	in	ADP
ajema-5949	98	26	quantum	quantum	ADJ
ajema-5949	98	27	mechanics	mechanic	NOUN
ajema-5949	98	28	and	and	CCONJ
ajema-5949	98	29	also	also	ADV
ajema-5949	98	30	quantum	quantum	ADJ
ajema-5949	98	31	field	field	NOUN
ajema-5949	98	32	theory	theory	NOUN
ajema-5949	98	33	.	.	PUNCT
ajema-5949	99	1	our	our	PRON
ajema-5949	99	2	knowledge	knowledge	NOUN
ajema-5949	99	3	of	of	ADP
ajema-5949	99	4	quantum	quantum	NOUN
ajema-5949	99	5	systems	system	NOUN
ajema-5949	99	6	and	and	CCONJ
ajema-5949	99	7	their	their	PRON
ajema-5949	99	8	symmetries	symmetry	NOUN
ajema-5949	99	9	is	be	AUX
ajema-5949	99	10	still	still	ADV
ajema-5949	99	11	greatly	greatly	ADV
ajema-5949	99	12	influenced	influence	VERB
ajema-5949	99	13	by	by	ADP
ajema-5949	99	14	quantum	quantum	ADJ
ajema-5949	99	15	groups	group	NOUN
ajema-5949	99	16	,	,	PUNCT
ajema-5949	99	17	which	which	PRON
ajema-5949	99	18	are	be	AUX
ajema-5949	99	19	used	use	VERB
ajema-5949	99	20	in	in	ADP
ajema-5949	99	21	many	many	ADJ
ajema-5949	99	22	branches	branch	NOUN
ajema-5949	99	23	of	of	ADP
ajema-5949	99	24	mathematics	mathematic	NOUN
ajema-5949	99	25	and	and	CCONJ
ajema-5949	99	26	physics	physic	NOUN
ajema-5949	99	27	.	.	PUNCT
ajema-5949	100	1	4	4	X
ajema-5949	100	2	.	.	X
ajema-5949	100	3	applications	application	NOUN
ajema-5949	100	4	in	in	ADP
ajema-5949	100	5	theoretical	theoretical	ADJ
ajema-5949	100	6	physics	physics	NOUN
ajema-5949	100	7	quantum	quantum	NOUN
ajema-5949	100	8	groups	group	NOUN
ajema-5949	100	9	have	have	AUX
ajema-5949	100	10	been	be	AUX
ajema-5949	100	11	used	use	VERB
ajema-5949	100	12	extensively	extensively	ADV
ajema-5949	100	13	in	in	ADP
ajema-5949	100	14	many	many	ADJ
ajema-5949	100	15	branches	branch	NOUN
ajema-5949	100	16	of	of	ADP
ajema-5949	100	17	theoretical	theoretical	ADJ
ajema-5949	100	18	physics	physic	NOUN
ajema-5949	100	19	,	,	PUNCT
ajema-5949	100	20	such	such	ADJ
ajema-5949	100	21	as	as	ADP
ajema-5949	100	22	quantum	quantum	ADJ
ajema-5949	100	23	mechanics	mechanic	NOUN
ajema-5949	100	24	,	,	PUNCT
ajema-5949	100	25	quantum	quantum	ADJ
ajema-5949	100	26	field	field	NOUN
ajema-5949	100	27	theory	theory	NOUN
ajema-5949	100	28	,	,	PUNCT
ajema-5949	100	29	integrable	integrable	ADJ
ajema-5949	100	30	systems	system	NOUN
ajema-5949	100	31	,	,	PUNCT
ajema-5949	100	32	and	and	CCONJ
ajema-5949	100	33	quantum	quantum	NOUN
ajema-5949	100	34	gravity	gravity	NOUN
ajema-5949	100	35	.	.	PUNCT
ajema-5949	101	1	their	their	PRON
ajema-5949	101	2	noncommutative	noncommutative	ADJ
ajema-5949	101	3	algebraic	algebraic	ADJ
ajema-5949	101	4	structure	structure	NOUN
ajema-5949	101	5	makes	make	VERB
ajema-5949	101	6	them	they	PRON
ajema-5949	101	7	a	a	DET
ajema-5949	101	8	powerful	powerful	ADJ
ajema-5949	101	9	tool	tool	NOUN
ajema-5949	101	10	for	for	ADP
ajema-5949	101	11	modeling	model	VERB
ajema-5949	101	12	phenomena	phenomenon	NOUN
ajema-5949	101	13	that	that	PRON
ajema-5949	101	14	can	can	AUX
ajema-5949	101	15	not	not	PART
ajema-5949	101	16	be	be	AUX
ajema-5949	101	17	captured	capture	VERB
ajema-5949	101	18	by	by	ADP
ajema-5949	101	19	classical	classical	ADJ
ajema-5949	101	20	symmetries	symmetry	NOUN
ajema-5949	101	21	.	.	PUNCT
ajema-5949	102	1	in	in	ADP
ajema-5949	102	2	this	this	DET
ajema-5949	102	3	section	section	NOUN
ajema-5949	102	4	,	,	PUNCT
ajema-5949	102	5	we	we	PRON
ajema-5949	102	6	explore	explore	VERB
ajema-5949	102	7	some	some	PRON
ajema-5949	102	8	of	of	ADP
ajema-5949	102	9	the	the	DET
ajema-5949	102	10	key	key	ADJ
ajema-5949	102	11	applications	application	NOUN
ajema-5949	102	12	of	of	ADP
ajema-5949	102	13	quantum	quantum	ADJ
ajema-5949	102	14	groups	group	NOUN
ajema-5949	102	15	in	in	ADP
ajema-5949	102	16	theoretical	theoretical	ADJ
ajema-5949	102	17	physics	physics	NOUN
ajema-5949	102	18	,	,	PUNCT
ajema-5949	102	19	highlighting	highlight	VERB
ajema-5949	102	20	their	their	PRON
ajema-5949	102	21	role	role	NOUN
ajema-5949	102	22	in	in	ADP
ajema-5949	102	23	describing	describe	VERB
ajema-5949	102	24	quantum	quantum	ADJ
ajema-5949	102	25	symmetries	symmetry	NOUN
ajema-5949	102	26	,	,	PUNCT
ajema-5949	102	27	integrable	integrable	ADJ
ajema-5949	102	28	systems	system	NOUN
ajema-5949	102	29	,	,	PUNCT
ajema-5949	102	30	quantum	quantum	NOUN
ajema-5949	102	31	spin	spin	NOUN
ajema-5949	102	32	chains	chain	NOUN
ajema-5949	102	33	,	,	PUNCT
ajema-5949	102	34	and	and	CCONJ
ajema-5949	102	35	quantum	quantum	NOUN
ajema-5949	102	36	gravity	gravity	NOUN
ajema-5949	102	37	.	.	PUNCT
ajema-5949	103	1	4.1	4.1	NUM
ajema-5949	103	2	.	.	PUNCT
ajema-5949	103	3	quantum	quantum	ADJ
ajema-5949	103	4	symmetries	symmetry	NOUN
ajema-5949	103	5	in	in	ADP
ajema-5949	103	6	quantum	quantum	ADJ
ajema-5949	103	7	mechanics	mechanic	NOUN
ajema-5949	103	8	and	and	CCONJ
ajema-5949	103	9	quantum	quantum	NOUN
ajema-5949	103	10	field	field	NOUN
ajema-5949	103	11	theory	theory	NOUN
ajema-5949	103	12	one	one	NUM
ajema-5949	103	13	of	of	ADP
ajema-5949	103	14	the	the	DET
ajema-5949	103	15	most	most	ADV
ajema-5949	103	16	fundamental	fundamental	ADJ
ajema-5949	103	17	applications	application	NOUN
ajema-5949	103	18	of	of	ADP
ajema-5949	103	19	quantum	quantum	ADJ
ajema-5949	103	20	groups	group	NOUN
ajema-5949	103	21	in	in	ADP
ajema-5949	103	22	theoretical	theoretical	ADJ
ajema-5949	103	23	physics	physics	NOUN
ajema-5949	103	24	is	be	AUX
ajema-5949	103	25	in	in	ADP
ajema-5949	103	26	the	the	DET
ajema-5949	103	27	study	study	NOUN
ajema-5949	103	28	of	of	ADP
ajema-5949	103	29	quantum	quantum	ADJ
ajema-5949	103	30	symmetries	symmetry	NOUN
ajema-5949	103	31	.	.	PUNCT
ajema-5949	104	1	in	in	ADP
ajema-5949	104	2	classical	classical	ADJ
ajema-5949	104	3	mechanics	mechanic	NOUN
ajema-5949	104	4	,	,	PUNCT
ajema-5949	104	5	symmetries	symmetry	NOUN
ajema-5949	104	6	are	be	AUX
ajema-5949	104	7	often	often	ADV
ajema-5949	104	8	represented	represent	VERB
ajema-5949	104	9	by	by	ADP
ajema-5949	104	10	lie	lie	NOUN
ajema-5949	104	11	groups	group	NOUN
ajema-5949	104	12	and	and	CCONJ
ajema-5949	104	13	lie	lie	VERB
ajema-5949	104	14	algebras	algebra	NOUN
ajema-5949	104	15	,	,	PUNCT
ajema-5949	104	16	but	but	CCONJ
ajema-5949	104	17	quantum	quantum	NOUN
ajema-5949	104	18	mechanics	mechanic	NOUN
ajema-5949	104	19	introduces	introduce	VERB
ajema-5949	104	20	non	non	ADJ
ajema-5949	104	21	-	-	NOUN
ajema-5949	104	22	commutativity	commutativity	NOUN
ajema-5949	104	23	into	into	ADP
ajema-5949	104	24	the	the	DET
ajema-5949	104	25	structure	structure	NOUN
ajema-5949	104	26	of	of	ADP
ajema-5949	104	27	symmetries	symmetry	NOUN
ajema-5949	104	28	.	.	PUNCT
ajema-5949	105	1	quantum	quantum	ADJ
ajema-5949	105	2	groups	group	NOUN
ajema-5949	105	3	,	,	PUNCT
ajema-5949	105	4	as	as	SCONJ
ajema-5949	105	5	deformations	deformation	NOUN
ajema-5949	105	6	of	of	ADP
ajema-5949	105	7	classical	classical	ADJ
ajema-5949	105	8	lie	lie	NOUN
ajema-5949	105	9	groups	group	NOUN
ajema-5949	105	10	,	,	PUNCT
ajema-5949	105	11	provide	provide	VERB
ajema-5949	105	12	a	a	DET
ajema-5949	105	13	natural	natural	ADJ
ajema-5949	105	14	249	249	NUM
ajema-5949	105	15	journal	journal	NOUN
ajema-5949	105	16	of	of	ADP
ajema-5949	105	17	engineering	engineering	NOUN
ajema-5949	105	18	,	,	PUNCT
ajema-5949	105	19	mechanics	mechanic	NOUN
ajema-5949	105	20	and	and	CCONJ
ajema-5949	105	21	architecture	architecture	NOUN
ajema-5949	105	22	www	www	NOUN
ajema-5949	105	23	.	.	PUNCT
ajema-5949	106	1	grnjournal.us	grnjournal.us	PROPN
ajema-5949	106	2	mathematical	mathematical	ADJ
ajema-5949	106	3	framework	framework	NOUN
ajema-5949	106	4	for	for	ADP
ajema-5949	106	5	describing	describe	VERB
ajema-5949	106	6	these	these	DET
ajema-5949	106	7	non	non	ADJ
ajema-5949	106	8	-	-	ADJ
ajema-5949	106	9	commutative	commutative	ADJ
ajema-5949	106	10	symmetries	symmetry	NOUN
ajema-5949	106	11	(	(	PUNCT
ajema-5949	106	12	chari	chari	PROPN
ajema-5949	106	13	&	&	CCONJ
ajema-5949	106	14	pressley	pressley	PROPN
ajema-5949	106	15	,	,	PUNCT
ajema-5949	106	16	1994	1994	NUM
