id	sid	tid	token	lemma	pos
ap-1350	1	1	wykresx.eps	wykresx.eps	X
ap-1350	1	2	acta	acta	PROPN
ap-1350	1	3	polytechnica	polytechnica	PROPN
ap-1350	1	4	vol	vol	NOUN
ap-1350	1	5	.	.	PUNCT
ap-1350	2	1	51	51	NUM
ap-1350	2	2	no	no	NOUN
ap-1350	2	3	.	.	PUNCT
ap-1350	3	1	1/2011	1/2011	NUM
ap-1350	3	2	quantum	quantum	ADJ
ap-1350	3	3	moment	moment	NOUN
ap-1350	3	4	map	map	VERB
ap-1350	3	5	and	and	CCONJ
ap-1350	3	6	invariant	invariant	ADJ
ap-1350	3	7	integration	integration	NOUN
ap-1350	3	8	theory	theory	NOUN
ap-1350	3	9	on	on	ADP
ap-1350	3	10	quantum	quantum	ADJ
ap-1350	3	11	spaces	space	NOUN
ap-1350	3	12	o.	o.	PROPN
ap-1350	3	13	osuna	osuna	PROPN
ap-1350	3	14	castro	castro	PROPN
ap-1350	3	15	,	,	PUNCT
ap-1350	4	1	e.	e.	PROPN
ap-1350	4	2	wagner	wagner	PROPN
ap-1350	4	3	abstract	abstract	PROPN
ap-1350	4	4	it	it	PRON
ap-1350	4	5	is	be	AUX
ap-1350	4	6	shown	show	VERB
ap-1350	4	7	that	that	SCONJ
ap-1350	4	8	,	,	PUNCT
ap-1350	4	9	on	on	ADP
ap-1350	4	10	the	the	DET
ap-1350	4	11	one	one	NUM
ap-1350	4	12	hand	hand	NOUN
ap-1350	4	13	,	,	PUNCT
ap-1350	4	14	quantum	quantum	ADJ
ap-1350	4	15	moment	moment	NOUN
ap-1350	4	16	maps	map	NOUN
ap-1350	4	17	give	give	VERB
ap-1350	4	18	rise	rise	NOUN
ap-1350	4	19	to	to	ADP
ap-1350	4	20	examples	example	NOUN
ap-1350	4	21	for	for	ADP
ap-1350	4	22	the	the	DET
ap-1350	4	23	operator	operator	NOUN
ap-1350	4	24	-	-	PUNCT
ap-1350	4	25	theoretic	theoretic	NOUN
ap-1350	4	26	approach	approach	NOUN
ap-1350	4	27	to	to	ADP
ap-1350	4	28	invariant	invariant	ADJ
ap-1350	4	29	integration	integration	NOUN
ap-1350	4	30	theory	theory	NOUN
ap-1350	4	31	developed	develop	VERB
ap-1350	4	32	by	by	ADP
ap-1350	4	33	k.-d	k.-d	PROPN
ap-1350	4	34	.	.	PUNCT
ap-1350	5	1	kürsten	kürsten	ADJ
ap-1350	5	2	and	and	CCONJ
ap-1350	5	3	the	the	DET
ap-1350	5	4	second	second	ADJ
ap-1350	5	5	author	author	NOUN
ap-1350	5	6	,	,	PUNCT
ap-1350	5	7	and	and	CCONJ
ap-1350	5	8	that	that	SCONJ
ap-1350	5	9	,	,	PUNCT
ap-1350	5	10	on	on	ADP
ap-1350	5	11	the	the	DET
ap-1350	5	12	other	other	ADJ
ap-1350	5	13	hand	hand	NOUN
ap-1350	5	14	,	,	PUNCT
ap-1350	5	15	the	the	DET
ap-1350	5	16	operator	operator	NOUN
ap-1350	5	17	-	-	PUNCT
ap-1350	5	18	theoretic	theoretic	NOUN
ap-1350	5	19	approach	approach	NOUN
ap-1350	5	20	to	to	ADP
ap-1350	5	21	invariant	invariant	ADJ
ap-1350	5	22	integration	integration	NOUN
ap-1350	5	23	theory	theory	NOUN
ap-1350	5	24	is	be	AUX
ap-1350	5	25	more	more	ADV
ap-1350	5	26	general	general	ADJ
ap-1350	5	27	since	since	SCONJ
ap-1350	5	28	it	it	PRON
ap-1350	5	29	also	also	ADV
ap-1350	5	30	applies	apply	VERB
ap-1350	5	31	to	to	ADP
ap-1350	5	32	examples	example	NOUN
ap-1350	5	33	without	without	ADP
ap-1350	5	34	a	a	DET
ap-1350	5	35	well	well	ADV
ap-1350	5	36	-	-	PUNCT
ap-1350	5	37	defined	define	VERB
ap-1350	5	38	quantum	quantum	ADJ
ap-1350	5	39	moment	moment	NOUN
ap-1350	5	40	map	map	NOUN
ap-1350	5	41	.	.	PUNCT
ap-1350	6	1	keywords	keyword	NOUN
ap-1350	6	2	:	:	PUNCT
ap-1350	6	3	quantum	quantum	ADJ
ap-1350	6	4	spaces	space	NOUN
ap-1350	6	5	,	,	PUNCT
ap-1350	6	6	invariant	invariant	ADJ
ap-1350	6	7	integration	integration	NOUN
ap-1350	6	8	theory	theory	NOUN
ap-1350	6	9	,	,	PUNCT
ap-1350	6	10	quantum	quantum	ADJ
ap-1350	6	11	moment	moment	NOUN
ap-1350	6	12	map	map	NOUN
ap-1350	6	13	.	.	PUNCT
ap-1350	7	1	1	1	NUM
ap-1350	7	2	introduction	introduction	NOUN
ap-1350	7	3	a	a	DET
ap-1350	7	4	noncommutative	noncommutative	ADJ
ap-1350	7	5	analogue	analogue	NOUN
ap-1350	7	6	of	of	ADP
ap-1350	7	7	an	an	DET
ap-1350	7	8	(	(	PUNCT
ap-1350	7	9	infinitesimal	infinitesimal	ADJ
ap-1350	7	10	)	)	PUNCT
ap-1350	7	11	group	group	NOUN
ap-1350	7	12	action	action	NOUN
ap-1350	7	13	on	on	ADP
ap-1350	7	14	a	a	DET
ap-1350	7	15	topological	topological	ADJ
ap-1350	7	16	space	space	NOUN
ap-1350	7	17	is	be	AUX
ap-1350	7	18	described	describe	VERB
ap-1350	7	19	by	by	ADP
ap-1350	7	20	the	the	DET
ap-1350	7	21	action	action	NOUN
ap-1350	7	22	of	of	ADP
ap-1350	7	23	a	a	DET
ap-1350	7	24	hopf	hopf	ADJ
ap-1350	7	25	algebra	algebra	NOUN
ap-1350	7	26	on	on	ADP
ap-1350	7	27	a	a	DET
ap-1350	7	28	noncommutative	noncommutative	ADJ
ap-1350	7	29	function	function	NOUN
ap-1350	7	30	algebra	algebra	NOUN
ap-1350	7	31	.	.	PUNCT
ap-1350	8	1	in	in	ADP
ap-1350	8	2	this	this	DET
ap-1350	8	3	setting	setting	NOUN
ap-1350	8	4	,	,	PUNCT
ap-1350	8	5	a	a	DET
ap-1350	8	6	generalization	generalization	NOUN
ap-1350	8	7	of	of	ADP
ap-1350	8	8	the	the	DET
ap-1350	8	9	classical	classical	ADJ
ap-1350	8	10	haar	haar	NOUN
ap-1350	8	11	measure	measure	NOUN
ap-1350	8	12	is	be	AUX
ap-1350	8	13	given	give	VERB
ap-1350	8	14	by	by	ADP
ap-1350	8	15	an	an	DET
ap-1350	8	16	invariant	invariant	ADJ
ap-1350	8	17	integral	integral	NOUN
ap-1350	8	18	,	,	PUNCT
ap-1350	8	19	that	that	ADV
ap-1350	8	20	is	is	ADV
ap-1350	8	21	,	,	PUNCT
ap-1350	8	22	a	a	DET
ap-1350	8	23	positive	positive	ADJ
ap-1350	8	24	linear	linear	ADJ
ap-1350	8	25	functional	functional	ADJ
ap-1350	8	26	with	with	ADP
ap-1350	8	27	certain	certain	ADJ
ap-1350	8	28	invariance	invariance	NOUN
ap-1350	8	29	properties	property	NOUN
ap-1350	8	30	.	.	PUNCT
ap-1350	9	1	usually	usually	ADV
ap-1350	9	2	the	the	DET
ap-1350	9	3	noncommutative	noncommutative	ADJ
ap-1350	9	4	function	function	NOUN
ap-1350	9	5	algebra	algebra	NOUN
ap-1350	9	6	is	be	AUX
ap-1350	9	7	generated	generate	VERB
ap-1350	9	8	by	by	ADP
ap-1350	9	9	a	a	DET
ap-1350	9	10	finite	finite	ADJ
ap-1350	9	11	set	set	NOUN
ap-1350	9	12	of	of	ADP
ap-1350	9	13	generators	generator	NOUN
ap-1350	9	14	which	which	PRON
ap-1350	9	15	are	be	AUX
ap-1350	9	16	considered	consider	VERB
ap-1350	9	17	as	as	ADP
ap-1350	9	18	coordinate	coordinate	NOUN
ap-1350	9	19	functions	function	NOUN
ap-1350	9	20	on	on	ADP
ap-1350	9	21	the	the	DET
ap-1350	9	22	quantum	quantum	ADJ
ap-1350	9	23	space	space	NOUN
ap-1350	9	24	.	.	PUNCT
ap-1350	10	1	as	as	ADP
ap-1350	10	2	in	in	ADP
ap-1350	10	3	the	the	DET
ap-1350	10	4	classical	classical	ADJ
ap-1350	10	5	case	case	NOUN
ap-1350	10	6	,	,	PUNCT
ap-1350	10	7	one	one	PRON
ap-1350	10	8	does	do	AUX
ap-1350	10	9	not	not	PART
ap-1350	10	10	expect	expect	VERB
ap-1350	10	11	that	that	SCONJ
ap-1350	10	12	polynomials	polynomial	NOUN
ap-1350	10	13	in	in	ADP
ap-1350	10	14	the	the	DET
ap-1350	10	15	coordinate	coordinate	NOUN
ap-1350	10	16	functions	function	NOUN
ap-1350	10	17	on	on	ADP
ap-1350	10	18	locally	locally	ADV
ap-1350	10	19	compact	compact	ADJ
ap-1350	10	20	quantum	quantum	NOUN
ap-1350	10	21	spaces	space	NOUN
ap-1350	10	22	are	be	AUX
ap-1350	10	23	integrable	integrable	ADJ
ap-1350	10	24	.	.	PUNCT
ap-1350	11	1	this	this	PRON