ajema-5949	106	17	)	)	PUNCT
ajema-5949	106	18	.	.	PUNCT
ajema-5949	107	1	in	in	ADP
ajema-5949	107	2	quantum	quantum	ADJ
ajema-5949	107	3	field	field	NOUN
ajema-5949	107	4	theory	theory	NOUN
ajema-5949	107	5	(	(	PUNCT
ajema-5949	107	6	qft	qft	PROPN
ajema-5949	107	7	)	)	PUNCT
ajema-5949	107	8	,	,	PUNCT
ajema-5949	107	9	quantum	quantum	NOUN
ajema-5949	107	10	groups	group	NOUN
ajema-5949	107	11	have	have	AUX
ajema-5949	107	12	been	be	AUX
ajema-5949	107	13	used	use	VERB
ajema-5949	107	14	to	to	PART
ajema-5949	107	15	describe	describe	VERB
ajema-5949	107	16	symmetries	symmetry	NOUN
ajema-5949	107	17	that	that	PRON
ajema-5949	107	18	are	be	AUX
ajema-5949	107	19	not	not	PART
ajema-5949	107	20	captured	capture	VERB
ajema-5949	107	21	by	by	ADP
ajema-5949	107	22	classical	classical	ADJ
ajema-5949	107	23	groups	group	NOUN
ajema-5949	107	24	.	.	PUNCT
ajema-5949	108	1	these	these	DET
ajema-5949	108	2	symmetries	symmetry	NOUN
ajema-5949	108	3	arise	arise	VERB
ajema-5949	108	4	in	in	ADP
ajema-5949	108	5	models	model	NOUN
ajema-5949	108	6	where	where	SCONJ
ajema-5949	108	7	the	the	DET
ajema-5949	108	8	spacetime	spacetime	NOUN
ajema-5949	108	9	is	be	AUX
ajema-5949	108	10	not	not	PART
ajema-5949	108	11	commutative	commutative	ADJ
ajema-5949	108	12	,	,	PUNCT
ajema-5949	108	13	such	such	ADJ
ajema-5949	108	14	as	as	ADP
ajema-5949	108	15	in	in	ADP
ajema-5949	108	16	certain	certain	ADJ
ajema-5949	108	17	models	model	NOUN
ajema-5949	108	18	of	of	ADP
ajema-5949	108	19	quantum	quantum	ADJ
ajema-5949	108	20	gravity	gravity	NOUN
ajema-5949	108	21	or	or	CCONJ
ajema-5949	108	22	in	in	ADP
ajema-5949	108	23	deformed	deform	VERB
ajema-5949	108	24	quantum	quantum	ADJ
ajema-5949	108	25	spaces	space	NOUN
ajema-5949	108	26	(	(	PUNCT
ajema-5949	108	27	drinfeld	drinfeld	PROPN
ajema-5949	108	28	,	,	PUNCT
ajema-5949	108	29	1986	1986	NUM
ajema-5949	108	30	)	)	PUNCT
ajema-5949	108	31	.	.	PUNCT
ajema-5949	109	1	quantum	quantum	NOUN
ajema-5949	109	2	groups	group	NOUN
ajema-5949	109	3	offer	offer	VERB
ajema-5949	109	4	a	a	DET
ajema-5949	109	5	way	way	NOUN
ajema-5949	109	6	to	to	PART
ajema-5949	109	7	generalize	generalize	VERB
ajema-5949	109	8	poincaré	poincaré	PROPN
ajema-5949	109	9	symmetry	symmetry	PROPN
ajema-5949	109	10	,	,	PUNCT
ajema-5949	109	11	which	which	PRON
ajema-5949	109	12	governs	govern	VERB
ajema-5949	109	13	the	the	DET
ajema-5949	109	14	behavior	behavior	NOUN
ajema-5949	109	15	of	of	ADP
ajema-5949	109	16	spacetime	spacetime	ADJ
ajema-5949	109	17	symmetries	symmetry	NOUN
ajema-5949	109	18	in	in	ADP
ajema-5949	109	19	relativistic	relativistic	ADJ
ajema-5949	109	20	quantum	quantum	NOUN
ajema-5949	109	21	theories	theory	NOUN
ajema-5949	109	22	.	.	PUNCT
ajema-5949	110	1	for	for	ADP
ajema-5949	110	2	instance	instance	NOUN
ajema-5949	110	3	,	,	PUNCT
ajema-5949	110	4	in	in	ADP
ajema-5949	110	5	the	the	DET
ajema-5949	110	6	context	context	NOUN
ajema-5949	110	7	of	of	ADP
ajema-5949	110	8	deformed	deformed	ADJ
ajema-5949	110	9	qft	qft	NOUN
ajema-5949	110	10	,	,	PUNCT
ajema-5949	110	11	the	the	DET
ajema-5949	110	12	symmetries	symmetry	NOUN
ajema-5949	110	13	of	of	ADP
ajema-5949	110	14	the	the	DET
ajema-5949	110	15	theory	theory	NOUN
ajema-5949	110	16	may	may	AUX
ajema-5949	110	17	be	be	AUX
ajema-5949	110	18	described	describe	VERB
ajema-5949	110	19	by	by	ADP
ajema-5949	110	20	quantum	quantum	ADJ
ajema-5949	110	21	groups	group	NOUN
ajema-5949	110	22	that	that	PRON
ajema-5949	110	23	act	act	VERB
ajema-5949	110	24	on	on	ADP
ajema-5949	110	25	the	the	DET
ajema-5949	110	26	space	space	NOUN
ajema-5949	110	27	of	of	ADP
ajema-5949	110	28	quantum	quantum	ADJ
ajema-5949	110	29	fields	field	NOUN
ajema-5949	110	30	,	,	PUNCT
ajema-5949	110	31	leading	lead	VERB
ajema-5949	110	32	to	to	ADP
ajema-5949	110	33	a	a	DET
ajema-5949	110	34	richer	rich	ADJ
ajema-5949	110	35	and	and	CCONJ
ajema-5949	110	36	more	more	ADV
ajema-5949	110	37	flexible	flexible	ADJ
ajema-5949	110	38	framework	framework	NOUN
ajema-5949	110	39	for	for	ADP
ajema-5949	110	40	the	the	DET
ajema-5949	110	41	description	description	NOUN
ajema-5949	110	42	of	of	ADP
ajema-5949	110	43	quantum	quantum	NOUN
ajema-5949	110	44	systems	system	NOUN
ajema-5949	110	45	(	(	PUNCT
ajema-5949	110	46	majid	majid	PROPN
ajema-5949	110	47	,	,	PUNCT
ajema-5949	110	48	1994	1994	NUM
ajema-5949	110	49	)	)	PUNCT
ajema-5949	110	50	.	.	PUNCT
ajema-5949	111	1	4.2	4.2	NUM
ajema-5949	111	2	.	.	PUNCT
ajema-5949	112	1	integrable	integrable	ADJ
ajema-5949	112	2	systems	system	NOUN
ajema-5949	112	3	quantum	quantum	NOUN
ajema-5949	112	4	groups	group	NOUN
ajema-5949	112	5	have	have	AUX
ajema-5949	112	6	found	find	VERB
ajema-5949	112	7	significant	significant	ADJ
ajema-5949	112	8	applications	application	NOUN
ajema-5949	112	9	in	in	ADP
ajema-5949	112	10	the	the	DET
ajema-5949	112	11	study	study	NOUN
ajema-5949	112	12	of	of	ADP
ajema-5949	112	13	integrable	integrable	ADJ
ajema-5949	112	14	systems	system	NOUN
ajema-5949	112	15	,	,	PUNCT
ajema-5949	112	16	which	which	PRON
ajema-5949	112	17	are	be	AUX
ajema-5949	112	18	systems	system	NOUN
ajema-5949	112	19	that	that	PRON
ajema-5949	112	20	possess	possess	VERB
ajema-5949	112	21	a	a	DET
ajema-5949	112	22	large	large	ADJ
ajema-5949	112	23	number	number	NOUN
ajema-5949	112	24	of	of	ADP
ajema-5949	112	25	conserved	conserve	VERB
ajema-5949	112	26	quantities	quantity	NOUN
ajema-5949	112	27	and	and	CCONJ
ajema-5949	112	28	can	can	AUX
ajema-5949	112	29	be	be	AUX
ajema-5949	112	30	solved	solve	VERB
ajema-5949	112	31	exactly	exactly	ADV
ajema-5949	112	32	.	.	PUNCT
ajema-5949	113	1	the	the	DET
ajema-5949	113	2	connection	connection	NOUN
ajema-5949	113	3	between	between	ADP
ajema-5949	113	4	quantum	quantum	ADJ
ajema-5949	113	5	groups	group	NOUN
ajema-5949	113	6	and	and	CCONJ
ajema-5949	113	7	integrable	integrable	ADJ
ajema-5949	113	8	systems	system	NOUN
ajema-5949	113	9	comes	come	VERB
ajema-5949	113	10	from	from	ADP
ajema-5949	113	11	the	the	DET
ajema-5949	113	12	fact	fact	NOUN
ajema-5949	113	13	that	that	SCONJ
ajema-5949	113	14	many	many	ADJ
ajema-5949	113	15	integrable	integrable	ADJ
ajema-5949	113	16	models	model	NOUN
ajema-5949	113	17	,	,	PUNCT
ajema-5949	113	18	such	such	ADJ
ajema-5949	113	19	as	as	ADP
ajema-5949	113	20	the	the	DET
ajema-5949	113	21	ones	one	NOUN
ajema-5949	113	22	studied	study	VERB
ajema-5949	113	23	in	in	ADP
ajema-5949	113	24	statistical	statistical	ADJ
ajema-5949	113	25	mechanics	mechanic	NOUN
ajema-5949	113	26	,	,	PUNCT
ajema-5949	113	27	can	can	AUX
ajema-5949	113	28	be	be	AUX
ajema-5949	113	29	viewed	view	VERB
ajema-5949	113	30	as	as	ADP
ajema-5949	113	31	quantum	quantum	NOUN
ajema-5949	113	32	systems	system	NOUN
ajema-5949	113	33	exhibiting	exhibit	VERB
ajema-5949	113	34	symmetries	symmetry	NOUN
ajema-5949	113	35	governed	govern	VERB
ajema-5949	113	36	by	by	ADP
ajema-5949	113	37	quantum	quantum	ADJ
ajema-5949	113	38	groups	group	NOUN
ajema-5949	113	39	(	(	PUNCT
ajema-5949	113	40	chari	chari	PROPN
ajema-5949	113	41	&	&	CCONJ
ajema-5949	113	42	pressley	pressley	PROPN
ajema-5949	113	43	,	,	PUNCT
ajema-5949	113	44	1994	1994	NUM
ajema-5949	113	45	)	)	PUNCT
ajema-5949	113	46	.	.	PUNCT
ajema-5949	114	1	a	a	DET
ajema-5949	114	2	key	key	ADJ
ajema-5949	114	3	example	example	NOUN
ajema-5949	114	4	is	be	AUX
ajema-5949	114	5	the	the	DET
ajema-5949	114	6	study	study	NOUN
ajema-5949	114	7	of	of	ADP
ajema-5949	114	8	the	the	DET
ajema-5949	114	9	heisenberg	heisenberg	PROPN
ajema-5949	114	10	spin	spin	PROPN
ajema-5949	114	11	chain	chain	NOUN
ajema-5949	114	12	and	and	CCONJ
ajema-5949	114	13	other	other	ADJ
ajema-5949	114	14	lattice	lattice	NOUN
ajema-5949	114	15	models	model	NOUN
ajema-5949	114	16	,	,	PUNCT
ajema-5949	114	17	where	where	SCONJ
ajema-5949	114	18	quantum	quantum	NOUN
ajema-5949	114	19	groups	group	NOUN
ajema-5949	114	20	provide	provide	VERB
ajema-5949	114	21	a	a	DET
ajema-5949	114	22	natural	natural	ADJ
ajema-5949	114	23	framework	framework	NOUN
ajema-5949	114	24	for	for	ADP
ajema-5949	114	25	understanding	understand	VERB
ajema-5949	114	26	the	the	DET
ajema-5949	114	27	symmetries	symmetry	NOUN
ajema-5949	114	28	of	of	ADP
ajema-5949	114	29	the	the	DET
ajema-5949	114	30	system	system	NOUN
ajema-5949	114	31	.	.	PUNCT
ajema-5949	115	1	in	in	ADP
ajema-5949	115	2	these	these	DET
ajema-5949	115	3	systems	system	NOUN
ajema-5949	115	4	,	,	PUNCT
ajema-5949	115	5	quantum	quantum	ADJ
ajema-5949	115	6	groups	group	NOUN
ajema-5949	115	7	act	act	VERB
ajema-5949	115	8	as	as	ADP
ajema-5949	115	9	symmetries	symmetry	NOUN
ajema-5949	115	10	that	that	PRON
ajema-5949	115	11	preserve	preserve	VERB
ajema-5949	115	12	the	the	DET
ajema-5949	115	13	integrability	integrability	NOUN
ajema-5949	115	14	of	of	ADP
ajema-5949	115	15	the	the	DET
ajema-5949	115	16	model	model	NOUN
ajema-5949	115	17	,	,	PUNCT
ajema-5949	115	18	and	and	CCONJ
ajema-5949	115	19	their	their	PRON
ajema-5949	115	20	representations	representation	NOUN
ajema-5949	115	21	correspond	correspond	VERB
ajema-5949	115	22	to	to	ADP
ajema-5949	115	23	the	the	DET
ajema-5949	115	24	states	state	NOUN
ajema-5949	115	25	of	of	ADP
ajema-5949	115	26	the	the	DET
ajema-5949	115	27	quantum	quantum	ADJ
ajema-5949	115	28	system	system	NOUN
ajema-5949	115	29	.	.	PUNCT
ajema-5949	116	1	the	the	DET
ajema-5949	116	2	integrability	integrability	NOUN
ajema-5949	116	3	of	of	ADP
ajema-5949	116	4	these	these	DET
ajema-5949	116	5	models	model	NOUN
ajema-5949	116	6	can	can	AUX
ajema-5949	116	7	be	be	AUX
ajema-5949	116	8	understood	understand	VERB
ajema-5949	116	9	in	in	ADP
ajema-5949	116	10	terms	term	NOUN
ajema-5949	116	11	of	of	ADP
ajema-5949	116	12	the	the	DET
ajema-5949	116	13	quantum	quantum	ADJ
ajema-5949	116	14	group	group	NOUN
ajema-5949	116	15	symmetries	symmetry	NOUN
ajema-5949	116	16	,	,	PUNCT
ajema-5949	116	17	which	which	PRON
ajema-5949	116	18	govern	govern	VERB
ajema-5949	116	19	the	the	DET
ajema-5949	116	20	exchange	exchange	NOUN
ajema-5949	116	21	interactions	interaction	NOUN
ajema-5949	116	22	between	between	ADP
ajema-5949	116	23	particles	particle	NOUN
ajema-5949	116	24	or	or	CCONJ
ajema-5949	116	25	spins	spin	NOUN
ajema-5949	116	26	(	(	PUNCT
ajema-5949	116	27	faddeev	faddeev	PROPN
ajema-5949	116	28	,	,	PUNCT
ajema-5949	116	29	reshetikhin	reshetikhin	PROPN
ajema-5949	116	30	,	,	PUNCT
ajema-5949	116	31	&	&	CCONJ
ajema-5949	116	32	takhtajan	takhtajan	ADJ
ajema-5949	116	33	,	,	PUNCT
ajema-5949	116	34	1989	1989	NUM
ajema-5949	116	35	)	)	PUNCT
ajema-5949	116	36	.	.	PUNCT
ajema-5949	117	1	for	for	ADP
ajema-5949	117	2	instance	instance	NOUN
ajema-5949	117	3	,	,	PUNCT
ajema-5949	117	4	the	the	DET
ajema-5949	117	5	quantum	quantum	NOUN
ajema-5949	117	6	group	group	NOUN
ajema-5949	117	7	is	be	AUX
ajema-5949	117	8	used	use	VERB
ajema-5949	117	9	in	in	ADP
ajema-5949	117	10	the	the	DET
ajema-5949	117	11	analysis	analysis	NOUN
ajema-5949	117	12	of	of	ADP
ajema-5949	117	13	the	the	DET
ajema-5949	117	14	xxz	xxz	PROPN
ajema-5949	117	15	model	model	NOUN
ajema-5949	117	16	,	,	PUNCT
ajema-5949	117	17	a	a	DET
ajema-5949	117	18	well	well	ADV
ajema-5949	117	19	-	-	PUNCT
ajema-5949	117	20	known	know	VERB
ajema-5949	117	21	integrable	integrable	ADJ
ajema-5949	117	22	model	model	NOUN
ajema-5949	117	23	in	in	ADP
ajema-5949	117	24	statistical	statistical	ADJ
ajema-5949	117	25	mechanics	mechanic	NOUN
ajema-5949	117	26	.	.	PUNCT
ajema-5949	118	1	the	the	DET
ajema-5949	118	2	symmetries	symmetry	NOUN
ajema-5949	118	3	of	of	ADP
ajema-5949	118	4	this	this	DET
ajema-5949	118	5	model	model	NOUN
ajema-5949	118	6	are	be	AUX
ajema-5949	118	7	governed	govern	VERB
ajema-5949	118	8	by	by	ADP
ajema-5949	118	9	the	the	DET
ajema-5949	118	10	quantum	quantum	NOUN
ajema-5949	118	11	group	group	NOUN
ajema-5949	118	12	,	,	PUNCT
ajema-5949	118	13	and	and	CCONJ
ajema-5949	118	14	its	its	PRON
ajema-5949	118	15	representation	representation	NOUN
ajema-5949	118	16	theory	theory	NOUN
ajema-5949	118	17	allows	allow	VERB
ajema-5949	118	18	for	for	ADP
ajema-5949	118	19	the	the	DET
ajema-5949	118	20	exact	exact	ADJ
ajema-5949	118	21	solution	solution	NOUN
ajema-5949	118	22	of	of	ADP
ajema-5949	118	23	the	the	DET
ajema-5949	118	24	system	system	NOUN
ajema-5949	118	25	(	(	PUNCT
ajema-5949	118	26	chari	chari	PROPN
ajema-5949	118	27	&	&	CCONJ
ajema-5949	118	28	pressley	pressley	PROPN
ajema-5949	118	29	,	,	PUNCT
ajema-5949	118	30	1994	1994	NUM
ajema-5949	118	31	)	)	PUNCT
ajema-5949	118	32	.	.	PUNCT
ajema-5949	119	1	the	the	DET
ajema-5949	119	2	study	study	NOUN
ajema-5949	119	3	of	of	ADP
ajema-5949	119	4	quantum	quantum	ADJ
ajema-5949	119	5	groups	group	NOUN
ajema-5949	119	6	in	in	ADP
ajema-5949	119	7	integrable	integrable	ADJ
ajema-5949	119	8	systems	system	NOUN
ajema-5949	119	9	is	be	AUX
ajema-5949	119	10	particularly	particularly	ADV
ajema-5949	119	11	important	important	ADJ
ajema-5949	119	12	in	in	ADP
ajema-5949	119	13	understanding	understand	VERB
ajema-5949	119	14	quantum	quantum	NOUN
ajema-5949	119	15	phase	phase	NOUN
ajema-5949	119	16	transitions	transition	NOUN
ajema-5949	119	17	,	,	PUNCT
ajema-5949	119	18	spin	spin	NOUN
ajema-5949	119	19	chains	chain	NOUN
ajema-5949	119	20	,	,	PUNCT
ajema-5949	119	21	and	and	CCONJ
ajema-5949	119	22	other	other	ADJ
ajema-5949	119	23	phenomena	phenomenon	NOUN
ajema-5949	119	24	in	in	ADP
ajema-5949	119	25	condensed	condense	VERB
ajema-5949	119	26	matter	matter	NOUN
ajema-5949	119	27	physics	physics	NOUN
ajema-5949	119	28	.	.	PUNCT
ajema-5949	120	1	4.3	4.3	NUM
ajema-5949	120	2	.	.	PUNCT
ajema-5949	120	3	quantum	quantum	NOUN
ajema-5949	120	4	spin	spin	NOUN
ajema-5949	120	5	chains	chain	NOUN
ajema-5949	120	6	and	and	CCONJ
ajema-5949	120	7	lattice	lattice	NOUN
ajema-5949	120	8	models	model	NOUN
ajema-5949	120	9	quantum	quantum	NOUN
ajema-5949	120	10	groups	group	NOUN
ajema-5949	120	11	have	have	AUX
ajema-5949	120	12	been	be	AUX
ajema-5949	120	13	extensively	extensively	ADV
ajema-5949	120	14	applied	apply	VERB
ajema-5949	120	15	in	in	ADP
ajema-5949	120	16	the	the	DET
ajema-5949	120	17	study	study	NOUN
ajema-5949	120	18	of	of	ADP
ajema-5949	120	19	quantum	quantum	NOUN
ajema-5949	120	20	spin	spin	NOUN
ajema-5949	120	21	chains	chain	NOUN
ajema-5949	120	22	,	,	PUNCT
ajema-5949	120	23	which	which	PRON
ajema-5949	120	24	are	be	AUX
ajema-5949	120	25	one	one	NUM
ajema-5949	120	26	-	-	PUNCT
ajema-5949	120	27	dimensional	dimensional	ADJ
ajema-5949	120	28	quantum	quantum	NOUN
ajema-5949	120	29	systems	system	NOUN
ajema-5949	120	30	consisting	consist	VERB
ajema-5949	120	31	of	of	ADP
ajema-5949	120	32	a	a	DET
ajema-5949	120	33	chain	chain	NOUN
ajema-5949	120	34	of	of	ADP
ajema-5949	120	35	spins	spin	NOUN
ajema-5949	120	36	that	that	PRON
ajema-5949	120	37	interact	interact	VERB
ajema-5949	120	38	according	accord	VERB
ajema-5949	120	39	to	to	ADP
ajema-5949	120	40	specific	specific	ADJ
ajema-5949	120	41	rules	rule	NOUN
ajema-5949	120	42	.	.	PUNCT
ajema-5949	121	1	these	these	DET
ajema-5949	121	2	systems	system	NOUN
ajema-5949	121	3	are	be	AUX
ajema-5949	121	4	important	important	ADJ
ajema-5949	121	5	in	in	ADP
ajema-5949	121	6	condensed	condense	VERB
ajema-5949	121	7	matter	matter	NOUN
ajema-5949	121	8	physics	physics	NOUN
ajema-5949	121	9	,	,	PUNCT
ajema-5949	121	10	as	as	SCONJ
ajema-5949	121	11	they	they	PRON
ajema-5949	121	12	serve	serve	VERB
ajema-5949	121	13	as	as	ADP
ajema-5949	121	14	simple	simple	ADJ
ajema-5949	121	15	models	model	NOUN
ajema-5949	121	16	for	for	ADP
ajema-5949	121	17	understanding	understand	VERB
ajema-5949	121	18	complex	complex	ADJ
ajema-5949	121	19	quantum	quantum	ADJ
ajema-5949	121	20	phenomena	phenomenon	NOUN
ajema-5949	121	21	such	such	ADJ
ajema-5949	121	22	as	as	ADP
ajema-5949	121	23	quantum	quantum	NOUN
ajema-5949	121	24	phase	phase	NOUN
ajema-5949	121	25	transitions	transition	NOUN
ajema-5949	121	26	and	and	CCONJ
ajema-5949	121	27	critical	critical	ADJ
ajema-5949	121	28	phenomena	phenomenon	NOUN