ap-1350	11	2	leads	lead	VERB
ap-1350	11	3	to	to	ADP
ap-1350	11	4	the	the	DET
ap-1350	11	5	problem	problem	NOUN
ap-1350	11	6	that	that	PRON
ap-1350	11	7	one	one	PRON
ap-1350	11	8	has	have	AUX
ap-1350	11	9	to	to	PART
ap-1350	11	10	associate	associate	VERB
ap-1350	11	11	algebras	algebra	NOUN
ap-1350	11	12	of	of	ADP
ap-1350	11	13	integrable	integrable	ADJ
ap-1350	11	14	(	(	PUNCT
ap-1350	11	15	and	and	CCONJ
ap-1350	11	16	differentiable	differentiable	ADJ
ap-1350	11	17	)	)	PUNCT
ap-1350	11	18	functions	function	NOUN
ap-1350	11	19	to	to	ADP
ap-1350	11	20	the	the	DET
ap-1350	11	21	noncommutative	noncommutative	ADJ
ap-1350	11	22	polynomial	polynomial	ADJ
ap-1350	11	23	algebra	algebra	NOUN
ap-1350	11	24	in	in	ADP
ap-1350	11	25	an	an	DET
ap-1350	11	26	appropriate	appropriate	ADJ
ap-1350	11	27	way	way	NOUN
ap-1350	11	28	.	.	PUNCT
ap-1350	12	1	in	in	ADP
ap-1350	12	2	the	the	DET
ap-1350	12	3	algebraic	algebraic	ADJ
ap-1350	12	4	approach	approach	NOUN
ap-1350	12	5	(	(	PUNCT
ap-1350	12	6	see	see	VERB
ap-1350	12	7	e.g.	e.g.	ADV
ap-1350	12	8	[	[	X
ap-1350	12	9	2	2	NUM
ap-1350	12	10	,	,	PUNCT
ap-1350	12	11	7	7	NUM
ap-1350	12	12	]	]	NUM
ap-1350	12	13	)	)	PUNCT
ap-1350	12	14	,	,	PUNCT
ap-1350	12	15	one	one	NUM
ap-1350	12	16	associates	associate	NOUN
ap-1350	12	17	function	function	NOUN
ap-1350	12	18	algebras	algebra	NOUN
ap-1350	12	19	by	by	ADP
ap-1350	12	20	imposing	impose	VERB
ap-1350	12	21	commutation	commutation	NOUN
ap-1350	12	22	relations	relation	NOUN
ap-1350	12	23	with	with	ADP
ap-1350	12	24	the	the	DET
ap-1350	12	25	generators	generator	NOUN
ap-1350	12	26	and	and	CCONJ
ap-1350	12	27	defines	define	VERB
ap-1350	12	28	the	the	DET
ap-1350	12	29	invariant	invariant	ADJ
ap-1350	12	30	integral	integral	NOUN
ap-1350	12	31	by	by	ADP
ap-1350	12	32	jackson	jackson	PROPN
ap-1350	12	33	-	-	PUNCT
ap-1350	12	34	type	type	NOUN
ap-1350	12	35	integrals	integral	NOUN
ap-1350	12	36	.	.	PUNCT
ap-1350	13	1	a	a	DET
ap-1350	13	2	more	more	ADV
ap-1350	13	3	rigorous	rigorous	ADJ
ap-1350	13	4	method	method	NOUN
ap-1350	13	5	was	be	AUX
ap-1350	13	6	developed	develop	VERB
ap-1350	13	7	by	by	ADP
ap-1350	13	8	kürsten	kürsten	ADJ
ap-1350	13	9	and	and	CCONJ
ap-1350	13	10	the	the	DET
ap-1350	13	11	second	second	ADJ
ap-1350	13	12	author	author	NOUN
ap-1350	13	13	in	in	ADP
ap-1350	13	14	[	[	X
ap-1350	13	15	3	3	NUM
ap-1350	13	16	]	]	PUNCT
ap-1350	13	17	,	,	PUNCT
ap-1350	13	18	based	base	VERB
ap-1350	13	19	on	on	ADP
ap-1350	13	20	hilbert	hilbert	NOUN
ap-1350	13	21	space	space	NOUN
ap-1350	13	22	representations	representation	NOUN
ap-1350	13	23	and	and	CCONJ
ap-1350	13	24	(	(	PUNCT
ap-1350	13	25	unbounded	unbounded	ADJ
ap-1350	13	26	)	)	PUNCT
ap-1350	13	27	operator	operator	NOUN
ap-1350	13	28	algebras	algebra	NOUN
ap-1350	13	29	.	.	PUNCT
ap-1350	14	1	the	the	DET
ap-1350	14	2	advantage	advantage	NOUN
ap-1350	14	3	of	of	ADP
ap-1350	14	4	this	this	DET
ap-1350	14	5	method	method	NOUN
ap-1350	14	6	becomes	become	VERB
ap-1350	14	7	apparent	apparent	ADJ
ap-1350	14	8	in	in	ADP
ap-1350	14	9	the	the	DET
ap-1350	14	10	examples	example	NOUN
ap-1350	14	11	of	of	ADP
ap-1350	14	12	[	[	X
ap-1350	14	13	5	5	NUM
ap-1350	14	14	]	]	PUNCT
ap-1350	14	15	,	,	PUNCT
ap-1350	14	16	where	where	SCONJ
ap-1350	14	17	the	the	DET
ap-1350	14	18	algebraic	algebraic	ADJ
ap-1350	14	19	approach	approach	NOUN
ap-1350	14	20	would	would	AUX
ap-1350	14	21	fail	fail	VERB
ap-1350	14	22	.	.	PUNCT
ap-1350	15	1	the	the	DET
ap-1350	15	2	first	first	ADJ
ap-1350	15	3	step	step	NOUN
ap-1350	15	4	of	of	ADP
ap-1350	15	5	the	the	DET
ap-1350	15	6	operator	operator	NOUN
ap-1350	15	7	-	-	PUNCT
ap-1350	15	8	theoretic	theoretic	NOUN
ap-1350	15	9	approach	approach	NOUN
ap-1350	15	10	is	be	AUX
ap-1350	15	11	to	to	PART
ap-1350	15	12	express	express	VERB
ap-1350	15	13	the	the	DET
ap-1350	15	14	action	action	NOUN
ap-1350	15	15	of	of	ADP
ap-1350	15	16	a	a	DET
ap-1350	15	17	hopf	hopf	ADJ
ap-1350	15	18	*	*	PUNCT
ap-1350	15	19	-algebra	-algebra	NOUN
ap-1350	15	20	u	u	NOUN
ap-1350	15	21	on	on	ADP
ap-1350	15	22	a	a	DET
ap-1350	15	23	*	*	PUNCT
ap-1350	15	24	-algebra	-algebra	NOUN
ap-1350	15	25	a	a	PRON
ap-1350	15	26	by	by	ADP
ap-1350	15	27	algebraic	algebraic	ADJ
ap-1350	15	28	relations	relation	NOUN
ap-1350	15	29	of	of	ADP
ap-1350	15	30	hilbert	hilbert	PROPN
ap-1350	15	31	space	space	NOUN
ap-1350	15	32	operators	operator	NOUN
ap-1350	15	33	.	.	PUNCT
ap-1350	16	1	it	it	PRON
ap-1350	16	2	should	should	AUX
ap-1350	16	3	be	be	AUX
ap-1350	16	4	noted	note	VERB
ap-1350	16	5	that	that	SCONJ
ap-1350	16	6	the	the	DET
ap-1350	16	7	operators	operator	NOUN
ap-1350	16	8	describing	describe	VERB
ap-1350	16	9	the	the	DET
ap-1350	16	10	action	action	NOUN
ap-1350	16	11	do	do	AUX
ap-1350	16	12	not	not	PART
ap-1350	16	13	have	have	VERB
ap-1350	16	14	to	to	PART
ap-1350	16	15	satisfy	satisfy	VERB
ap-1350	16	16	the	the	DET
ap-1350	16	17	commutation	commutation	NOUN
ap-1350	16	18	relations	relation	NOUN
ap-1350	16	19	of	of	ADP
ap-1350	16	20	u	u	PROPN
ap-1350	16	21	.	.	PUNCT
ap-1350	17	1	on	on	ADP
ap-1350	17	2	the	the	DET
ap-1350	17	3	other	other	ADJ
ap-1350	17	4	hand	hand	NOUN
ap-1350	17	5	,	,	PUNCT
ap-1350	17	6	any	any	DET
ap-1350	17	7	joint	joint	ADJ
ap-1350	17	8	representation	representation	NOUN
ap-1350	17	9	of	of	ADP
ap-1350	17	10	u	u	NOUN
ap-1350	17	11	and	and	CCONJ
ap-1350	17	12	a	a	PRON
ap-1350	17	13	on	on	ADP
ap-1350	17	14	the	the	DET
ap-1350	17	15	same	same	ADJ
ap-1350	17	16	hilbert	hilbert	NOUN
ap-1350	17	17	space	space	NOUN
ap-1350	17	18	allows	allow	VERB
ap-1350	17	19	one	one	NUM
ap-1350	17	20	to	to	PART
ap-1350	17	21	equip	equip	VERB
ap-1350	17	22	a	a	PRON
ap-1350	17	23	with	with	ADP
ap-1350	17	24	a	a	DET
ap-1350	17	25	u	u	NOUN
ap-1350	17	26	-	-	NOUN
ap-1350	17	27	action	action	NOUN
ap-1350	17	28	,	,	PUNCT
ap-1350	17	29	given	give	VERB
ap-1350	17	30	by	by	ADP
ap-1350	17	31	the	the	DET
ap-1350	17	32	formulas	formula	NOUN
ap-1350	17	33	of	of	ADP
ap-1350	17	34	the	the	DET
ap-1350	17	35	adjoint	adjoint	PROPN
ap-1350	17	36	action	action	NOUN
ap-1350	17	37	,	,	PUNCT
ap-1350	17	38	provided	provide	VERB
ap-1350	17	39	that	that	SCONJ
ap-1350	17	40	a	a	PRON
ap-1350	17	41	is	be	AUX
ap-1350	17	42	invariant	invariant	ADJ
ap-1350	17	43	under	under	ADP
ap-1350	17	44	these	these	DET
ap-1350	17	45	algebraic	algebraic	ADJ
ap-1350	17	46	expressions	expression	NOUN
ap-1350	18	1	[	[	X
ap-1350	18	2	6	6	NUM
ap-1350	18	3	]	]	PUNCT
ap-1350	18	4	.	.	PUNCT
ap-1350	19	1	this	this	PRON
ap-1350	19	2	will	will	AUX
ap-1350	19	3	be	be	AUX
ap-1350	19	4	automatically	automatically	ADV
ap-1350	19	5	the	the	DET