ajema-5949	121	29	.	.	PUNCT
ajema-5949	122	1	the	the	DET
ajema-5949	122	2	symmetries	symmetry	NOUN
ajema-5949	122	3	of	of	ADP
ajema-5949	122	4	quantum	quantum	NOUN
ajema-5949	122	5	spin	spin	NOUN
ajema-5949	122	6	chains	chain	NOUN
ajema-5949	122	7	are	be	AUX
ajema-5949	122	8	often	often	ADV
ajema-5949	122	9	described	describe	VERB
ajema-5949	122	10	by	by	ADP
ajema-5949	122	11	quantum	quantum	ADJ
ajema-5949	122	12	groups	group	NOUN
ajema-5949	122	13	.	.	PUNCT
ajema-5949	123	1	for	for	ADP
ajema-5949	123	2	example	example	NOUN
ajema-5949	123	3	,	,	PUNCT
ajema-5949	123	4	the	the	DET
ajema-5949	123	5	xxz	xxz	PROPN
ajema-5949	123	6	model	model	NOUN
ajema-5949	123	7	in	in	ADP
ajema-5949	123	8	condensed	condense	VERB
ajema-5949	123	9	matter	matter	NOUN
ajema-5949	123	10	physics	physics	NOUN
ajema-5949	123	11	can	can	AUX
ajema-5949	123	12	be	be	AUX
ajema-5949	123	13	analyzed	analyze	VERB
ajema-5949	123	14	using	use	VERB
ajema-5949	123	15	quantum	quantum	ADJ
ajema-5949	123	16	groups	group	NOUN
ajema-5949	123	17	,	,	PUNCT
ajema-5949	123	18	where	where	SCONJ
ajema-5949	123	19	the	the	DET
ajema-5949	123	20	quantum	quantum	ADJ
ajema-5949	123	21	group	group	NOUN
ajema-5949	123	22	governs	govern	VERB
ajema-5949	123	23	the	the	DET
ajema-5949	123	24	interactions	interaction	NOUN
ajema-5949	123	25	between	between	ADP
ajema-5949	123	26	spins	spin	NOUN
ajema-5949	123	27	.	.	PUNCT
ajema-5949	124	1	the	the	DET
ajema-5949	124	2	representations	representation	NOUN
ajema-5949	124	3	of	of	ADP
ajema-5949	124	4	describe	describe	VERB
ajema-5949	124	5	the	the	DET
ajema-5949	124	6	different	different	ADJ
ajema-5949	124	7	spin	spin	NOUN
ajema-5949	124	8	states	state	NOUN
ajema-5949	124	9	,	,	PUNCT
ajema-5949	124	10	and	and	CCONJ
ajema-5949	124	11	the	the	DET
ajema-5949	124	12	quantum	quantum	PROPN
ajema-5949	124	13	group	group	NOUN
ajema-5949	124	14	symmetry	symmetry	NOUN
ajema-5949	124	15	preserves	preserve	VERB
ajema-5949	124	16	the	the	DET
ajema-5949	124	17	integrability	integrability	NOUN
ajema-5949	124	18	of	of	ADP
ajema-5949	124	19	the	the	DET
ajema-5949	124	20	model	model	NOUN
ajema-5949	124	21	(	(	PUNCT
ajema-5949	124	22	faddeev	faddeev	NOUN
ajema-5949	124	23	et	et	PROPN
ajema-5949	124	24	al	al	PROPN
ajema-5949	124	25	.	.	PROPN
ajema-5949	124	26	,	,	PUNCT
ajema-5949	124	27	1989	1989	NUM
ajema-5949	124	28	)	)	PUNCT
ajema-5949	124	29	.	.	PUNCT
ajema-5949	125	1	furthermore	furthermore	ADV
ajema-5949	125	2	,	,	PUNCT
ajema-5949	125	3	quantum	quantum	ADJ
ajema-5949	125	4	groups	group	NOUN
ajema-5949	125	5	are	be	AUX
ajema-5949	125	6	also	also	ADV
ajema-5949	125	7	used	use	VERB
ajema-5949	125	8	to	to	PART
ajema-5949	125	9	study	study	VERB
ajema-5949	125	10	lattice	lattice	NOUN
ajema-5949	125	11	models	model	NOUN
ajema-5949	125	12	with	with	ADP
ajema-5949	125	13	quantum	quantum	ADJ
ajema-5949	125	14	symmetries	symmetry	NOUN
ajema-5949	125	15	,	,	PUNCT
ajema-5949	125	16	such	such	ADJ
ajema-5949	125	17	as	as	ADP
ajema-5949	125	18	the	the	DET
ajema-5949	125	19	spin	spin	NOUN
ajema-5949	125	20	-	-	PUNCT
ajema-5949	125	21	lattice	lattice	NOUN
ajema-5949	125	22	models	model	NOUN
ajema-5949	125	23	in	in	ADP
ajema-5949	125	24	statistical	statistical	ADJ
ajema-5949	125	25	mechanics	mechanic	NOUN
ajema-5949	125	26	.	.	PUNCT
ajema-5949	126	1	in	in	ADP
ajema-5949	126	2	these	these	DET
ajema-5949	126	3	models	model	NOUN
ajema-5949	126	4	,	,	PUNCT
ajema-5949	126	5	the	the	DET
ajema-5949	126	6	quantum	quantum	NOUN
ajema-5949	126	7	group	group	NOUN
ajema-5949	126	8	symmetries	symmetry	NOUN
ajema-5949	126	9	govern	govern	VERB
ajema-5949	126	10	the	the	DET
ajema-5949	126	11	interactions	interaction	NOUN
ajema-5949	126	12	between	between	ADP
ajema-5949	126	13	lattice	lattice	NOUN
ajema-5949	126	14	sites	site	NOUN
ajema-5949	126	15	,	,	PUNCT
ajema-5949	126	16	and	and	CCONJ
ajema-5949	126	17	their	their	PRON
ajema-5949	126	18	representations	representation	NOUN
ajema-5949	126	19	describe	describe	VERB
ajema-5949	126	20	the	the	DET
ajema-5949	126	21	quantum	quantum	ADJ
ajema-5949	126	22	states	state	NOUN
ajema-5949	126	23	of	of	ADP
ajema-5949	126	24	the	the	DET
ajema-5949	126	25	system	system	NOUN
ajema-5949	126	26	.	.	PUNCT
ajema-5949	127	1	these	these	DET
ajema-5949	127	2	models	model	NOUN
ajema-5949	127	3	are	be	AUX
ajema-5949	127	4	crucial	crucial	ADJ
ajema-5949	127	5	for	for	ADP
ajema-5949	127	6	understanding	understand	VERB
ajema-5949	127	7	the	the	DET
ajema-5949	127	8	behavior	behavior	NOUN
ajema-5949	127	9	of	of	ADP
ajema-5949	127	10	materials	material	NOUN
ajema-5949	127	11	at	at	ADP
ajema-5949	127	12	the	the	DET
ajema-5949	127	13	quantum	quantum	ADJ
ajema-5949	127	14	level	level	NOUN
ajema-5949	127	15	and	and	CCONJ
ajema-5949	127	16	are	be	AUX
ajema-5949	127	17	often	often	ADV
ajema-5949	127	18	used	use	VERB
ajema-5949	127	19	to	to	PART
ajema-5949	127	20	study	study	VERB
ajema-5949	127	21	quantum	quantum	ADJ
ajema-5949	127	22	critical	critical	ADJ
ajema-5949	127	23	phenomena	phenomenon	NOUN
ajema-5949	127	24	and	and	CCONJ
ajema-5949	127	25	quantum	quantum	NOUN
ajema-5949	127	26	entanglement	entanglement	NOUN
ajema-5949	127	27	in	in	ADP
ajema-5949	127	28	condensed	condense	VERB
ajema-5949	127	29	matter	matter	NOUN
ajema-5949	127	30	systems	system	NOUN
ajema-5949	127	31	(	(	PUNCT
ajema-5949	127	32	majid	majid	PROPN
ajema-5949	127	33	,	,	PUNCT
ajema-5949	127	34	1994	1994	NUM
ajema-5949	127	35	)	)	PUNCT
ajema-5949	127	36	.	.	PUNCT
ajema-5949	128	1	250	250	NUM
ajema-5949	128	2	journal	journal	NOUN
ajema-5949	128	3	of	of	ADP
ajema-5949	128	4	engineering	engineering	NOUN
ajema-5949	128	5	,	,	PUNCT
ajema-5949	128	6	mechanics	mechanic	NOUN
ajema-5949	128	7	and	and	CCONJ
ajema-5949	128	8	architecture	architecture	NOUN
ajema-5949	128	9	www	www	NOUN
ajema-5949	128	10	.	.	PUNCT
ajema-5949	129	1	grnjournal.us	grnjournal.us	X
ajema-5949	129	2	4.4	4.4	NUM
ajema-5949	129	3	.	.	PUNCT
ajema-5949	129	4	quantum	quantum	ADJ
ajema-5949	129	5	gravity	gravity	NOUN
ajema-5949	129	6	and	and	CCONJ
ajema-5949	129	7	non	non	ADJ
ajema-5949	129	8	-	-	ADJ
ajema-5949	129	9	commutative	commutative	ADJ
ajema-5949	129	10	spacetime	spacetime	NOUN
ajema-5949	129	11	quantum	quantum	NOUN
ajema-5949	129	12	groups	group	NOUN
ajema-5949	129	13	are	be	AUX
ajema-5949	129	14	also	also	ADV
ajema-5949	129	15	essential	essential	ADJ
ajema-5949	129	16	to	to	ADP
ajema-5949	129	17	the	the	DET
ajema-5949	129	18	study	study	NOUN
ajema-5949	129	19	of	of	ADP
ajema-5949	129	20	quantum	quantum	ADJ
ajema-5949	129	21	gravity	gravity	NOUN
ajema-5949	129	22	and	and	CCONJ
ajema-5949	129	23	non	non	ADJ
ajema-5949	129	24	-	-	ADJ
ajema-5949	129	25	commutative	commutative	ADJ
ajema-5949	129	26	geometry	geometry	NOUN
ajema-5949	129	27	.	.	PUNCT
ajema-5949	130	1	specifically	specifically	ADV
ajema-5949	130	2	,	,	PUNCT
ajema-5949	130	3	quantum	quantum	ADJ
ajema-5949	130	4	groups	group	NOUN
ajema-5949	130	5	offer	offer	VERB
ajema-5949	130	6	a	a	DET
ajema-5949	130	7	framework	framework	NOUN
ajema-5949	130	8	for	for	ADP
ajema-5949	130	9	characterizing	characterize	VERB
ajema-5949	130	10	spacetime	spacetime	NOUN
ajema-5949	130	11	symmetries	symmetry	NOUN
ajema-5949	130	12	at	at	ADP
ajema-5949	130	13	the	the	DET
ajema-5949	130	14	planck	planck	NOUN
ajema-5949	130	15	scale	scale	NOUN
ajema-5949	130	16	,	,	PUNCT
ajema-5949	130	17	where	where	SCONJ
ajema-5949	130	18	spacetime	spacetime	NOUN
ajema-5949	130	19	may	may	AUX
ajema-5949	130	20	become	become	VERB
ajema-5949	130	21	fundamentally	fundamentally	ADV
ajema-5949	130	22	non	non	ADJ
ajema-5949	130	23	-	-	ADJ
ajema-5949	130	24	commutative	commutative	ADJ
ajema-5949	130	25	and	and	CCONJ
ajema-5949	130	26	where	where	SCONJ
ajema-5949	130	27	quantum	quantum	ADJ
ajema-5949	130	28	effects	effect	NOUN
ajema-5949	130	29	are	be	AUX
ajema-5949	130	30	anticipated	anticipate	VERB
ajema-5949	130	31	to	to	PART
ajema-5949	130	32	predominate	predominate	VERB
ajema-5949	130	33	.	.	PUNCT
ajema-5949	131	1	alain	alain	PROPN
ajema-5949	131	2	connes	conne	NOUN
ajema-5949	131	3	(	(	PUNCT
ajema-5949	131	4	1994	1994	NUM
ajema-5949	131	5	)	)	PUNCT
ajema-5949	131	6	developed	develop	VERB
ajema-5949	131	7	noncommutative	noncommutative	ADJ
ajema-5949	131	8	geometry	geometry	NOUN
ajema-5949	131	9	,	,	PUNCT
ajema-5949	131	10	which	which	PRON
ajema-5949	131	11	offers	offer	VERB
ajema-5949	131	12	a	a	DET
ajema-5949	131	13	natural	natural	ADJ
ajema-5949	131	14	environment	environment	NOUN
ajema-5949	131	15	for	for	ADP
ajema-5949	131	16	studying	study	VERB
ajema-5949	131	17	quantum	quantum	ADJ
ajema-5949	131	18	gravity	gravity	NOUN
ajema-5949	131	19	.	.	PUNCT
ajema-5949	132	1	the	the	DET
ajema-5949	132	2	symmetries	symmetry	NOUN
ajema-5949	132	3	of	of	ADP
ajema-5949	132	4	non	non	ADJ
ajema-5949	132	5	-	-	ADJ
ajema-5949	132	6	commutative	commutative	ADJ
ajema-5949	132	7	spaces	space	NOUN
ajema-5949	132	8	are	be	AUX
ajema-5949	132	9	described	describe	VERB
ajema-5949	132	10	by	by	ADP
ajema-5949	132	11	quantum	quantum	ADJ
ajema-5949	132	12	groups	group	NOUN
ajema-5949	132	13	.	.	PUNCT
ajema-5949	133	1	the	the	DET
ajema-5949	133	2	structure	structure	NOUN
ajema-5949	133	3	of	of	ADP
ajema-5949	133	4	spacetime	spacetime	NOUN
ajema-5949	133	5	is	be	AUX
ajema-5949	133	6	thought	think	VERB
ajema-5949	133	7	to	to	PART
ajema-5949	133	8	be	be	AUX
ajema-5949	133	9	discrete	discrete	ADJ
ajema-5949	133	10	and	and	CCONJ
ajema-5949	133	11	non	non	ADJ
ajema-5949	133	12	-	-	ADJ
ajema-5949	133	13	commutative	commutative	ADJ
ajema-5949	133	14	at	at	ADP
ajema-5949	133	15	very	very	ADV
ajema-5949	133	16	small	small	ADJ
ajema-5949	133	17	scales	scale	NOUN
ajema-5949	133	18	in	in	ADP
ajema-5949	133	19	quantum	quantum	ADJ
ajema-5949	133	20	gravity	gravity	NOUN
ajema-5949	133	21	models	model	NOUN
ajema-5949	133	22	,	,	PUNCT
ajema-5949	133	23	such	such	ADJ
ajema-5949	133	24	as	as	ADP
ajema-5949	133	25	loop	loop	NOUN
ajema-5949	133	26	quantum	quantum	NOUN
ajema-5949	133	27	gravity	gravity	NOUN
ajema-5949	133	28	.	.	PUNCT
ajema-5949	134	1	these	these	DET
ajema-5949	134	2	discrete	discrete	ADJ
ajema-5949	134	3	and	and	CCONJ
ajema-5949	134	4	non	non	ADJ
ajema-5949	134	5	-	-	ADJ
ajema-5949	134	6	commutative	commutative	ADJ
ajema-5949	134	7	symmetries	symmetry	NOUN
ajema-5949	134	8	can	can	AUX
ajema-5949	134	9	be	be	AUX
ajema-5949	134	10	modeled	model	VERB
ajema-5949	134	11	using	use	VERB
ajema-5949	134	12	quantum	quantum	ADJ
ajema-5949	134	13	groups	group	NOUN
ajema-5949	134	14	because	because	SCONJ
ajema-5949	134	15	of	of	ADP
ajema-5949	134	16	their	their	PRON
ajema-5949	134	17	algebraic	algebraic	ADJ
ajema-5949	134	18	structure	structure	NOUN
ajema-5949	134	19	.	.	PUNCT
ajema-5949	135	1	when	when	SCONJ
ajema-5949	135	2	attempting	attempt	VERB
ajema-5949	135	3	to	to	PART
ajema-5949	135	4	reconcile	reconcile	VERB
ajema-5949	135	5	quantum	quantum	ADJ
ajema-5949	135	6	physics	physics	NOUN
ajema-5949	135	7	with	with	ADP
ajema-5949	135	8	general	general	ADJ
ajema-5949	135	9	relativity	relativity	NOUN
ajema-5949	135	10	,	,	PUNCT
ajema-5949	135	11	the	the	DET
ajema-5949	135	12	non	non	ADJ
ajema-5949	135	13	-	-	ADJ
ajema-5949	135	14	commutative	commutative	ADJ
ajema-5949	135	15	character	character	NOUN
ajema-5949	135	16	of	of	ADP
ajema-5949	135	17	quantum	quantum	NOUN
ajema-5949	135	18	groups	group	NOUN
ajema-5949	135	19	is	be	AUX
ajema-5949	135	20	especially	especially	ADV
ajema-5949	135	21	important	important	ADJ
ajema-5949	135	22	since	since	SCONJ
ajema-5949	135	23	the	the	DET
ajema-5949	135	24	traditional	traditional	ADJ
ajema-5949	135	25	concepts	concept	NOUN
ajema-5949	135	26	of	of	ADP
ajema-5949	135	27	smooth	smooth	ADJ
ajema-5949	135	28	spacetime	spacetime	NOUN
ajema-5949	135	29	and	and	CCONJ
ajema-5949	135	30	classical	classical	ADJ
ajema-5949	135	31	symmetries	symmetry	NOUN
ajema-5949	135	32	fail	fail	VERB
ajema-5949	135	33	at	at	ADP
ajema-5949	135	34	the	the	DET
ajema-5949	135	35	quantum	quantum	ADJ
ajema-5949	135	36	level	level	NOUN
ajema-5949	135	37	(	(	PUNCT
ajema-5949	135	38	connes	conne	NOUN
ajema-5949	135	39	,	,	PUNCT
ajema-5949	135	40	1994	1994	NUM
ajema-5949	135	41	)	)	PUNCT
ajema-5949	135	42	.	.	PUNCT
ajema-5949	136	1	quantum	quantum	ADJ
ajema-5949	136	2	groups	group	NOUN
ajema-5949	136	3	are	be	AUX
ajema-5949	136	4	also	also	ADV
ajema-5949	136	5	used	use	VERB
ajema-5949	136	6	in	in	ADP
ajema-5949	136	7	the	the	DET
ajema-5949	136	8	study	study	NOUN
ajema-5949	136	9	of	of	ADP
ajema-5949	136	10	quantum	quantum	ADJ
ajema-5949	136	11	deformation	deformation	NOUN
ajema-5949	136	12	of	of	ADP
ajema-5949	136	13	spacetime	spacetime	ADJ
ajema-5949	136	14	symmetries	symmetry	NOUN
ajema-5949	136	15	,	,	PUNCT
ajema-5949	136	16	such	such	ADJ
ajema-5949	136	17	as	as	ADP
ajema-5949	136	18	the	the	DET
ajema-5949	136	19	deformation	deformation	NOUN
ajema-5949	136	20	of	of	ADP
ajema-5949	136	21	the	the	DET
ajema-5949	136	22	poincaré	poincaré	PROPN
ajema-5949	136	23	group	group	NOUN
ajema-5949	136	24	at	at	ADP
ajema-5949	136	25	the	the	DET
ajema-5949	136	26	quantum	quantum	ADJ
ajema-5949	136	27	level	level	NOUN
ajema-5949	136	28	.	.	PUNCT
ajema-5949	137	1	the	the	DET
ajema-5949	137	2	coordinates	coordinate	NOUN
ajema-5949	137	3	no	no	ADV
ajema-5949	137	4	longer	long	ADV
ajema-5949	137	5	commute	commute	VERB
ajema-5949	137	6	in	in	ADP
ajema-5949	137	7	this	this	DET
ajema-5949	137	8	quantum	quantum	ADJ
ajema-5949	137	9	deformation	deformation	NOUN
ajema-5949	137	10	,	,	PUNCT
ajema-5949	137	11	which	which	PRON
ajema-5949	137	12	creates	create	VERB
ajema-5949	137	13	a	a	DET
ajema-5949	137	14	novel	novel	ADJ
ajema-5949	137	15	understanding	understanding	NOUN
ajema-5949	137	16	of	of	ADP
ajema-5949	137	17	spacetime	spacetime	NOUN
ajema-5949	137	18	that	that	PRON
ajema-5949	137	19	may	may	AUX
ajema-5949	137	20	be	be	AUX
ajema-5949	137	21	crucial	crucial	ADJ
ajema-5949	137	22	for	for	ADP
ajema-5949	137	23	explaining	explain	VERB
ajema-5949	137	24	the	the	DET
ajema-5949	137	25	structure	structure	NOUN
ajema-5949	137	26	of	of	ADP
ajema-5949	137	27	spacetime	spacetime	NOUN
ajema-5949	137	28	at	at	ADP
ajema-5949	137	29	the	the	DET
ajema-5949	137	30	planck	planck	NOUN
ajema-5949	137	31	scale	scale	NOUN
ajema-5949	137	32	and	and	CCONJ
ajema-5949	137	33	beyond	beyond	ADP
ajema-5949	137	34	(	(	PUNCT
ajema-5949	137	35	majid	majid	PROPN
ajema-5949	137	36	,	,	PUNCT
ajema-5949	137	37	1994	1994	NUM
ajema-5949	137	38	)	)	PUNCT
ajema-5949	137	39	.	.	PUNCT
ajema-5949	138	1	4.5	4.5	NUM
ajema-5949	138	2	.	.	PUNCT
ajema-5949	138	3	string	string	NOUN
ajema-5949	138	4	theory	theory	NOUN
ajema-5949	138	5	and	and	CCONJ
ajema-5949	138	6	conformal	conformal	ADJ
ajema-5949	138	7	field	field	NOUN
ajema-5949	138	8	theory	theory	NOUN
ajema-5949	138	9	additionally	additionally	ADV
ajema-5949	138	10	,	,	PUNCT
ajema-5949	138	11	quantum	quantum	ADJ
ajema-5949	138	12	groups	group	NOUN
ajema-5949	138	13	have	have	AUX
ajema-5949	138	14	been	be	AUX
ajema-5949	138	15	used	use	VERB
ajema-5949	138	16	in	in	ADP
ajema-5949	138	17	conformal	conformal	ADJ
ajema-5949	138	18	field	field	NOUN
ajema-5949	138	19	theory	theory	NOUN
ajema-5949	138	20	(	(	PUNCT
ajema-5949	138	21	cft	cft	PROPN
ajema-5949	138	22	)	)	PUNCT
ajema-5949	138	23	and	and	CCONJ
ajema-5949	138	24	string	string	NOUN
ajema-5949	138	25	theory	theory	NOUN
ajema-5949	138	26	.	.	PUNCT
ajema-5949	139	1	quantum	quantum	ADJ
ajema-5949	139	2	groups	group	NOUN
ajema-5949	139	3	,	,	PUNCT
ajema-5949	139	4	which	which	PRON
ajema-5949	139	5	offer	offer	VERB
ajema-5949	139	6	a	a	DET
ajema-5949	139	7	more	more	ADV
ajema-5949	139	8	adaptable	adaptable	ADJ
ajema-5949	139	9	and	and	CCONJ
ajema-5949	139	10	general	general	ADJ
ajema-5949	139	11	framework	framework	NOUN
ajema-5949	139	12	for	for	ADP
ajema-5949	139	13	characterizing	characterize	VERB
ajema-5949	139	14	symmetries	symmetry	NOUN