ap-1350	19	6	case	case	NOUN
ap-1350	19	7	if	if	SCONJ
ap-1350	19	8	there	there	PRON
ap-1350	19	9	is	be	VERB
ap-1350	19	10	a	a	DET
ap-1350	19	11	*	*	PUNCT
ap-1350	19	12	-homomorphism	-homomorphism	NOUN
ap-1350	19	13	from	from	ADP
ap-1350	19	14	u	u	NOUN
ap-1350	19	15	into	into	ADP
ap-1350	19	16	a.	a.	NOUN
ap-1350	19	17	then	then	ADV
ap-1350	19	18	one	one	NUM
ap-1350	19	19	only	only	ADV
ap-1350	19	20	has	have	VERB
ap-1350	19	21	to	to	PART
ap-1350	19	22	consider	consider	VERB
ap-1350	19	23	*	*	NOUN
ap-1350	19	24	-representations	-representation	NOUN
ap-1350	19	25	of	of	ADP
ap-1350	19	26	a	a	PRON
ap-1350	19	27	on	on	ADP
ap-1350	19	28	a	a	DET
ap-1350	19	29	hilbert	hilbert	NOUN
ap-1350	19	30	space	space	NOUN
ap-1350	19	31	and	and	CCONJ
ap-1350	19	32	the	the	DET
ap-1350	19	33	methods	method	NOUN
ap-1350	19	34	from	from	ADP
ap-1350	19	35	[	[	X
ap-1350	19	36	3	3	NUM
ap-1350	19	37	]	]	PUNCT
ap-1350	19	38	will	will	AUX
ap-1350	19	39	apply	apply	VERB
ap-1350	19	40	without	without	ADP
ap-1350	19	41	restrictions	restriction	NOUN
ap-1350	19	42	.	.	PUNCT
ap-1350	20	1	in	in	ADP
ap-1350	20	2	[	[	X
ap-1350	20	3	2	2	NUM
ap-1350	20	4	]	]	PUNCT
ap-1350	20	5	,	,	PUNCT
ap-1350	20	6	korogodsky	korogodsky	PROPN
ap-1350	20	7	called	call	VERB
ap-1350	20	8	a	a	DET
ap-1350	20	9	*	*	PUNCT
ap-1350	20	10	-homomorphism	-homomorphism	PROPN
ap-1350	20	11	from	from	ADP
ap-1350	20	12	u	u	NOUN
ap-1350	20	13	into	into	ADP
ap-1350	20	14	a	a	DET
ap-1350	20	15	intertwining	intertwine	VERB
ap-1350	20	16	the	the	DET
ap-1350	20	17	(	(	PUNCT
ap-1350	20	18	adjoint	adjoint	NOUN
ap-1350	20	19	)	)	PUNCT
ap-1350	20	20	action	action	NOUN
ap-1350	20	21	a	a	DET
ap-1350	20	22	“	"	PUNCT
ap-1350	20	23	quantum	quantum	ADJ
ap-1350	20	24	moment	moment	NOUN
ap-1350	20	25	map	map	NOUN
ap-1350	20	26	”	"	PUNCT
ap-1350	20	27	.	.	PUNCT
ap-1350	21	1	the	the	DET
ap-1350	21	2	aim	aim	NOUN
ap-1350	21	3	of	of	ADP
ap-1350	21	4	this	this	DET
ap-1350	21	5	paper	paper	NOUN
ap-1350	21	6	is	be	AUX
ap-1350	21	7	to	to	PART
ap-1350	21	8	show	show	VERB
ap-1350	21	9	that	that	SCONJ
ap-1350	21	10	,	,	PUNCT
ap-1350	21	11	on	on	ADP
ap-1350	21	12	the	the	DET
ap-1350	21	13	one	one	NUM
ap-1350	21	14	hand	hand	NOUN
ap-1350	21	15	,	,	PUNCT
ap-1350	21	16	quantum	quantum	ADJ
ap-1350	21	17	moment	moment	NOUN
ap-1350	21	18	maps	map	NOUN
ap-1350	21	19	give	give	VERB
ap-1350	21	20	rise	rise	NOUN
ap-1350	21	21	to	to	ADP
ap-1350	21	22	examples	example	NOUN
ap-1350	21	23	for	for	ADP
ap-1350	21	24	the	the	DET
ap-1350	21	25	operator	operator	NOUN
ap-1350	21	26	-	-	PUNCT
ap-1350	21	27	theoretic	theoretic	NOUN
ap-1350	21	28	approach	approach	NOUN
ap-1350	21	29	to	to	ADP
ap-1350	21	30	invariant	invariant	ADJ
ap-1350	21	31	integration	integration	NOUN
ap-1350	21	32	theory	theory	NOUN
ap-1350	21	33	.	.	PUNCT
ap-1350	22	1	on	on	ADP
ap-1350	22	2	the	the	DET
ap-1350	22	3	other	other	ADJ
ap-1350	22	4	hand	hand	NOUN
ap-1350	22	5	,	,	PUNCT
ap-1350	22	6	we	we	PRON
ap-1350	22	7	demonstrate	demonstrate	VERB
ap-1350	22	8	that	that	SCONJ
ap-1350	22	9	the	the	DET
ap-1350	22	10	operator	operator	NOUN
ap-1350	22	11	-	-	PUNCT
ap-1350	22	12	theoretic	theoretic	NOUN
ap-1350	22	13	approach	approach	NOUN
ap-1350	22	14	to	to	ADP
ap-1350	22	15	invariant	invariant	ADJ
ap-1350	22	16	integration	integration	NOUN
ap-1350	22	17	theory	theory	NOUN
ap-1350	22	18	is	be	AUX
ap-1350	22	19	more	more	ADV
ap-1350	22	20	general	general	ADJ
ap-1350	22	21	,	,	PUNCT
ap-1350	22	22	since	since	SCONJ
ap-1350	22	23	it	it	PRON
ap-1350	22	24	also	also	ADV
ap-1350	22	25	applies	apply	VERB
ap-1350	22	26	to	to	ADP
ap-1350	22	27	cases	case	NOUN
ap-1350	22	28	where	where	SCONJ
ap-1350	22	29	the	the	DET
ap-1350	22	30	operators	operator	NOUN
ap-1350	22	31	describing	describe	VERB
ap-1350	22	32	the	the	DET
ap-1350	22	33	action	action	NOUN
ap-1350	22	34	do	do	AUX
ap-1350	22	35	not	not	PART
ap-1350	22	36	satisfy	satisfy	VERB
ap-1350	22	37	the	the	DET
ap-1350	22	38	commutation	commutation	NOUN
ap-1350	22	39	relations	relation	NOUN
ap-1350	22	40	of	of	ADP
ap-1350	22	41	u	u	PRON
ap-1350	22	42	and	and	CCONJ
ap-1350	22	43	hence	hence	ADV
ap-1350	22	44	do	do	AUX
ap-1350	22	45	not	not	PART
ap-1350	22	46	define	define	VERB
ap-1350	22	47	a	a	DET
ap-1350	22	48	quantum	quantum	ADJ
ap-1350	22	49	moment	moment	NOUN
ap-1350	22	50	map	map	NOUN
ap-1350	22	51	.	.	PUNCT
ap-1350	23	1	2	2	NUM
ap-1350	23	2	operator	operator	NOUN
ap-1350	23	3	-	-	PUNCT
ap-1350	23	4	theoretic	theoretic	NOUN
ap-1350	23	5	approach	approach	NOUN
ap-1350	23	6	to	to	ADP
ap-1350	23	7	invariant	invariant	ADJ
ap-1350	23	8	integration	integration	NOUN
ap-1350	23	9	theory	theory	NOUN
ap-1350	23	10	for	for	ADP
ap-1350	23	11	details	detail	NOUN
ap-1350	23	12	on	on	ADP
ap-1350	23	13	quantum	quantum	ADJ
ap-1350	23	14	groups	group	NOUN
ap-1350	23	15	and	and	CCONJ
ap-1350	23	16	related	related	ADJ
ap-1350	23	17	notions	notion	NOUN
ap-1350	23	18	,	,	PUNCT
ap-1350	23	19	we	we	PRON
ap-1350	23	20	refer	refer	VERB
ap-1350	23	21	the	the	DET
ap-1350	23	22	reader	reader	NOUN
ap-1350	23	23	to	to	ADP
ap-1350	23	24	[	[	X
ap-1350	23	25	1	1	NUM
ap-1350	23	26	]	]	PUNCT
ap-1350	23	27	.	.	PUNCT
ap-1350	24	1	let	let	VERB
ap-1350	24	2	u	u	PRON
ap-1350	24	3	be	be	AUX
ap-1350	24	4	a	a	DET
ap-1350	24	5	hopf	hopf	ADJ
ap-1350	24	6	*	*	PUNCT
ap-1350	24	7	-algebra	-algebra	NOUN
ap-1350	24	8	with	with	ADP
ap-1350	24	9	hopf	hopf	ADJ
ap-1350	24	10	structure	structure	NOUN
ap-1350	24	11	δ	δ	PROPN
ap-1350	24	12	,	,	PUNCT
ap-1350	24	13	ε	ε	PROPN
ap-1350	24	14	and	and	CCONJ
ap-1350	24	15	s	s	PROPN
ap-1350	24	16	,	,	PUNCT
ap-1350	24	17	where	where	SCONJ
ap-1350	24	18	δ	δ	NOUN
ap-1350	24	19	:	:	PUNCT
ap-1350	24	20	u	u	PROPN
ap-1350	24	21	→	→	SYM
ap-1350	24	22	u⊗u	u⊗u	PROPN
ap-1350	24	23	and	and	CCONJ
ap-1350	24	24	ε	ε	PROPN
ap-1350	24	25	:	:	PUNCT
ap-1350	24	26	u	u	X
ap-1350	24	27	→	→	SYM
ap-1350	24	28	c	c	X
ap-1350	24	29	are	be	AUX
ap-1350	24	30	*	*	PUNCT
ap-1350	24	31	-homomorphisms	-homomorphism	NOUN
ap-1350	24	32	and	and	CCONJ
ap-1350	24	33	s	s	VERB
ap-1350	24	34	:	:	PUNCT
ap-1350	24	35	u	u	X
ap-1350	24	36	→	→	SYM
ap-1350	24	37	u	u	PROPN
ap-1350	24	38	is	be	AUX
ap-1350	24	39	an	an	DET
ap-1350	24	40	anti	anti	ADJ
ap-1350	24	41	-	-	NOUN
ap-1350	24	42	homomorphism	homomorphism	ADJ
ap-1350	24	43	satisfying	satisfy	VERB
ap-1350	24	44	certain	certain	ADJ
ap-1350	24	45	conditions	condition	NOUN
ap-1350	24	46	.	.	PUNCT
ap-1350	25	1	we	we	PRON
ap-1350	25	2	will	will	AUX
ap-1350	25	3	use	use	VERB
ap-1350	25	4	sweedler	sweedler	NOUN
ap-1350	25	5	-	-	PUNCT
ap-1350	25	6	heinemann	heinemann	NOUN