ajema-5949	139	15	in	in	ADP
ajema-5949	139	16	the	the	DET
ajema-5949	139	17	quantum	quantum	NOUN
ajema-5949	139	18	regime	regime	NOUN
ajema-5949	139	19	,	,	PUNCT
ajema-5949	139	20	are	be	AUX
ajema-5949	139	21	frequently	frequently	ADV
ajema-5949	139	22	added	add	VERB
ajema-5949	139	23	to	to	ADP
ajema-5949	139	24	the	the	DET
ajema-5949	139	25	symmetry	symmetry	NOUN
ajema-5949	139	26	groups	group	NOUN
ajema-5949	139	27	that	that	PRON
ajema-5949	139	28	control	control	VERB
ajema-5949	139	29	the	the	DET
ajema-5949	139	30	interactions	interaction	NOUN
ajema-5949	139	31	of	of	ADP
ajema-5949	139	32	fields	field	NOUN
ajema-5949	139	33	and	and	CCONJ
ajema-5949	139	34	particles	particle	NOUN
ajema-5949	139	35	in	in	ADP
ajema-5949	139	36	these	these	DET
ajema-5949	139	37	theories	theory	NOUN
ajema-5949	139	38	.	.	PUNCT
ajema-5949	140	1	in	in	ADP
ajema-5949	140	2	the	the	DET
ajema-5949	140	3	context	context	NOUN
ajema-5949	140	4	of	of	ADP
ajema-5949	140	5	cft	cft	PROPN
ajema-5949	140	6	,	,	PUNCT
ajema-5949	140	7	quantum	quantum	ADJ
ajema-5949	140	8	groups	group	NOUN
ajema-5949	140	9	appear	appear	VERB
ajema-5949	140	10	in	in	ADP
ajema-5949	140	11	the	the	DET
ajema-5949	140	12	study	study	NOUN
ajema-5949	140	13	of	of	ADP
ajema-5949	140	14	w	w	NOUN
ajema-5949	140	15	-	-	PUNCT
ajema-5949	140	16	algebras	algebra	NOUN
ajema-5949	140	17	,	,	PUNCT
ajema-5949	140	18	which	which	PRON
ajema-5949	140	19	generalize	generalize	VERB
ajema-5949	140	20	the	the	DET
ajema-5949	140	21	virasoro	virasoro	NOUN
ajema-5949	140	22	algebra	algebra	PROPN
ajema-5949	140	23	and	and	CCONJ
ajema-5949	140	24	are	be	AUX
ajema-5949	140	25	used	use	VERB
ajema-5949	140	26	to	to	PART
ajema-5949	140	27	describe	describe	VERB
ajema-5949	140	28	symmetries	symmetry	NOUN
ajema-5949	140	29	of	of	ADP
ajema-5949	140	30	two	two	NUM
ajema-5949	140	31	-	-	PUNCT
ajema-5949	140	32	dimensional	dimensional	ADJ
ajema-5949	140	33	conformal	conformal	ADJ
ajema-5949	140	34	field	field	NOUN
ajema-5949	140	35	theories	theory	NOUN
ajema-5949	140	36	.	.	PUNCT
ajema-5949	141	1	quantum	quantum	ADJ
ajema-5949	141	2	groups	group	NOUN
ajema-5949	141	3	are	be	AUX
ajema-5949	141	4	also	also	ADV
ajema-5949	141	5	used	use	VERB
ajema-5949	141	6	in	in	ADP
ajema-5949	141	7	the	the	DET
ajema-5949	141	8	study	study	NOUN
ajema-5949	141	9	of	of	ADP
ajema-5949	141	10	integrable	integrable	ADJ
ajema-5949	141	11	models	model	NOUN
ajema-5949	141	12	in	in	ADP
ajema-5949	141	13	string	string	NOUN
ajema-5949	141	14	theory	theory	NOUN
ajema-5949	141	15	,	,	PUNCT
ajema-5949	141	16	where	where	SCONJ
ajema-5949	141	17	their	their	PRON
ajema-5949	141	18	representations	representation	NOUN
ajema-5949	141	19	play	play	VERB
ajema-5949	141	20	a	a	DET
ajema-5949	141	21	crucial	crucial	ADJ
ajema-5949	141	22	role	role	NOUN
ajema-5949	141	23	in	in	ADP
ajema-5949	141	24	the	the	DET
ajema-5949	141	25	analysis	analysis	NOUN
ajema-5949	141	26	of	of	ADP
ajema-5949	141	27	string	string	NOUN
ajema-5949	141	28	interactions	interaction	NOUN
ajema-5949	141	29	and	and	CCONJ
ajema-5949	141	30	the	the	DET
ajema-5949	141	31	solutions	solution	NOUN
ajema-5949	141	32	to	to	ADP
ajema-5949	141	33	string	string	NOUN
ajema-5949	141	34	field	field	NOUN
ajema-5949	141	35	equations	equation	NOUN
ajema-5949	141	36	(	(	PUNCT
ajema-5949	141	37	faddeev	faddeev	NOUN
ajema-5949	141	38	et	et	PROPN
ajema-5949	141	39	al	al	PROPN
ajema-5949	141	40	.	.	PROPN
ajema-5949	141	41	,	,	PUNCT
ajema-5949	141	42	1989	1989	NUM
ajema-5949	141	43	)	)	PUNCT
ajema-5949	141	44	.	.	PUNCT
ajema-5949	142	1	thus	thus	ADV
ajema-5949	142	2	,	,	PUNCT
ajema-5949	142	3	quantum	quantum	ADJ
ajema-5949	142	4	groups	group	NOUN
ajema-5949	142	5	offer	offer	VERB
ajema-5949	142	6	a	a	DET
ajema-5949	142	7	helpful	helpful	ADJ
ajema-5949	142	8	tool	tool	NOUN
ajema-5949	142	9	for	for	ADP
ajema-5949	142	10	comprehending	comprehend	VERB
ajema-5949	142	11	string	string	NOUN
ajema-5949	142	12	theory	theory	NOUN
ajema-5949	142	13	's	's	PART
ajema-5949	142	14	algebraic	algebraic	ADJ
ajema-5949	142	15	structure	structure	NOUN
ajema-5949	142	16	and	and	CCONJ
ajema-5949	142	17	related	related	ADJ
ajema-5949	142	18	symmetries	symmetry	NOUN
ajema-5949	142	19	.	.	PUNCT
ajema-5949	143	1	quantum	quantum	ADJ
ajema-5949	143	2	groups	group	NOUN
ajema-5949	143	3	have	have	VERB
ajema-5949	143	4	a	a	DET
ajema-5949	143	5	wide	wide	ADJ
ajema-5949	143	6	range	range	NOUN
ajema-5949	143	7	of	of	ADP
ajema-5949	143	8	applications	application	NOUN
ajema-5949	143	9	in	in	ADP
ajema-5949	143	10	theoretical	theoretical	ADJ
ajema-5949	143	11	physics	physics	NOUN
ajema-5949	143	12	,	,	PUNCT
ajema-5949	143	13	offering	offer	VERB
ajema-5949	143	14	a	a	DET
ajema-5949	143	15	framework	framework	NOUN
ajema-5949	143	16	for	for	ADP
ajema-5949	143	17	understanding	understand	VERB
ajema-5949	143	18	quantum	quantum	ADJ
ajema-5949	143	19	symmetries	symmetry	NOUN
ajema-5949	143	20	,	,	PUNCT
ajema-5949	143	21	integrable	integrable	ADJ
ajema-5949	143	22	systems	system	NOUN
ajema-5949	143	23	,	,	PUNCT
ajema-5949	143	24	quantum	quantum	NOUN
ajema-5949	143	25	spin	spin	NOUN
ajema-5949	143	26	chains	chain	NOUN
ajema-5949	143	27	,	,	PUNCT
ajema-5949	143	28	and	and	CCONJ
ajema-5949	143	29	quantum	quantum	NOUN
ajema-5949	143	30	gravity	gravity	NOUN
ajema-5949	143	31	.	.	PUNCT
ajema-5949	144	1	their	their	PRON
ajema-5949	144	2	non	non	ADJ
ajema-5949	144	3	-	-	ADJ
ajema-5949	144	4	commutative	commutative	ADJ
ajema-5949	144	5	structure	structure	NOUN
ajema-5949	144	6	makes	make	VERB
ajema-5949	144	7	them	they	PRON
ajema-5949	144	8	an	an	DET
ajema-5949	144	9	essential	essential	ADJ
ajema-5949	144	10	tool	tool	NOUN
ajema-5949	144	11	in	in	ADP
ajema-5949	144	12	the	the	DET
ajema-5949	144	13	study	study	NOUN
ajema-5949	144	14	of	of	ADP
ajema-5949	144	15	quantum	quantum	NOUN
ajema-5949	144	16	systems	system	NOUN
ajema-5949	144	17	,	,	PUNCT
ajema-5949	144	18	particularly	particularly	ADV
ajema-5949	144	19	in	in	ADP
ajema-5949	144	20	areas	area	NOUN
ajema-5949	144	21	where	where	SCONJ
ajema-5949	144	22	classical	classical	ADJ
ajema-5949	144	23	symmetries	symmetry	NOUN
ajema-5949	144	24	are	be	AUX
ajema-5949	144	25	not	not	PART
ajema-5949	144	26	sufficient	sufficient	ADJ
ajema-5949	144	27	to	to	PART
ajema-5949	144	28	describe	describe	VERB
ajema-5949	144	29	the	the	DET
ajema-5949	144	30	behavior	behavior	NOUN
ajema-5949	144	31	of	of	ADP
ajema-5949	144	32	particles	particle	NOUN
ajema-5949	144	33	and	and	CCONJ
ajema-5949	144	34	fields	field	NOUN
ajema-5949	144	35	at	at	ADP
ajema-5949	144	36	the	the	DET
ajema-5949	144	37	quantum	quantum	ADJ
ajema-5949	144	38	level	level	NOUN
ajema-5949	144	39	.	.	PUNCT
ajema-5949	145	1	as	as	SCONJ
ajema-5949	145	2	theoretical	theoretical	ADJ
ajema-5949	145	3	physics	physics	NOUN
ajema-5949	145	4	continues	continue	VERB
ajema-5949	145	5	to	to	PART
ajema-5949	145	6	explore	explore	VERB
ajema-5949	145	7	the	the	DET
ajema-5949	145	8	fundamental	fundamental	ADJ
ajema-5949	145	9	nature	nature	NOUN
ajema-5949	145	10	of	of	ADP
ajema-5949	145	11	the	the	DET
ajema-5949	145	12	universe	universe	NOUN
ajema-5949	145	13	,	,	PUNCT
ajema-5949	145	14	quantum	quantum	ADJ
ajema-5949	145	15	groups	group	NOUN
ajema-5949	145	16	will	will	AUX
ajema-5949	145	17	undoubtedly	undoubtedly	ADV
ajema-5949	145	18	remain	remain	VERB
ajema-5949	145	19	a	a	DET
ajema-5949	145	20	key	key	ADJ
ajema-5949	145	21	mathematical	mathematical	ADJ
ajema-5949	145	22	tool	tool	NOUN
ajema-5949	145	23	for	for	ADP
ajema-5949	145	24	understanding	understand	VERB
ajema-5949	145	25	the	the	DET
ajema-5949	145	26	symmetries	symmetry	NOUN
ajema-5949	145	27	that	that	PRON
ajema-5949	145	28	govern	govern	VERB
ajema-5949	145	29	the	the	DET
ajema-5949	145	30	quantum	quantum	ADJ
ajema-5949	145	31	world	world	NOUN
ajema-5949	145	32	.	.	PUNCT
ajema-5949	146	1	5	5	X
ajema-5949	146	2	.	.	X
ajema-5949	146	3	conclusion	conclusion	NOUN