ap-1350	25	7	notation	notation	NOUN
ap-1350	25	8	and	and	CCONJ
ap-1350	25	9	write	write	VERB
ap-1350	25	10	δ(f	δ(f	PROPN
ap-1350	25	11	)	)	PUNCT
ap-1350	25	12	=	=	PUNCT
ap-1350	26	1	f(1	f(1	PROPN
ap-1350	26	2	)	)	PUNCT
ap-1350	26	3	⊗	⊗	PROPN
ap-1350	26	4	f(2	f(2	PROPN
ap-1350	26	5	)	)	PUNCT
ap-1350	26	6	.	.	PUNCT
ap-1350	27	1	a	a	DET
ap-1350	27	2	*	*	PUNCT
ap-1350	27	3	-algebra	-algebra	NOUN
ap-1350	27	4	x	x	VERB
ap-1350	27	5	is	be	AUX
ap-1350	27	6	called	call	VERB
ap-1350	27	7	a	a	DET
ap-1350	27	8	left	left	ADJ
ap-1350	27	9	u	u	NOUN
ap-1350	27	10	-	-	NOUN
ap-1350	27	11	module	module	NOUN
ap-1350	27	12	*	*	PUNCT
ap-1350	27	13	-algebra	-algebra	NOUN
ap-1350	27	14	if	if	SCONJ
ap-1350	27	15	there	there	PRON
ap-1350	27	16	is	be	VERB
ap-1350	27	17	a	a	DET
ap-1350	27	18	left	left	ADJ
ap-1350	27	19	u	u	NOUN
ap-1350	27	20	-	-	NOUN
ap-1350	27	21	action	action	ADJ
ap-1350	27	22	�	�	PROPN
ap-1350	27	23	on	on	ADP
ap-1350	27	24	x	x	SYM
ap-1350	27	25	such	such	ADJ
ap-1350	27	26	that	that	SCONJ
ap-1350	27	27	f	f	PROPN
ap-1350	27	28	�	�	PROPN
ap-1350	27	29	(	(	PUNCT
ap-1350	27	30	xy	xy	NOUN
ap-1350	27	31	)	)	PUNCT
ap-1350	27	32	=	=	SYM
ap-1350	27	33	(	(	PUNCT
ap-1350	27	34	f(1	f(1	PROPN
ap-1350	27	35	)	)	PUNCT
ap-1350	27	36	�	�	PROPN
ap-1350	27	37	x)(f(2	x)(f(2	SYM
ap-1350	27	38	)	)	PUNCT
ap-1350	27	39	�	�	PROPN
ap-1350	27	40	y	y	PROPN
ap-1350	27	41	)	)	PUNCT
ap-1350	27	42	,	,	PUNCT
ap-1350	27	43	(	(	PUNCT
ap-1350	27	44	f	f	PROPN
ap-1350	27	45	�	�	PROPN
ap-1350	27	46	x)∗	x)∗	PUNCT
ap-1350	28	1	=	=	PUNCT
ap-1350	28	2	s(f)∗	s(f)∗	NOUN
ap-1350	28	3	�	�	PROPN
ap-1350	28	4	x∗	x∗	PROPN
ap-1350	28	5	,	,	PUNCT
ap-1350	28	6	(	(	PUNCT
ap-1350	28	7	1	1	X
ap-1350	28	8	)	)	PUNCT
ap-1350	28	9	x	x	NOUN
ap-1350	28	10	,	,	PUNCT
ap-1350	28	11	y	y	PROPN
ap-1350	28	12	∈	∈	PROPN
ap-1350	28	13	x	x	X
ap-1350	28	14	,	,	PUNCT
ap-1350	28	15	f	f	PROPN
ap-1350	28	16	∈	∈	PROPN
ap-1350	28	17	u	u	PROPN
ap-1350	28	18	.	.	PUNCT
ap-1350	29	1	for	for	ADP
ap-1350	29	2	unital	unital	ADJ
ap-1350	29	3	algebras	algebra	NOUN
ap-1350	29	4	,	,	PUNCT
ap-1350	29	5	one	one	PRON
ap-1350	29	6	also	also	ADV
ap-1350	29	7	requires	require	VERB
ap-1350	29	8	f	f	PROPN
ap-1350	29	9	�	�	PROPN
ap-1350	29	10	1	1	NUM
ap-1350	29	11	=	=	SYM
ap-1350	29	12	ε(f)1	ε(f)1	PROPN
ap-1350	29	13	.	.	PUNCT
ap-1350	29	14	by	by	ADP
ap-1350	29	15	an	an	DET
ap-1350	29	16	invariant	invariant	ADJ
ap-1350	29	17	integral	integral	NOUN
ap-1350	29	18	we	we	PRON
ap-1350	29	19	mean	mean	VERB
ap-1350	29	20	a	a	DET
ap-1350	29	21	positive	positive	ADJ
ap-1350	29	22	linear	linear	ADJ
ap-1350	29	23	functional	functional	ADJ
ap-1350	29	24	h	h	NOUN
ap-1350	29	25	on	on	ADP
ap-1350	29	26	x	x	PUNCT
ap-1350	29	27	satisfying	satisfy	VERB
ap-1350	29	28	h(f	h(f	PROPN
ap-1350	29	29	�	�	PROPN
ap-1350	29	30	x	x	SYM
ap-1350	29	31	)	)	PUNCT
ap-1350	30	1	=	=	SYM
ap-1350	30	2	ε(f)h(x	ε(f)h(x	NOUN
ap-1350	30	3	)	)	PUNCT
ap-1350	30	4	,	,	PUNCT
ap-1350	30	5	x	x	PUNCT
ap-1350	30	6	∈	∈	PROPN
ap-1350	30	7	x	x	X
ap-1350	30	8	,	,	PUNCT
ap-1350	30	9	f	f	PROPN
ap-1350	30	10	∈	∈	PROPN
ap-1350	30	11	u	u	PROPN
ap-1350	30	12	.	.	PUNCT
ap-1350	31	1	(	(	PUNCT
ap-1350	31	2	2	2	NUM
ap-1350	31	3	)	)	PUNCT
ap-1350	31	4	29	29	NUM
ap-1350	31	5	acta	acta	PROPN
ap-1350	31	6	polytechnica	polytechnica	PROPN
ap-1350	31	7	vol	vol	NOUN
ap-1350	31	8	.	.	PUNCT
ap-1350	32	1	51	51	NUM
ap-1350	32	2	no	no	NOUN
ap-1350	32	3	.	.	PUNCT
ap-1350	33	1	1/2011	1/2011	NUM
ap-1350	33	2	given	give	VERB
ap-1350	33	3	a	a	DET
ap-1350	33	4	dense	dense	ADJ
ap-1350	33	5	linear	linear	NOUN
ap-1350	33	6	subspaced	subspaced	NOUN
ap-1350	33	7	of	of	ADP
ap-1350	33	8	a	a	DET
ap-1350	33	9	hilbert	hilbert	NOUN
ap-1350	33	10	space	space	NOUN
ap-1350	33	11	h	h	NOUN
ap-1350	33	12	,	,	PUNCT
ap-1350	33	13	consider	consider	VERB
ap-1350	33	14	the	the	DET
ap-1350	33	15	*	*	PUNCT
ap-1350	33	16	-algebra	-algebra	NOUN
ap-1350	33	17	l+(d	l+(d	PROPN
ap-1350	33	18	)	)	PUNCT
ap-1350	33	19	:	:	PUNCT
ap-1350	34	1	=	=	SYM
ap-1350	34	2	{	{	PUNCT
ap-1350	34	3	x	x	PUNCT
ap-1350	34	4	∈	∈	PROPN
ap-1350	34	5	end(d	end(d	PROPN
ap-1350	34	6	)	)	PUNCT
ap-1350	34	7	;	;	PUNCT
ap-1350	35	1	d	d	PROPN
ap-1350	35	2	⊂	⊂	PROPN
ap-1350	35	3	d(x∗	d(x∗	PROPN
ap-1350	35	4	)	)	PUNCT
ap-1350	35	5	,	,	PUNCT
ap-1350	35	6	x∗d	x∗d	PROPN
ap-1350	36	1	⊂	⊂	PROPN
ap-1350	36	2	d	d	X
ap-1350	36	3	}	}	PUNCT
ap-1350	36	4	with	with	ADP
ap-1350	36	5	involution	involution	NOUN
ap-1350	36	6	x	x	SYM
ap-1350	36	7	�	�	PROPN
ap-1350	36	8	→	→	SYM
ap-1350	36	9	x∗	x∗	PROPN
ap-1350	36	10	⇁	⇁	PROPN
ap-1350	36	11	d.	d.	PROPN
ap-1350	36	12	an	an	PRON
ap-1350	36	13	(	(	PUNCT
ap-1350	36	14	unbounded	unbounded	ADJ
ap-1350	36	15	)	)	PUNCT
ap-1350	36	16	*	*	PUNCT
ap-1350	36	17	-representation	-representation	NOUN
ap-1350	36	18	of	of	ADP
ap-1350	36	19	x	x	SYM
ap-1350	36	20	is	be	AUX
ap-1350	36	21	a	a	DET
ap-1350	36	22	*	*	PUNCT
ap-1350	36	23	-homomorphism	-homomorphism	PROPN
ap-1350	36	24	π	π	NOUN
ap-1350	36	25	:	:	PUNCT
ap-1350	36	26	x	x	SYM
ap-1350	36	27	→	→	SYM
ap-1350	36	28	l+(d	l+(d	PROPN
ap-1350	36	29	)	)	PUNCT
ap-1350	36	30	.	.	PUNCT
ap-1350	37	1	if	if	SCONJ
ap-1350	37	2	for	for	ADP
ap-1350	37	3	each	each	DET
ap-1350	37	4	f	f	PROPN
ap-1350	37	5	∈	∈	PROPN
ap-1350	37	6	u	u	NOUN
ap-1350	37	7	there	there	PRON
ap-1350	37	8	exists	exist	VERB
ap-1350	37	9	a	a	DET
ap-1350	37	10	finite	finite	ADJ
ap-1350	37	11	number	number	NOUN
ap-1350	37	12	of	of	ADP
ap-1350	37	13	operators	operators	PROPN
ap-1350	37	14	li	li	PROPN
ap-1350	37	15	,	,	PUNCT
ap-1350	37	16	ri	ri	PROPN
ap-1350	37	17	∈	∈	PROPN
ap-1350	37	18	l+(d	l+(d	PROPN
ap-1350	37	19	)	)	PUNCT
ap-1350	38	1	such	such	ADJ
ap-1350	38	2	that	that	SCONJ
ap-1350	38	3	π(f	π(f	PROPN
ap-1350	38	4	�	�	PROPN
ap-1350	38	5	x	x	NOUN
ap-1350	38	6	)	)	PUNCT
ap-1350	38	7	=	=	PUNCT
ap-1350	39	1	∑	∑	PUNCT
ap-1350	39	2	i	i	PRON
ap-1350	39	3	liπ(x)ri	liπ(x)ri	ADJ
ap-1350	39	4	,	,	PUNCT
ap-1350	39	5	x	x	SYM
ap-1350	39	6	∈	∈	NOUN
ap-1350	39	7	x	x	X
ap-1350	39	8	,	,	PUNCT
ap-1350	39	9	(	(	PUNCT
ap-1350	39	10	3	3	X
ap-1350	39	11	)	)	PUNCT
ap-1350	39	12	then	then	ADV
ap-1350	39	13	we	we	PRON
ap-1350	39	14	say	say	VERB
ap-1350	39	15	that	that	SCONJ
ap-1350	39	16	we	we	PRON
ap-1350	39	17	have	have	VERB
ap-1350	39	18	an	an	DET
ap-1350	39	19	operator	operator	NOUN
ap-1350	39	20	expansion	expansion	NOUN
ap-1350	39	21	of	of	ADP
ap-1350	39	22	the	the	DET
ap-1350	39	23	action	action	NOUN
ap-1350	39	24	.	.	PUNCT
ap-1350	40	1	obviously	obviously	ADV
ap-1350	40	2	,	,	PUNCT
ap-1350	40	3	it	it	PRON
ap-1350	40	4	suffices	suffice	VERB
ap-1350	40	5	to	to	PART
ap-1350	40	6	know	know	VERB