ajema-5949	146	4	quantum	quantum	NOUN
ajema-5949	146	5	groups	group	NOUN
ajema-5949	146	6	represent	represent	VERB
ajema-5949	146	7	a	a	DET
ajema-5949	146	8	profound	profound	ADJ
ajema-5949	146	9	extension	extension	NOUN
ajema-5949	146	10	of	of	ADP
ajema-5949	146	11	classical	classical	ADJ
ajema-5949	146	12	symmetries	symmetry	NOUN
ajema-5949	146	13	,	,	PUNCT
ajema-5949	146	14	offering	offer	VERB
ajema-5949	146	15	a	a	DET
ajema-5949	146	16	noncommutative	noncommutative	ADJ
ajema-5949	146	17	algebraic	algebraic	ADJ
ajema-5949	146	18	framework	framework	NOUN
ajema-5949	146	19	that	that	PRON
ajema-5949	146	20	is	be	AUX
ajema-5949	146	21	central	central	ADJ
ajema-5949	146	22	to	to	ADP
ajema-5949	146	23	many	many	ADJ
ajema-5949	146	24	areas	area	NOUN
ajema-5949	146	25	of	of	ADP
ajema-5949	146	26	modern	modern	ADJ
ajema-5949	146	27	theoretical	theoretical	ADJ
ajema-5949	146	28	physics	physics	NOUN
ajema-5949	146	29	and	and	CCONJ
ajema-5949	146	30	mathematics	mathematic	NOUN
ajema-5949	146	31	.	.	PUNCT
ajema-5949	147	1	their	their	PRON
ajema-5949	147	2	development	development	NOUN
ajema-5949	147	3	as	as	ADP
ajema-5949	147	4	deformations	deformation	NOUN
ajema-5949	147	5	of	of	ADP
ajema-5949	147	6	classical	classical	ADJ
ajema-5949	147	7	lie	lie	NOUN
ajema-5949	147	8	groups	group	NOUN
ajema-5949	147	9	has	have	AUX
ajema-5949	147	10	opened	open	VERB
ajema-5949	147	11	up	up	ADP
ajema-5949	147	12	new	new	ADJ
ajema-5949	147	13	possibilities	possibility	NOUN
ajema-5949	147	14	for	for	ADP
ajema-5949	147	15	describing	describe	VERB
ajema-5949	147	16	quantum	quantum	ADJ
ajema-5949	147	17	symmetries	symmetry	NOUN
ajema-5949	147	18	and	and	CCONJ
ajema-5949	147	19	systems	system	NOUN
ajema-5949	147	20	where	where	SCONJ
ajema-5949	147	21	traditional	traditional	ADJ
ajema-5949	147	22	commutative	commutative	ADJ
ajema-5949	147	23	structures	structure	NOUN
ajema-5949	147	24	break	break	VERB
ajema-5949	147	25	down	down	ADP
ajema-5949	147	26	.	.	PUNCT
ajema-5949	148	1	quantum	quantum	NOUN
ajema-5949	148	2	groups	group	NOUN
ajema-5949	148	3	offer	offer	VERB
ajema-5949	148	4	a	a	DET
ajema-5949	148	5	rigorous	rigorous	ADJ
ajema-5949	148	6	mathematical	mathematical	ADJ
ajema-5949	148	7	tool	tool	NOUN
ajema-5949	148	8	for	for	ADP
ajema-5949	148	9	comprehending	comprehend	VERB
ajema-5949	148	10	intricate	intricate	ADJ
ajema-5949	148	11	phenomena	phenomenon	NOUN
ajema-5949	148	12	in	in	ADP
ajema-5949	148	13	the	the	DET
ajema-5949	148	14	quantum	quantum	ADJ
ajema-5949	148	15	realm	realm	NOUN
ajema-5949	148	16	,	,	PUNCT
ajema-5949	148	17	including	include	VERB
ajema-5949	148	18	quantum	quantum	ADJ
ajema-5949	148	19	mechanics	mechanic	NOUN
ajema-5949	148	20	,	,	PUNCT
ajema-5949	148	21	quantum	quantum	ADJ
ajema-5949	148	22	field	field	NOUN
ajema-5949	148	23	theory	theory	NOUN
ajema-5949	148	24	,	,	PUNCT
ajema-5949	148	25	integrable	integrable	ADJ
ajema-5949	148	26	systems	system	NOUN
ajema-5949	148	27	,	,	PUNCT
ajema-5949	148	28	and	and	CCONJ
ajema-5949	148	29	quantum	quantum	NOUN
ajema-5949	148	30	gravity	gravity	NOUN
ajema-5949	148	31	.	.	PUNCT
ajema-5949	149	1	quantum	quantum	ADJ
ajema-5949	149	2	groups	group	NOUN
ajema-5949	149	3	are	be	AUX
ajema-5949	149	4	ideal	ideal	ADJ
ajema-5949	149	5	for	for	ADP
ajema-5949	149	6	modeling	model	VERB
ajema-5949	149	7	quantum	quantum	ADJ
ajema-5949	149	8	spaces	space	NOUN
ajema-5949	149	9	,	,	PUNCT
ajema-5949	149	10	quantum	quantum	ADJ
ajema-5949	149	11	symmetries	symmetry	NOUN
ajema-5949	149	12	,	,	PUNCT
ajema-5949	149	13	and	and	CCONJ
ajema-5949	149	14	lattice	lattice	NOUN
ajema-5949	149	15	models	model	NOUN
ajema-5949	149	16	in	in	ADP
ajema-5949	149	17	condensed	condense	VERB
ajema-5949	149	18	matter	matter	NOUN
ajema-5949	149	19	physics	physics	NOUN
ajema-5949	149	20	due	due	ADP
ajema-5949	149	21	to	to	ADP
ajema-5949	149	22	their	their	PRON
ajema-5949	149	23	fundamental	fundamental	ADJ
ajema-5949	149	24	mathematical	mathematical	ADJ
ajema-5949	149	25	characteristics	characteristic	NOUN
ajema-5949	149	26	,	,	PUNCT
ajema-5949	149	27	including	include	VERB
ajema-5949	149	28	their	their	PRON
ajema-5949	149	29	hopf	hopf	ADJ
ajema-5949	149	30	algebra	algebra	NOUN
ajema-5949	149	31	structure	structure	NOUN
ajema-5949	149	32	,	,	PUNCT
ajema-5949	149	33	non	non	ADJ
ajema-5949	149	34	-	-	ADJ
ajema-5949	149	35	commutative	commutative	ADJ
ajema-5949	149	36	nature	nature	NOUN
ajema-5949	149	37	,	,	PUNCT
ajema-5949	149	38	and	and	CCONJ
ajema-5949	149	39	representation	representation	NOUN
ajema-5949	149	40	theory	theory	NOUN
ajema-5949	149	41	.	.	PUNCT
ajema-5949	150	1	because	because	SCONJ
ajema-5949	150	2	quantum	quantum	ADJ
ajema-5949	150	3	groups	group	NOUN
ajema-5949	150	4	maintain	maintain	VERB
ajema-5949	150	5	the	the	DET
ajema-5949	150	6	integrability	integrability	NOUN
ajema-5949	150	7	of	of	ADP
ajema-5949	150	8	models	model	NOUN
ajema-5949	150	9	and	and	CCONJ
ajema-5949	150	10	enable	enable	VERB
ajema-5949	150	11	exact	exact	ADJ
ajema-5949	150	12	solutions	solution	NOUN
ajema-5949	150	13	,	,	PUNCT
ajema-5949	150	14	these	these	DET
ajema-5949	150	15	251	251	NUM
ajema-5949	150	16	journal	journal	NOUN
ajema-5949	150	17	of	of	ADP
ajema-5949	150	18	engineering	engineering	NOUN
ajema-5949	150	19	,	,	PUNCT
ajema-5949	150	20	mechanics	mechanic	NOUN
ajema-5949	150	21	and	and	CCONJ
ajema-5949	150	22	architecture	architecture	NOUN
ajema-5949	150	23	www	www	NOUN
ajema-5949	150	24	.	.	PUNCT
ajema-5949	151	1	grnjournal.us	grnjournal.us	X
ajema-5949	151	2	characteristics	characteristic	NOUN
ajema-5949	151	3	are	be	AUX
ajema-5949	151	4	especially	especially	ADV
ajema-5949	151	5	helpful	helpful	ADJ
ajema-5949	151	6	in	in	ADP
ajema-5949	151	7	integrable	integrable	ADJ
ajema-5949	151	8	systems	system	NOUN
ajema-5949	151	9	.	.	PUNCT
ajema-5949	152	1	moreover	moreover	ADV
ajema-5949	152	2	,	,	PUNCT
ajema-5949	152	3	the	the	DET
ajema-5949	152	4	role	role	NOUN
ajema-5949	152	5	of	of	ADP
ajema-5949	152	6	quantum	quantum	ADJ
ajema-5949	152	7	groups	group	NOUN
ajema-5949	152	8	in	in	ADP
ajema-5949	152	9	quantum	quantum	ADJ
ajema-5949	152	10	gravity	gravity	NOUN
ajema-5949	152	11	and	and	CCONJ
ajema-5949	152	12	non	non	ADJ
ajema-5949	152	13	-	-	ADJ
ajema-5949	152	14	commutative	commutative	ADJ
ajema-5949	152	15	geometry	geometry	NOUN
ajema-5949	152	16	underscores	underscore	VERB
ajema-5949	152	17	their	their	PRON
ajema-5949	152	18	importance	importance	NOUN
ajema-5949	152	19	in	in	ADP
ajema-5949	152	20	the	the	DET
ajema-5949	152	21	search	search	NOUN
ajema-5949	152	22	for	for	ADP
ajema-5949	152	23	a	a	DET
ajema-5949	152	24	unified	unified	ADJ
ajema-5949	152	25	theory	theory	NOUN
ajema-5949	152	26	of	of	ADP
ajema-5949	152	27	quantum	quantum	ADJ
ajema-5949	152	28	spacetime	spacetime	NOUN
ajema-5949	152	29	.	.	PUNCT
ajema-5949	153	1	as	as	SCONJ
ajema-5949	153	2	theoretical	theoretical	ADJ
ajema-5949	153	3	physics	physics	NOUN
ajema-5949	153	4	continues	continue	VERB
ajema-5949	153	5	to	to	PART
ajema-5949	153	6	delve	delve	VERB
ajema-5949	153	7	into	into	ADP
ajema-5949	153	8	the	the	DET
ajema-5949	153	9	fundamental	fundamental	ADJ
ajema-5949	153	10	aspects	aspect	NOUN
ajema-5949	153	11	of	of	ADP
ajema-5949	153	12	quantum	quantum	ADJ
ajema-5949	153	13	mechanics	mechanic	NOUN
ajema-5949	153	14	and	and	CCONJ
ajema-5949	153	15	spacetime	spacetime	NOUN
ajema-5949	153	16	,	,	PUNCT
ajema-5949	153	17	quantum	quantum	ADJ
ajema-5949	153	18	groups	group	NOUN
ajema-5949	153	19	will	will	AUX
ajema-5949	153	20	undoubtedly	undoubtedly	ADV
ajema-5949	153	21	remain	remain	VERB
ajema-5949	153	22	a	a	DET
ajema-5949	153	23	central	central	ADJ
ajema-5949	153	24	tool	tool	NOUN
ajema-5949	153	25	for	for	ADP
ajema-5949	153	26	describing	describe	VERB
ajema-5949	153	27	the	the	DET
ajema-5949	153	28	symmetries	symmetry	NOUN
ajema-5949	153	29	and	and	CCONJ
ajema-5949	153	30	structures	structure	NOUN
ajema-5949	153	31	that	that	PRON