ap-1350	40	7	the	the	DET
ap-1350	40	8	operators	operator	NOUN
ap-1350	40	9	li	li	PROPN
ap-1350	40	10	,	,	PUNCT
ap-1350	40	11	ri	ri	PROPN
ap-1350	40	12	for	for	ADP
ap-1350	40	13	a	a	DET
ap-1350	40	14	set	set	NOUN
ap-1350	40	15	of	of	ADP
ap-1350	40	16	generators	generator	NOUN
ap-1350	40	17	of	of	ADP
ap-1350	40	18	u	u	PROPN
ap-1350	40	19	.	.	PUNCT
ap-1350	41	1	let	let	VERB
ap-1350	41	2	a	a	DET
ap-1350	41	3	denote	denote	NOUN
ap-1350	41	4	the	the	DET
ap-1350	41	5	*	*	PUNCT
ap-1350	41	6	-subalgebra	-subalgebra	NOUN
ap-1350	41	7	of	of	ADP
ap-1350	41	8	l+(d	l+(d	PROPN
ap-1350	41	9	)	)	PUNCT
ap-1350	41	10	generated	generate	VERB
ap-1350	41	11	by	by	ADP
ap-1350	41	12	π(x	π(x	ADP
ap-1350	41	13	)	)	PUNCT
ap-1350	41	14	and	and	CCONJ
ap-1350	41	15	the	the	DET
ap-1350	41	16	operators	operator	NOUN
ap-1350	41	17	li	li	PROPN
ap-1350	41	18	,	,	PUNCT
ap-1350	41	19	ri	ri	PROPN
ap-1350	41	20	for	for	ADP
ap-1350	41	21	a	a	DET
ap-1350	41	22	set	set	NOUN
ap-1350	41	23	of	of	ADP
ap-1350	41	24	generators	generator	NOUN
ap-1350	41	25	of	of	ADP
ap-1350	41	26	u	u	PROPN
ap-1350	41	27	.	.	PUNCT
ap-1350	42	1	set	set	VERB
ap-1350	42	2	s(a	s(a	PROPN
ap-1350	42	3	)	)	PUNCT
ap-1350	43	1	:	:	PUNCT
ap-1350	43	2	=	=	X
ap-1350	43	3	{	{	PUNCT
ap-1350	43	4	t	t	PROPN
ap-1350	43	5	∈	∈	PROPN
ap-1350	43	6	l+(d	l+(d	PROPN
ap-1350	43	7	)	)	PUNCT
ap-1350	43	8	;	;	PUNCT
ap-1350	43	9	t̄h	t̄h	PROPN
ap-1350	43	10	⊂	⊂	PROPN
ap-1350	43	11	d	d	PROPN
ap-1350	43	12	,	,	PUNCT
ap-1350	43	13	t̄∗h	t̄∗h	VERB
ap-1350	43	14	⊂	⊂	PROPN
ap-1350	43	15	d	d	X
ap-1350	43	16	,	,	PUNCT
ap-1350	43	17	atb	atb	PROPN
ap-1350	43	18	∈	∈	PROPN
ap-1350	43	19	l1(h	l1(h	PROPN
ap-1350	43	20	)	)	PUNCT
ap-1350	43	21	∀a	∀a	NOUN
ap-1350	43	22	,	,	PUNCT
ap-1350	43	23	b	b	X
ap-1350	43	24	∈	∈	PROPN
ap-1350	43	25	a	a	PRON
ap-1350	43	26	}	}	PUNCT
ap-1350	43	27	,	,	PUNCT
ap-1350	43	28	(	(	PUNCT
ap-1350	43	29	4	4	X
ap-1350	43	30	)	)	PUNCT
ap-1350	43	31	where	where	SCONJ
ap-1350	43	32	the	the	DET
ap-1350	43	33	bar	bar	NOUN
ap-1350	43	34	denotes	denote	VERB
ap-1350	43	35	the	the	DET
ap-1350	43	36	closure	closure	NOUN
ap-1350	43	37	of	of	ADP
ap-1350	43	38	closeable	closeable	ADJ
ap-1350	43	39	operators	operator	NOUN
ap-1350	43	40	on	on	ADP
ap-1350	43	41	d	d	PROPN
ap-1350	43	42	,	,	PUNCT
ap-1350	43	43	and	and	CCONJ
ap-1350	43	44	l1(h	l1(h	X
ap-1350	43	45	)	)	PUNCT
ap-1350	43	46	is	be	AUX
ap-1350	43	47	the	the	DET
ap-1350	43	48	schatten	schatten	ADJ
ap-1350	43	49	class	class	NOUN
ap-1350	43	50	of	of	ADP
ap-1350	43	51	trace	trace	NOUN
ap-1350	43	52	class	class	NOUN
ap-1350	43	53	operators	operator	NOUN
ap-1350	43	54	on	on	ADP
ap-1350	43	55	h.	h.	PROPN
ap-1350	43	56	the	the	DET
ap-1350	43	57	*	*	PUNCT
ap-1350	43	58	-algebra	-algebra	PROPN
ap-1350	43	59	s(a	s(a	NOUN
ap-1350	43	60	)	)	PUNCT
ap-1350	43	61	will	will	AUX
ap-1350	43	62	be	be	AUX
ap-1350	43	63	considered	consider	VERB
ap-1350	43	64	as	as	ADP
ap-1350	43	65	an	an	DET
ap-1350	43	66	algebra	algebra	NOUN
ap-1350	43	67	of	of	ADP
ap-1350	43	68	differentiable	differentiable	ADJ
ap-1350	43	69	functions	function	NOUN
ap-1350	43	70	which	which	PRON
ap-1350	43	71	vanish	vanish	VERB
ap-1350	43	72	sufficiently	sufficiently	ADV
ap-1350	43	73	rapidly	rapidly	ADV
ap-1350	43	74	at	at	ADP
ap-1350	43	75	“	"	PUNCT
ap-1350	43	76	infinity	infinity	NOUN
ap-1350	43	77	”	"	PUNCT
ap-1350	43	78	.	.	PUNCT
ap-1350	44	1	if	if	SCONJ
ap-1350	44	2	the	the	DET
ap-1350	44	3	operators	operator	NOUN
ap-1350	44	4	from	from	ADP
ap-1350	44	5	the	the	DET
ap-1350	44	6	operator	operator	NOUN
ap-1350	44	7	expansion	expansion	NOUN
ap-1350	44	8	satisfy	satisfy	VERB
ap-1350	44	9	convenient	convenient	ADJ
ap-1350	44	10	commutation	commutation	NOUN
ap-1350	44	11	relations	relation	NOUN
ap-1350	44	12	(	(	PUNCT
ap-1350	44	13	but	but	CCONJ
ap-1350	44	14	not	not	PART
ap-1350	44	15	necessarily	necessarily	ADV
ap-1350	44	16	the	the	DET
ap-1350	44	17	defining	define	VERB
ap-1350	44	18	relations	relation	NOUN
ap-1350	44	19	of	of	ADP
ap-1350	44	20	u	u	NOUN
ap-1350	44	21	)	)	PUNCT
ap-1350	44	22	,	,	PUNCT
ap-1350	44	23	then	then	ADV
ap-1350	44	24	the	the	DET
ap-1350	44	25	u	u	NOUN
ap-1350	44	26	-	-	NOUN
ap-1350	44	27	action	action	NOUN
ap-1350	44	28	can	can	AUX
ap-1350	44	29	be	be	AUX
ap-1350	44	30	expanded	expand	VERB
ap-1350	44	31	to	to	ADP
ap-1350	44	32	s(a	s(a	PROPN
ap-1350	44	33	)	)	PUNCT
ap-1350	44	34	.	.	PUNCT
ap-1350	45	1	in	in	ADP
ap-1350	45	2	favorable	favorable	ADJ
ap-1350	45	3	cases	case	NOUN
ap-1350	45	4	,	,	PUNCT
ap-1350	45	5	one	one	PRON
ap-1350	45	6	can	can	AUX
ap-1350	45	7	define	define	VERB
ap-1350	45	8	an	an	DET
ap-1350	45	9	invariant	invariant	ADJ
ap-1350	45	10	integral	integral	NOUN
ap-1350	45	11	by	by	ADP
ap-1350	45	12	a	a	DET
ap-1350	45	13	weighted	weighted	ADJ
ap-1350	45	14	trace	trace	NOUN
ap-1350	45	15	on	on	ADP
ap-1350	45	16	s(a	s(a	PROPN
ap-1350	45	17	)	)	PUNCT
ap-1350	45	18	,	,	PUNCT
ap-1350	45	19	where	where	SCONJ
ap-1350	45	20	the	the	DET
ap-1350	45	21	weight	weight	NOUN
ap-1350	45	22	is	be	AUX
ap-1350	45	23	easily	easily	ADV
ap-1350	45	24	guessed	guess	VERB
ap-1350	45	25	from	from	ADP
ap-1350	45	26	the	the	DET
ap-1350	45	27	operator	operator	NOUN
ap-1350	45	28	expansion	expansion	NOUN
ap-1350	45	29	of	of	ADP
ap-1350	45	30	the	the	DET
ap-1350	45	31	action	action	NOUN
ap-1350	45	32	by	by	ADP
ap-1350	45	33	analogy	analogy	NOUN
ap-1350	45	34	to	to	ADP
ap-1350	45	35	the	the	DET
ap-1350	45	36	well	well	ADV
ap-1350	45	37	-	-	PUNCT
ap-1350	45	38	known	know	VERB
ap-1350	45	39	quantum	quantum	NOUN
ap-1350	45	40	trace	trace	NOUN
ap-1350	45	41	(	(	PUNCT
ap-1350	45	42	see	see	VERB
ap-1350	45	43	[	[	X
ap-1350	45	44	3	3	NUM
ap-1350	45	45	,	,	PUNCT
ap-1350	45	46	5	5	NUM
ap-1350	45	47	]	]	NUM
ap-1350	45	48	)	)	PUNCT
ap-1350	45	49	.	.	PUNCT
ap-1350	46	1	a	a	DET
ap-1350	46	2	hopf	hopf	ADJ
ap-1350	46	3	algebra	algebra	NOUN
ap-1350	46	4	u	u	NOUN
ap-1350	46	5	acts	act	VERB
ap-1350	46	6	always	always	ADV
ap-1350	46	7	on	on	ADP
ap-1350	46	8	itself	itself	PRON
ap-1350	46	9	by	by	ADP
ap-1350	46	10	the	the	DET
ap-1350	46	11	(	(	PUNCT
ap-1350	46	12	left	left	ADJ
ap-1350	46	13	)	)	PUNCT
ap-1350	46	14	adjoint	adjoint	NOUN
ap-1350	46	15	action	action	NOUN
ap-1350	46	16	:	:	PUNCT
ap-1350	46	17	adl(f)(x	adl(f)(x	NUM
ap-1350	46	18	)	)	PUNCT
ap-1350	47	1	:	:	PUNCT
ap-1350	47	2	=	=	PUNCT
ap-1350	47	3	f(1	f(1	PROPN
ap-1350	47	4	)	)	PUNCT
ap-1350	47	5	xs(f(2	xs(f(2	NUM
ap-1350	47	6	)	)	PUNCT
ap-1350	47	7	)	)	PUNCT
ap-1350	47	8	,	,	PUNCT
ap-1350	47	9	f	f	X
ap-1350	47	10	,	,	PUNCT
ap-1350	47	11	x	x	SYM
ap-1350	47	12	∈	∈	PROPN
ap-1350	47	13	u	u	NOUN
ap-1350	47	14	,	,	PUNCT
ap-1350	47	15	(	(	PUNCT
ap-1350	47	16	5	5	NUM
ap-1350	47	17	)	)	PUNCT
ap-1350	47	18	in	in	ADP
ap-1350	47	19	[	[	X
ap-1350	47	20	2	2	NUM
ap-1350	47	21	]	]	PUNCT
ap-1350	47	22	,	,	PUNCT
ap-1350	47	23	l.	l.	PROPN
ap-1350	47	24	i.	i.	PROPN
ap-1350	47	25	korogodsky	korogodsky	PROPN
ap-1350	47	26	defined	define	VERB
ap-1350	47	27	a	a	DET
ap-1350	47	28	quantum	quantum	ADJ
ap-1350	47	29	moment	moment	NOUN
ap-1350	47	30	map	map	NOUN
ap-1350	47	31	as	as	ADP
ap-1350	47	32	a	a	DET
ap-1350	47	33	*	*	PUNCT
ap-1350	47	34	-homomorphism	-homomorphism	PROPN
ap-1350	47	35	ρ	ρ	NOUN
ap-1350	47	36	:	:	PUNCT
ap-1350	47	37	u	u	NOUN
ap-1350	47	38	→	→	PUNCT
ap-1350	47	39	x	x	X
ap-1350	47	40	such	such	ADJ
ap-1350	47	41	that	that	DET
ap-1350	47	42	ρ(adl(f)(x	ρ(adl(f)(x	NOUN
ap-1350	47	43	)	)	PUNCT
ap-1350	47	44	)	)	PUNCT
ap-1350	48	1	=	=	SYM
ap-1350	48	2	f	f	X
ap-1350	48	3	�	�	PROPN
ap-1350	48	4	ρ(x	ρ(x	PROPN
ap-1350	48	5	)	)	PUNCT
ap-1350	48	6	for	for	ADP
ap-1350	48	7	all	all	DET
ap-1350	48	8	f	f	NOUN
ap-1350	48	9	,	,	PUNCT
ap-1350	48	10	x	x	SYM
ap-1350	48	11	∈	∈	PROPN
ap-1350	48	12	u	u	NOUN
ap-1350	48	13	.	.	PUNCT
ap-1350	49	1	then	then	ADV
ap-1350	49	2	any	any	DET
ap-1350	49	3	*	*	PUNCT
ap-1350	49	4	-representation	-representation	PROPN
ap-1350	49	5	π	π	NOUN
ap-1350	49	6	:	:	PUNCT
ap-1350	49	7	x	x	SYM
ap-1350	49	8	→	→	SYM
ap-1350	49	9	l+(d	l+(d	PROPN
ap-1350	49	10	)	)	PUNCT
ap-1350	49	11	leads	lead	VERB
ap-1350	49	12	to	to	ADP
ap-1350	49	13	a	a	DET
ap-1350	49	14	*	*	ADJ
ap-1350	49	15	-representation	-representation	PROPN
ap-1350	49	16	π	π	PROPN
ap-1350	49	17	◦	◦	NOUN
ap-1350	49	18	ρ	ρ	X
ap-1350	49	19	:	:	PUNCT
ap-1350	49	20	u	u	PROPN
ap-1350	49	21	→	→	SYM
ap-1350	49	22	l+(d	l+(d	PROPN
ap-1350	49	23	)	)	PUNCT
ap-1350	49	24	,	,	PUNCT
ap-1350	49	25	and	and	CCONJ
ap-1350	49	26	it	it	PRON
ap-1350	49	27	follows	follow	VERB
ap-1350	49	28	easily	easily	ADV
ap-1350	49	29	from	from	ADP
ap-1350	49	30	the	the	DET
ap-1350	49	31	hopf	hopf	ADJ
ap-1350	49	32	algebra	algebra	NOUN
ap-1350	49	33	structure	structure	NOUN
ap-1350	49	34	of	of	ADP
ap-1350	49	35	u	u	PRON
ap-1350	49	36	that	that	DET
ap-1350	49	37	adl(f)(x	adl(f)(x	NOUN
ap-1350	49	38	)	)	PUNCT
ap-1350	49	39	:	:	PUNCT
ap-1350	50	1	=	=	PUNCT
ap-1350	50	2	π(ρ(f(1)))x	π(ρ(f(1)))x	NOUN
ap-1350	50	3	π(ρ(s(f(2	π(ρ(s(f(2	ADJ
ap-1350	50	4	)	)	PUNCT
ap-1350	50	5	)	)	PUNCT
ap-1350	50	6	)	)	PUNCT
ap-1350	50	7	)	)	PUNCT
ap-1350	50	8	,	,	PUNCT
ap-1350	50	9	f	f	PROPN
ap-1350	50	10	∈	∈	PROPN
ap-1350	50	11	u	u	PROPN
ap-1350	50	12	,	,	PUNCT
ap-1350	50	13	x	x	PROPN
ap-1350	50	14	∈	∈	PROPN
ap-1350	50	15	l+(d	l+(d	PROPN
ap-1350	50	16	)	)	PUNCT
ap-1350	50	17	,	,	PUNCT
ap-1350	50	18	(	(	PUNCT
ap-1350	50	19	6	6	X
ap-1350	50	20	)	)	PUNCT
ap-1350	50	21	defines	define	VERB
ap-1350	50	22	a	a	DET
ap-1350	50	23	left	left	ADJ
ap-1350	50	24	u	u	NOUN
ap-1350	50	25	-	-	NOUN
ap-1350	50	26	action	action	NOUN
ap-1350	50	27	on	on	ADP
ap-1350	50	28	l+(d	l+(d	PROPN
ap-1350	50	29	)	)	PUNCT
ap-1350	50	30	turning	turn	VERB
ap-1350	50	31	it	it	PRON
ap-1350	50	32	into	into	ADP
ap-1350	50	33	a	a	DET
ap-1350	50	34	umodule	umodule	NOUN
ap-1350	50	35	*	*	PUNCT
ap-1350	50	36	-algebra	-algebra	NOUN
ap-1350	50	37	.	.	PUNCT
ap-1350	51	1	moreover	moreover	ADV
ap-1350	51	2	,	,	PUNCT
ap-1350	51	3	the	the	DET
ap-1350	51	4	algebra	algebra	PROPN
ap-1350	51	5	s(a	s(a	PROPN
ap-1350	51	6	)	)	PUNCT
ap-1350	51	7	is	be	AUX
ap-1350	51	8	invariant	invariant	ADJ
ap-1350	51	9	under	under	ADP
ap-1350	51	10	this	this	DET
ap-1350	51	11	action	action	NOUN
ap-1350	51	12	.	.	PUNCT
ap-1350	52	1	suppose	suppose	VERB
ap-1350	52	2	furthermore	furthermore	ADV
ap-1350	52	3	that	that	SCONJ
ap-1350	52	4	u	u	PROPN
ap-1350	52	5	denotes	denote	VERB
ap-1350	52	6	the	the	DET
ap-1350	52	7	quantized	quantize	VERB
ap-1350	52	8	universal	universal	ADJ
ap-1350	52	9	enveloping	enveloping	NOUN
ap-1350	52	10	algebra	algebra	NOUN
ap-1350	52	11	of	of	ADP
ap-1350	52	12	a	a	DET
ap-1350	52	13	semisimple	semisimple	ADJ
ap-1350	52	14	lie	lie	NOUN
ap-1350	52	15	algebra	algebra	NOUN
ap-1350	52	16	.	.	PUNCT
ap-1350	53	1	then	then	ADV
ap-1350	53	2	there	there	PRON
ap-1350	53	3	exists	exist	VERB
ap-1350	53	4	a	a	DET
ap-1350	53	5	distinguished	distinguished	ADJ
ap-1350	53	6	element	element	NOUN
ap-1350	53	7	γ	γ	NOUN
ap-1350	53	8	in	in	ADP
ap-1350	53	9	u	u	PRON
ap-1350	53	10	such	such	ADJ
ap-1350	53	11	that	that	SCONJ
ap-1350	53	12	γf	γf	PROPN
ap-1350	53	13	=	=	PUNCT
ap-1350	53	14	s2(f)γ	s2(f)γ	NOUN
ap-1350	53	15	for	for	ADP
ap-1350	53	16	all	all	PRON
ap-1350	53	17	f	f	PROPN
ap-1350	53	18	∈	∈	PROPN
ap-1350	53	19	u	u	NOUN
ap-1350	53	20	.	.	PUNCT
ap-1350	54	1	by	by	ADP
ap-1350	54	2	the	the	DET
ap-1350	54	3	definition	definition	NOUN
ap-1350	54	4	of	of	ADP
ap-1350	54	5	s(a	s(a	PROPN
ap-1350	54	6	)	)	PUNCT
ap-1350	54	7	,	,	PUNCT
ap-1350	54	8	the	the	DET
ap-1350	54	9	traces	trace	NOUN
ap-1350	54	10	tr(π(ρ(γ))f	tr(π(ρ(γ))f	NOUN
ap-1350	54	11	)	)	PUNCT
ap-1350	54	12	are	be	AUX
ap-1350	54	13	well	well	ADV
ap-1350	54	14	-	-	PUNCT
ap-1350	54	15	defined	define	VERB
ap-1350	54	16	and	and	CCONJ
ap-1350	54	17	we	we	PRON
ap-1350	54	18	can	can	AUX
ap-1350	54	19	state	state	VERB
ap-1350	54	20	the	the	DET
ap-1350	54	21	following	following	NOUN
ap-1350	54	22	theorem	theorem	NOUN
ap-1350	54	23	:	:	PUNCT
ap-1350	54	24	theorem	theorem	ADJ
ap-1350	54	25	1	1	NUM
ap-1350	54	26	let	let	VERB
ap-1350	54	27	ρ	ρ	NOUN
ap-1350	54	28	:	:	PUNCT
ap-1350	54	29	u	u	NOUN
ap-1350	54	30	→	→	PUNCT
ap-1350	54	31	x	x	PART
ap-1350	54	32	be	be	AUX
ap-1350	54	33	a	a	DET
ap-1350	54	34	quantum	quantum	ADJ
ap-1350	54	35	moment	moment	NOUN
ap-1350	54	36	map	map	NOUN
ap-1350	54	37	and	and	CCONJ
ap-1350	54	38	π	π	X
ap-1350	54	39	:	:	PUNCT
ap-1350	54	40	x	x	SYM
ap-1350	54	41	→	→	SYM
ap-1350	54	42	l+(d	l+(d	PROPN
ap-1350	54	43	)	)	PUNCT
ap-1350	54	44	a	a	DET
ap-1350	54	45	*	*	PUNCT
ap-1350	54	46	-representation	-representation	NOUN
ap-1350	54	47	such	such	ADJ
ap-1350	54	48	that	that	DET
ap-1350	54	49	±π(ρ(γ	±π(ρ(γ	NOUN
ap-1350	54	50	)	)	PUNCT
ap-1350	54	51	)	)	PUNCT
ap-1350	55	1	is	be	AUX
ap-1350	55	2	a	a	DET
ap-1350	55	3	non	non	ADJ
ap-1350	55	4	-	-	ADJ
ap-1350	55	5	negative	negative	ADJ
ap-1350	55	6	selfadjoint	selfadjoint	NOUN
ap-1350	55	7	operator	operator	NOUN
ap-1350	55	8	.	.	PUNCT
ap-1350	56	1	then	then	ADV
ap-1350	56	2	h(f	h(f	ADV
ap-1350	56	3	)	)	PUNCT
ap-1350	56	4	:	:	PUNCT
ap-1350	57	1	=	=	X
ap-1350	57	2	±tr(π(ρ(γ))f	±tr(π(ρ(γ))f	PROPN
ap-1350	57	3	)	)	PUNCT
ap-1350	57	4	,	,	PUNCT
ap-1350	57	5	f	f	PROPN
ap-1350	57	6	∈	∈	PROPN
ap-1350	57	7	s(a	s(a	PROPN