ajema-5949	153	32	govern	govern	VERB
ajema-5949	153	33	the	the	DET
ajema-5949	153	34	behavior	behavior	NOUN
ajema-5949	153	35	of	of	ADP
ajema-5949	153	36	matter	matter	NOUN
ajema-5949	153	37	and	and	CCONJ
ajema-5949	153	38	fields	field	NOUN
ajema-5949	153	39	at	at	ADP
ajema-5949	153	40	the	the	DET
ajema-5949	153	41	quantum	quantum	ADJ
ajema-5949	153	42	level	level	NOUN
ajema-5949	153	43	.	.	PUNCT
ajema-5949	154	1	their	their	PRON
ajema-5949	154	2	applications	application	NOUN
ajema-5949	154	3	in	in	ADP
ajema-5949	154	4	string	string	NOUN
ajema-5949	154	5	theory	theory	NOUN
ajema-5949	154	6	,	,	PUNCT
ajema-5949	154	7	conformal	conformal	ADJ
ajema-5949	154	8	field	field	NOUN
ajema-5949	154	9	theory	theory	NOUN
ajema-5949	154	10	,	,	PUNCT
ajema-5949	154	11	and	and	CCONJ
ajema-5949	154	12	quantum	quantum	NOUN
ajema-5949	154	13	gravity	gravity	NOUN
ajema-5949	154	14	highlight	highlight	VERB
ajema-5949	154	15	their	their	PRON
ajema-5949	154	16	versatility	versatility	NOUN
ajema-5949	154	17	and	and	CCONJ
ajema-5949	154	18	the	the	DET
ajema-5949	154	19	potential	potential	NOUN
ajema-5949	154	20	for	for	ADP
ajema-5949	154	21	future	future	ADJ
ajema-5949	154	22	breakthroughs	breakthrough	NOUN
ajema-5949	154	23	in	in	ADP
ajema-5949	154	24	our	our	PRON
ajema-5949	154	25	understanding	understanding	NOUN
ajema-5949	154	26	of	of	ADP
ajema-5949	154	27	the	the	DET
ajema-5949	154	28	quantum	quantum	ADJ
ajema-5949	154	29	universe	universe	NOUN
ajema-5949	154	30	.	.	PUNCT
ajema-5949	155	1	the	the	DET
ajema-5949	155	2	interplay	interplay	NOUN
ajema-5949	155	3	between	between	ADP
ajema-5949	155	4	quantum	quantum	ADJ
ajema-5949	155	5	groups	group	NOUN
ajema-5949	155	6	and	and	CCONJ
ajema-5949	155	7	non	non	ADJ
ajema-5949	155	8	-	-	ADJ
ajema-5949	155	9	commutative	commutative	ADJ
ajema-5949	155	10	geometry	geometry	NOUN
ajema-5949	155	11	provides	provide	VERB
ajema-5949	155	12	an	an	DET
ajema-5949	155	13	exciting	exciting	ADJ
ajema-5949	155	14	avenue	avenue	NOUN
ajema-5949	155	15	for	for	ADP
ajema-5949	155	16	exploring	explore	VERB
ajema-5949	155	17	new	new	ADJ
ajema-5949	155	18	models	model	NOUN
ajema-5949	155	19	of	of	ADP
ajema-5949	155	20	spacetime	spacetime	NOUN
ajema-5949	155	21	and	and	CCONJ
ajema-5949	155	22	the	the	DET
ajema-5949	155	23	very	very	ADJ
ajema-5949	155	24	fabric	fabric	NOUN
ajema-5949	155	25	of	of	ADP
ajema-5949	155	26	reality	reality	NOUN
ajema-5949	155	27	,	,	PUNCT
ajema-5949	155	28	further	far	ADV
ajema-5949	155	29	solidifying	solidify	VERB
ajema-5949	155	30	quantum	quantum	ADJ
ajema-5949	155	31	groups	group	NOUN
ajema-5949	155	32	as	as	ADP
ajema-5949	155	33	an	an	DET
ajema-5949	155	34	indispensable	indispensable	ADJ
ajema-5949	155	35	part	part	NOUN
ajema-5949	155	36	of	of	ADP
ajema-5949	155	37	modern	modern	ADJ
ajema-5949	155	38	theoretical	theoretical	ADJ
ajema-5949	155	39	physics	physics	NOUN
ajema-5949	155	40	.	.	PUNCT
ajema-5949	156	1	references	reference	NOUN
ajema-5949	156	2	1	1	NUM
ajema-5949	156	3	.	.	PUNCT
ajema-5949	157	1	chari	chari	PROPN
ajema-5949	157	2	,	,	PUNCT
ajema-5949	157	3	v.	v.	PROPN
ajema-5949	157	4	,	,	PUNCT
ajema-5949	157	5	&	&	CCONJ
ajema-5949	157	6	pressley	pressley	PROPN
ajema-5949	157	7	,	,	PUNCT
ajema-5949	157	8	a.	a.	NOUN
ajema-5949	157	9	(	(	PUNCT
ajema-5949	157	10	1994	1994	NUM
ajema-5949	157	11	)	)	PUNCT
ajema-5949	157	12	.	.	PUNCT
ajema-5949	158	1	a	a	DET
ajema-5949	158	2	guide	guide	NOUN
ajema-5949	158	3	to	to	ADP
ajema-5949	158	4	quantum	quantum	ADJ
ajema-5949	158	5	groups	group	NOUN
ajema-5949	158	6	.	.	PUNCT
ajema-5949	159	1	cambridge	cambridge	PROPN
ajema-5949	159	2	university	university	PROPN
ajema-5949	159	3	press	press	NOUN
ajema-5949	159	4	.	.	PUNCT
ajema-5949	160	1	2	2	X
ajema-5949	160	2	.	.	X
ajema-5949	160	3	connes	conne	NOUN
ajema-5949	160	4	,	,	PUNCT
ajema-5949	160	5	a.	a.	NOUN
ajema-5949	160	6	(	(	PUNCT
ajema-5949	160	7	1994	1994	NUM
ajema-5949	160	8	)	)	PUNCT
ajema-5949	160	9	.	.	PUNCT
ajema-5949	161	1	noncommutative	noncommutative	PROPN
ajema-5949	161	2	geometry	geometry	NOUN
ajema-5949	161	3	.	.	PUNCT
ajema-5949	162	1	academic	academic	ADJ
ajema-5949	162	2	press	press	NOUN
ajema-5949	162	3	.	.	PUNCT
ajema-5949	163	1	3	3	X
ajema-5949	163	2	.	.	NUM
ajema-5949	163	3	drinfeld	drinfeld	PROPN
ajema-5949	163	4	,	,	PUNCT
ajema-5949	163	5	v.	v.	PROPN
ajema-5949	163	6	g.	g.	PROPN
ajema-5949	163	7	(	(	PUNCT
ajema-5949	163	8	1986	1986	NUM
ajema-5949	163	9	)	)	PUNCT
ajema-5949	163	10	.	.	PUNCT
ajema-5949	164	1	quantum	quantum	ADJ
ajema-5949	164	2	groups	group	NOUN
ajema-5949	164	3	.	.	PUNCT
ajema-5949	165	1	proceedings	proceeding	NOUN
ajema-5949	165	2	of	of	ADP
ajema-5949	165	3	the	the	DET
ajema-5949	165	4	international	international	ADJ
ajema-5949	165	5	congress	congress	PROPN
ajema-5949	165	6	of	of	ADP
ajema-5949	165	7	mathematicians	mathematician	NOUN
ajema-5949	165	8	,	,	PUNCT
ajema-5949	165	9	798	798	NUM
ajema-5949	165	10	-	-	SYM
ajema-5949	165	11	820	820	NUM
ajema-5949	165	12	.	.	PUNCT
ajema-5949	166	1	4	4	X
ajema-5949	166	2	.	.	X
ajema-5949	166	3	jimbo	jimbo	PROPN
ajema-5949	166	4	,	,	PUNCT
ajema-5949	166	5	m.	m.	NOUN
ajema-5949	166	6	(	(	PUNCT
ajema-5949	166	7	1985	1985	NUM
ajema-5949	166	8	)	)	PUNCT
ajema-5949	166	9	.	.	PUNCT
ajema-5949	167	1	a	a	DET
ajema-5949	167	2	q	q	NOUN
ajema-5949	167	3	-	-	PUNCT
ajema-5949	167	4	analog	analog	NOUN
ajema-5949	167	5	of	of	ADP
ajema-5949	167	6	u(g	u(g	PROPN
ajema-5949	167	7	)	)	PUNCT
ajema-5949	167	8	and	and	CCONJ
ajema-5949	167	9	the	the	DET
ajema-5949	167	10	quantized	quantize	VERB
ajema-5949	167	11	universal	universal	ADJ
ajema-5949	167	12	enveloping	enveloping	NOUN
ajema-5949	167	13	algebra	algebra	NOUN
ajema-5949	167	14	.	.	PUNCT
ajema-5949	168	1	letters	letter	NOUN
ajema-5949	168	2	in	in	ADP
ajema-5949	168	3	mathematical	mathematical	ADJ
ajema-5949	168	4	physics	physics	NOUN
ajema-5949	168	5	,	,	PUNCT
ajema-5949	168	6	10(1	10(1	NUM
ajema-5949	168	7	)	)	PUNCT
ajema-5949	168	8	,	,	PUNCT
ajema-5949	168	9	63	63	NUM
ajema-5949	168	10	-	-	SYM
ajema-5949	168	11	69	69	NUM
ajema-5949	168	12	.	.	PUNCT
ajema-5949	169	1	5	5	NUM
ajema-5949	169	2	.	.	X
ajema-5949	169	3	faddeev	faddeev	PROPN
ajema-5949	169	4	,	,	PUNCT
ajema-5949	169	5	l.	l.	PROPN
ajema-5949	169	6	d.	d.	PROPN
ajema-5949	169	7	,	,	PUNCT
ajema-5949	169	8	reshetikhin	reshetikhin	PROPN
ajema-5949	169	9	,	,	PUNCT
ajema-5949	169	10	n.	n.	PROPN
ajema-5949	169	11	y.	y.	PROPN
ajema-5949	169	12	,	,	PUNCT
ajema-5949	169	13	&	&	CCONJ
ajema-5949	169	14	takhtajan	takhtajan	PROPN
ajema-5949	169	15	,	,	PUNCT
ajema-5949	169	16	l.	l.	PROPN
ajema-5949	169	17	a.	a.	PROPN
ajema-5949	169	18	(	(	PUNCT
ajema-5949	169	19	1989	1989	NUM
ajema-5949	169	20	)	)	PUNCT
ajema-5949	169	21	.	.	PUNCT
ajema-5949	170	1	quantization	quantization	NOUN
ajema-5949	170	2	of	of	ADP
ajema-5949	170	3	lie	lie	NOUN
ajema-5949	170	4	groups	group	NOUN
ajema-5949	170	5	and	and	CCONJ
ajema-5949	170	6	lie	lie	VERB
ajema-5949	170	7	algebras	algebra	NOUN
ajema-5949	170	8	.	.	PUNCT
ajema-5949	171	1	algebra	algebra	NOUN
ajema-5949	171	2	i	i	PRON
ajema-5949	171	3	analiz	analiz	NOUN
ajema-5949	171	4	,	,	PUNCT
ajema-5949	171	5	1(1	1(1	NUM
ajema-5949	171	6	)	)	PUNCT
ajema-5949	171	7	,	,	PUNCT
ajema-5949	171	8	178	178	NUM
ajema-5949	171	9	-	-	SYM
ajema-5949	171	10	206	206	NUM
ajema-5949	171	11	.	.	PUNCT
ajema-5949	172	1	6	6	NUM
ajema-5949	172	2	.	.	X
ajema-5949	172	3	majid	majid	PROPN
ajema-5949	172	4	,	,	PUNCT
ajema-5949	172	5	s.	s.	PROPN
ajema-5949	172	6	(	(	PUNCT
ajema-5949	172	7	1994	1994	NUM
ajema-5949	172	8	)	)	PUNCT
ajema-5949	172	9	.	.	PUNCT
ajema-5949	173	1	foundations	foundation	NOUN
ajema-5949	173	2	of	of	ADP
ajema-5949	173	3	quantum	quantum	NOUN
ajema-5949	173	4	group	group	NOUN
ajema-5949	173	5	theory	theory	NOUN
ajema-5949	173	6	.	.	PUNCT
ajema-5949	174	1	cambridge	cambridge	PROPN
ajema-5949	174	2	university	university	PROPN
ajema-5949	174	3	press	press	NOUN
ajema-5949	174	4	.	.	PUNCT