ap-1350	57	8	)	)	PUNCT
ap-1350	57	9	,	,	PUNCT
ap-1350	57	10	(	(	PUNCT
ap-1350	57	11	7	7	X
ap-1350	57	12	)	)	PUNCT
ap-1350	57	13	defines	define	VERB
ap-1350	57	14	an	an	DET
ap-1350	57	15	invariant	invariant	ADJ
ap-1350	57	16	integral	integral	NOUN
ap-1350	57	17	on	on	ADP
ap-1350	57	18	the	the	DET
ap-1350	57	19	u	u	NOUN
ap-1350	57	20	-	-	NOUN
ap-1350	57	21	module	module	NOUN
ap-1350	57	22	*	*	PUNCT
ap-1350	57	23	-algebra	-algebra	NOUN
ap-1350	57	24	s(a	s(a	NOUN
ap-1350	57	25	)	)	PUNCT
ap-1350	57	26	.	.	PUNCT
ap-1350	58	1	proof	proof	NOUN
ap-1350	58	2	.	.	PUNCT
ap-1350	59	1	the	the	DET
ap-1350	59	2	invariance	invariance	NOUN
ap-1350	59	3	of	of	ADP
ap-1350	59	4	h	h	NOUN
ap-1350	59	5	follows	follow	VERB
ap-1350	59	6	from	from	ADP
ap-1350	59	7	the	the	DET
ap-1350	59	8	same	same	ADJ
ap-1350	59	9	formulas	formula	NOUN
ap-1350	59	10	as	as	ADP
ap-1350	59	11	in	in	ADP
ap-1350	59	12	the	the	DET
ap-1350	59	13	proof	proof	NOUN
ap-1350	59	14	of	of	ADP
ap-1350	59	15	the	the	DET
ap-1350	59	16	invariance	invariance	NOUN
ap-1350	59	17	of	of	ADP
ap-1350	59	18	the	the	DET
ap-1350	59	19	quantum	quantum	ADJ
ap-1350	59	20	trace	trace	NOUN
ap-1350	59	21	in	in	ADP
ap-1350	59	22	[	[	X
ap-1350	59	23	1	1	NUM
ap-1350	59	24	,	,	PUNCT
ap-1350	59	25	section	section	NOUN
ap-1350	59	26	7.1.6	7.1.6	PROPN
ap-1350	59	27	]	]	PUNCT
ap-1350	59	28	by	by	ADP
ap-1350	59	29	applying	apply	VERB
ap-1350	59	30	the	the	DET
ap-1350	59	31	trace	trace	NOUN
ap-1350	59	32	property	property	NOUN
ap-1350	59	33	tr(af	tr(af	PROPN
ap-1350	59	34	)	)	PUNCT
ap-1350	59	35	=	=	SYM
ap-1350	59	36	tr(fa	tr(fa	PROPN
ap-1350	59	37	)	)	PUNCT
ap-1350	59	38	which	which	PRON
ap-1350	59	39	continues	continue	VERB
ap-1350	59	40	to	to	PART
ap-1350	59	41	hold	hold	VERB
ap-1350	59	42	for	for	ADP
ap-1350	59	43	all	all	DET
ap-1350	59	44	f	f	PROPN
ap-1350	59	45	∈	∈	PROPN
ap-1350	59	46	s(a	s(a	PROPN
ap-1350	59	47	)	)	PUNCT
ap-1350	59	48	and	and	CCONJ
ap-1350	59	49	a	a	DET
ap-1350	59	50	∈	∈	PROPN
ap-1350	59	51	a	a	PRON
ap-1350	59	52	,	,	PUNCT
ap-1350	59	53	see	see	VERB
ap-1350	59	54	[	[	X
ap-1350	59	55	3	3	NUM
ap-1350	59	56	]	]	PUNCT
ap-1350	59	57	.	.	PUNCT
ap-1350	60	1	�	�	PROPN
ap-1350	60	2	3	3	NUM
ap-1350	60	3	example	example	NOUN
ap-1350	60	4	:	:	PUNCT
ap-1350	60	5	a	a	DET
ap-1350	60	6	quantum	quantum	ADJ
ap-1350	60	7	hyperboloid	hyperboloid	NOUN
ap-1350	60	8	let	let	VERB
ap-1350	60	9	q	q	PROPN
ap-1350	60	10	∈	∈	PROPN
ap-1350	60	11	(	(	PUNCT
ap-1350	60	12	0	0	NUM
ap-1350	60	13	,	,	PUNCT
ap-1350	60	14	1	1	NUM
ap-1350	60	15	)	)	PUNCT
ap-1350	60	16	and	and	CCONJ
ap-1350	60	17	s	s	NOUN
ap-1350	60	18	∈	∈	PROPN
ap-1350	61	1	[	[	X
ap-1350	61	2	−1	−1	NOUN
ap-1350	61	3	,	,	PUNCT
ap-1350	61	4	1	1	NUM
ap-1350	61	5	)	)	PUNCT
ap-1350	61	6	.	.	PUNCT
ap-1350	62	1	following	follow	VERB
ap-1350	62	2	[	[	X
ap-1350	62	3	2	2	NUM
ap-1350	62	4	]	]	PUNCT
ap-1350	62	5	,	,	PUNCT
ap-1350	62	6	we	we	PRON
ap-1350	62	7	define	define	VERB
ap-1350	62	8	the	the	DET
ap-1350	62	9	two	two	NUM
ap-1350	62	10	-	-	PUNCT
ap-1350	62	11	sheet	sheet	NOUN
ap-1350	62	12	quantum	quantum	ADJ
ap-1350	62	13	hyperboloid	hyperboloid	NOUN
ap-1350	62	14	x	x	X
ap-1350	62	15	:	:	PUNCT
ap-1350	62	16	=	=	NOUN
ap-1350	62	17	oq(xs,1	oq(xs,1	ADJ
ap-1350	62	18	)	)	PUNCT
ap-1350	62	19	(	(	PUNCT
ap-1350	62	20	after	after	ADP
ap-1350	62	21	a	a	DET
ap-1350	62	22	slight	slight	ADJ
ap-1350	62	23	reparametrization	reparametrization	NOUN
ap-1350	62	24	)	)	PUNCT
ap-1350	62	25	as	as	ADP
ap-1350	62	26	the	the	DET
ap-1350	62	27	*	*	PUNCT
ap-1350	62	28	-algebra	-algebra	NOUN
ap-1350	62	29	generated	generate	VERB
ap-1350	62	30	by	by	ADP
ap-1350	62	31	y	y	PROPN
ap-1350	62	32	,	,	PUNCT
ap-1350	62	33	y∗	y∗	ADV
ap-1350	62	34	and	and	CCONJ
ap-1350	62	35	x	x	SYM
ap-1350	62	36	=	=	PUNCT
ap-1350	62	37	x∗	x∗	PROPN
ap-1350	62	38	with	with	ADP
ap-1350	62	39	commutation	commutation	NOUN
ap-1350	62	40	relations	relation	NOUN
ap-1350	62	41	yx	yx	NOUN
ap-1350	62	42	=	=	PUNCT
ap-1350	62	43	q2xy	q2xy	PROPN
ap-1350	62	44	,	,	PUNCT
ap-1350	62	45	xy∗	xy∗	PUNCT
ap-1350	62	46	=	=	SYM
ap-1350	62	47	q2y∗x	q2y∗x	PROPN
ap-1350	62	48	,	,	PUNCT
ap-1350	62	49	y∗y	y∗y	PUNCT
ap-1350	62	50	=	=	SYM
ap-1350	62	51	(	(	PUNCT
ap-1350	62	52	q−2x	q−2x	NOUN
ap-1350	62	53	−	−	PROPN
ap-1350	62	54	s)(q−2x−	s)(q−2x−	NOUN
ap-1350	62	55	1	1	NUM
ap-1350	62	56	)	)	PUNCT
ap-1350	62	57	,	,	PUNCT
ap-1350	62	58	yy∗	yy∗	NOUN
ap-1350	62	59	=	=	PUNCT
ap-1350	62	60	(	(	PUNCT
ap-1350	62	61	x	x	SYM
ap-1350	62	62	−	−	PROPN
ap-1350	62	63	s)(x	s)(x	PROPN
ap-1350	62	64	−	−	PROPN
ap-1350	62	65	1	1	NUM
ap-1350	62	66	)	)	PUNCT
ap-1350	62	67	.	.	PUNCT
ap-1350	63	1	the	the	DET
ap-1350	63	2	hopf	hopf	ADJ
ap-1350	63	3	*	*	PUNCT
ap-1350	63	4	-algebra	-algebra	NOUN
ap-1350	63	5	u	u	NOUN
ap-1350	63	6	:	:	PUNCT
ap-1350	63	7	=	=	SYM
ap-1350	63	8	uq(su1,1	uq(su1,1	X
ap-1350	63	9	)	)	PUNCT
ap-1350	63	10	is	be	AUX
ap-1350	63	11	generated	generate	VERB
ap-1350	63	12	by	by	ADP
ap-1350	63	13	e	e	PROPN
ap-1350	63	14	,	,	PUNCT
ap-1350	63	15	f	f	PROPN
ap-1350	63	16	,	,	PUNCT
ap-1350	63	17	k	k	PROPN
ap-1350	63	18	and	and	CCONJ
ap-1350	63	19	its	its	PRON
ap-1350	63	20	inverse	inverse	NOUN
ap-1350	63	21	k−1	k−1	PROPN
ap-1350	63	22	with	with	ADP
ap-1350	63	23	relations	relation	NOUN
ap-1350	63	24	ke	ke	NOUN
ap-1350	63	25	=	=	PUNCT
ap-1350	63	26	q2ek	q2ek	X
ap-1350	63	27	,	,	PUNCT
ap-1350	63	28	fk	fk	INTJ
ap-1350	63	29	=	=	PUNCT
ap-1350	63	30	q2kf	q2kf	X
ap-1350	63	31	,	,	PUNCT
ap-1350	63	32	ef	ef	PROPN
ap-1350	63	33	−	−	PROPN
ap-1350	63	34	fe	fe	X
ap-1350	63	35	=	=	PUNCT
ap-1350	63	36	(	(	PUNCT
ap-1350	63	37	q	q	X
ap-1350	63	38	−	−	PROPN
ap-1350	63	39	q−1)−1(k	q−1)−1(k	NOUN
ap-1350	63	40	−k−1	−k−1	NUM
ap-1350	63	41	)	)	PUNCT
ap-1350	63	42	,	,	PUNCT
ap-1350	63	43	with	with	ADP
ap-1350	63	44	hopf	hopf	ADJ
ap-1350	63	45	structure	structure	NOUN
ap-1350	63	46	δ(e	δ(e	ADV
ap-1350	63	47	)	)	PUNCT
ap-1350	63	48	=	=	SYM
ap-1350	64	1	e	e	X
ap-1350	64	2	⊗	⊗	NOUN
ap-1350	64	3	1	1	NUM
ap-1350	64	4	+	+	NOUN
ap-1350	64	5	k	k	PROPN
ap-1350	64	6	⊗	⊗	PROPN
ap-1350	64	7	e	e	PROPN
ap-1350	64	8	,	,	PUNCT
ap-1350	64	9	δ(f	δ(f	PROPN
ap-1350	64	10	)	)	PUNCT
ap-1350	65	1	=	=	PUNCT
ap-1350	65	2	f	f	X
ap-1350	65	3	⊗k−1	⊗k−1	NUM
ap-1350	66	1	+	+	X
ap-1350	66	2	1⊗	1⊗	NUM
ap-1350	66	3	f	f	NOUN
ap-1350	66	4	,	,	PUNCT
ap-1350	66	5	δ(k	δ(k	NOUN
ap-1350	66	6	)	)	PUNCT
ap-1350	66	7	=	=	SYM
ap-1350	67	1	k	k	NOUN
ap-1350	67	2	⊗k	⊗k	NOUN
ap-1350	67	3	,	,	PUNCT
ap-1350	67	4	ε(e	ε(e	X
ap-1350	67	5	)	)	PUNCT
ap-1350	67	6	=	=	SYM
ap-1350	67	7	ε(f	ε(f	PROPN
ap-1350	67	8	)	)	PUNCT
ap-1350	67	9	=	=	SYM
ap-1350	67	10	0	0	NUM
ap-1350	67	11	,	,	PUNCT
ap-1350	67	12	ε(k	ε(k	PROPN
ap-1350	67	13	)	)	PUNCT
ap-1350	67	14	=	=	SYM
ap-1350	67	15	1	1	NUM
ap-1350	67	16	,	,	PUNCT
ap-1350	67	17	s(e	s(e	PROPN
ap-1350	67	18	)	)	PUNCT
ap-1350	67	19	=	=	PUNCT
ap-1350	67	20	−k−1e	−k−1e	NOUN
ap-1350	67	21	,	,	PUNCT
ap-1350	67	22	s(f	s(f	PROPN
ap-1350	67	23	)	)	PUNCT
ap-1350	68	1	=	=	SYM
ap-1350	68	2	−fk	−fk	NOUN
ap-1350	68	3	,	,	PUNCT
ap-1350	68	4	s(k	s(k	ADV
ap-1350	68	5	)	)	PUNCT
ap-1350	68	6	=	=	SYM
ap-1350	68	7	k−1	k−1	PROPN
ap-1350	68	8	,	,	PUNCT
ap-1350	68	9	and	and	CCONJ
ap-1350	68	10	with	with	ADP
ap-1350	68	11	involution	involution	NOUN
ap-1350	68	12	k∗	k∗	NOUN
ap-1350	68	13	=	=	SYM
ap-1350	68	14	k	k	PROPN
ap-1350	68	15	,	,	PUNCT
ap-1350	68	16	e∗	e∗	PROPN
ap-1350	68	17	=	=	SYM
ap-1350	68	18	−kf	−kf	PROPN
ap-1350	68	19	.	.	PUNCT
ap-1350	69	1	the	the	DET
ap-1350	69	2	quantum	quantum	ADJ
ap-1350	69	3	hyperboloid	hyperboloid	NOUN
ap-1350	69	4	x	x	X
ap-1350	69	5	becomes	become	VERB
ap-1350	69	6	a	a	DET
ap-1350	69	7	u	u	NOUN
ap-1350	69	8	-	-	NOUN
ap-1350	69	9	module	module	NOUN
ap-1350	69	10	*	*	PUNCT
ap-1350	69	11	-algebra	-algebra	NOUN
ap-1350	69	12	with	with	ADP
ap-1350	69	13	the	the	DET
ap-1350	69	14	action	action	NOUN
ap-1350	69	15	defined	define	VERB
ap-1350	69	16	by	by	ADP
ap-1350	69	17	k	k	PROPN
ap-1350	69	18	�	�	PROPN
ap-1350	69	19	y	y	PROPN
ap-1350	69	20	=	=	SYM
ap-1350	69	21	q2y	q2y	PROPN
ap-1350	69	22	,	,	PUNCT
ap-1350	69	23	e	e	X
ap-1350	69	24	�	�	PROPN
ap-1350	69	25	y	y	PROPN
ap-1350	69	26	=	=	SYM
ap-1350	69	27	0	0	PROPN
ap-1350	69	28	,	,	PUNCT
ap-1350	69	29	f	f	PROPN
ap-1350	69	30	�	�	PROPN
ap-1350	69	31	y	y	PROPN
ap-1350	69	32	=	=	PROPN
ap-1350	69	33	q1/2((1	q1/2((1	PROPN
ap-1350	69	34	+	+	CCONJ
ap-1350	69	35	q−2)x	q−2)x	NOUN
ap-1350	69	36	−	−	PROPN
ap-1350	69	37	(	(	PUNCT
ap-1350	69	38	1	1	NUM
ap-1350	69	39	+	+	NUM
ap-1350	69	40	s	s	NOUN
ap-1350	69	41	)	)	PUNCT
ap-1350	69	42	)	)	PUNCT
ap-1350	69	43	,	,	PUNCT
ap-1350	69	44	k	k	PROPN
ap-1350	69	45	�	�	PROPN
ap-1350	69	46	x	x	PUNCT
ap-1350	69	47	=	=	SYM
ap-1350	69	48	x	x	NOUN
ap-1350	69	49	,	,	PUNCT
ap-1350	69	50	e	e	X
ap-1350	69	51	�	�	PROPN
ap-1350	69	52	x	x	X
ap-1350	69	53	=	=	SYM
ap-1350	69	54	q1/2y	q1/2y	PROPN
ap-1350	69	55	,	,	PUNCT
ap-1350	69	56	f	f	PROPN
ap-1350	69	57	�	�	PROPN
ap-1350	69	58	x	x	PUNCT
ap-1350	69	59	=	=	SYM
ap-1350	69	60	q5/2y∗	q5/2y∗	PROPN
ap-1350	69	61	,	,	PUNCT
ap-1350	69	62	k	k	PROPN
ap-1350	69	63	�	�	PROPN
ap-1350	69	64	y∗	y∗	PROPN
ap-1350	69	65	=	=	SYM
ap-1350	69	66	q−2y∗	q−2y∗	PROPN
ap-1350	69	67	,	,	PUNCT
ap-1350	69	68	e	e	X
ap-1350	69	69	�	�	PROPN
ap-1350	69	70	y∗	y∗	PROPN
ap-1350	69	71	=	=	PRON
ap-1350	69	72	q−3/2((1	q−3/2((1	NOUN
ap-1350	69	73	+	+	CCONJ
ap-1350	69	74	q−2)x	q−2)x	NOUN
ap-1350	69	75	−	−	PROPN
ap-1350	69	76	(	(	PUNCT
ap-1350	69	77	1	1	NUM
ap-1350	69	78	+	+	NUM
ap-1350	69	79	s	s	NOUN
ap-1350	69	80	)	)	PUNCT
ap-1350	69	81	)	)	PUNCT
ap-1350	69	82	,	,	PUNCT
ap-1350	69	83	f	f	PROPN
ap-1350	69	84	�	�	PROPN
ap-1350	69	85	y∗	y∗	PROPN
ap-1350	69	86	=	=	SYM
ap-1350	69	87	0	0	NUM
ap-1350	69	88	.	.	NUM
ap-1350	69	89	30	30	NUM
ap-1350	69	90	acta	acta	PROPN
ap-1350	69	91	polytechnica	polytechnica	PROPN
ap-1350	69	92	vol	vol	NOUN
ap-1350	69	93	.	.	PUNCT
ap-1350	70	1	51	51	NUM
ap-1350	70	2	no	no	NOUN
ap-1350	70	3	.	.	PUNCT
ap-1350	71	1	1/2011	1/2011	NUM
ap-1350	71	2	let	let	VERB
ap-1350	71	3	i	i	PRON
ap-1350	71	4	be	be	AUX
ap-1350	71	5	an	an	DET
ap-1350	71	6	at	at	ADP
ap-1350	71	7	most	most	ADV
ap-1350	71	8	countable	countable	ADJ
ap-1350	71	9	index	index	NOUN
ap-1350	71	10	set	set	NOUN
ap-1350	71	11	,	,	PUNCT
ap-1350	71	12	h0	h0	VERB
ap-1350	71	13	a	a	DET
ap-1350	71	14	hilbert	hilbert	NOUN
ap-1350	71	15	space	space	NOUN
ap-1350	71	16	,	,	PUNCT
ap-1350	71	17	and	and	CCONJ
ap-1350	71	18	h	h	NOUN
ap-1350	71	19	=	=	PROPN
ap-1350	71	20	⊕	⊕	PROPN
ap-1350	71	21	i∈i	i∈i	PROPN
ap-1350	71	22	h0	h0	PROPN
ap-1350	71	23	.	.	PUNCT
ap-1350	72	1	we	we	PRON
ap-1350	72	2	denote	denote	VERB
ap-1350	72	3	by	by	ADP
ap-1350	72	4	ηi	ηi	PROPN
ap-1350	72	5	the	the	DET
ap-1350	72	6	vector	vector	NOUN
ap-1350	72	7	of	of	ADP
ap-1350	72	8	h	h	PRON
ap-1350	72	9	which	which	PRON
ap-1350	72	10	has	have	VERB
ap-1350	72	11	the	the	DET
ap-1350	72	12	element	element	PROPN
ap-1350	72	13	η	η	PROPN
ap-1350	72	14	∈	∈	PROPN
ap-1350	72	15	h0	h0	NOUN
ap-1350	72	16	as	as	ADP
ap-1350	72	17	its	its	PRON
ap-1350	72	18	i	i	PROPN
ap-1350	72	19	-	-	PUNCT
ap-1350	72	20	th	th	VERB
ap-1350	72	21	component	component	NOUN
ap-1350	72	22	and	and	CCONJ
ap-1350	72	23	zero	zero	NUM
ap-1350	72	24	otherwise	otherwise	ADV
ap-1350	72	25	.	.	PUNCT
ap-1350	73	1	it	it	PRON
ap-1350	73	2	is	be	AUX
ap-1350	73	3	understood	understand	VERB
ap-1350	73	4	that	that	SCONJ
ap-1350	73	5	ηi	ηi	NOUN
ap-1350	73	6	=	=	SYM
ap-1350	73	7	0	0	NUM
ap-1350	73	8	whenever	whenever	SCONJ
ap-1350	73	9	i	i	PRON
ap-1350	73	10	/∈	/∈	PUNCT
ap-1350	73	11	i.	i.	PROPN
ap-1350	73	12	let	let	VERB
ap-1350	73	13	u	u	PRON
ap-1350	73	14	be	be	AUX
ap-1350	73	15	a	a	DET
ap-1350	73	16	unitary	unitary	ADJ
ap-1350	73	17	operator	operator	NOUN
ap-1350	73	18	on	on	ADP
ap-1350	73	19	h0	h0	PROPN
ap-1350	73	20	,	,	PUNCT
ap-1350	73	21	and	and	CCONJ
ap-1350	73	22	let	let	VERB
ap-1350	73	23	a	a	PRON
ap-1350	73	24	and	and	CCONJ
ap-1350	73	25	b	b	NOUN
ap-1350	73	26	be	be	AUX
ap-1350	73	27	selfadjoint	selfadjoint	NOUN
ap-1350	73	28	operators	operator	NOUN
ap-1350	73	29	on	on	ADP
ap-1350	73	30	the	the	DET
ap-1350	73	31	hilbert	hilbert	PROPN
ap-1350	73	32	space	space	NOUN
ap-1350	73	33	h0	h0	PROPN
ap-1350	73	34	such	such	ADJ
ap-1350	73	35	that	that	DET
ap-1350	73	36	spec	spec	PROPN
ap-1350	73	37	(	(	PUNCT
ap-1350	73	38	a	a	X
ap-1350	73	39	)	)	PUNCT
ap-1350	73	40	⊂	⊂	PROPN
ap-1350	74	1	[	[	X
ap-1350	74	2	q2	q2	NOUN
ap-1350	74	3	,	,	PUNCT
ap-1350	74	4	1	1	NUM
ap-1350	74	5	]	]	PUNCT
ap-1350	74	6	,	,	PUNCT
ap-1350	74	7	spec	spec	PROPN
ap-1350	74	8	(	(	PUNCT
ap-1350	74	9	b	b	NOUN
ap-1350	74	10	)	)	PUNCT
ap-1350	74	11	⊂	⊂	PROPN
ap-1350	75	1	[	[	X
ap-1350	75	2	q2	q2	NOUN
ap-1350	75	3	,	,	PUNCT
ap-1350	75	4	s	s	PART
ap-1350	75	5	]	]	X
ap-1350	75	6	,	,	PUNCT
ap-1350	75	7	q2	q2	PROPN
ap-1350	75	8	is	be	AUX
ap-1350	75	9	not	not	PART
ap-1350	75	10	an	an	DET
ap-1350	75	11	eigenvalue	eigenvalue	NOUN
ap-1350	75	12	of	of	ADP
ap-1350	75	13	a	a	PRON
ap-1350	75	14	and	and	CCONJ
ap-1350	75	15	b	b	NOUN
ap-1350	75	16	,	,	PUNCT
ap-1350	75	17	and	and	CCONJ
ap-1350	75	18	s	s	VERB
ap-1350	75	19	is	be	AUX
ap-1350	75	20	not	not	PART
ap-1350	75	21	an	an	DET
ap-1350	75	22	eigenvalue	eigenvalue	NOUN
ap-1350	75	23	of	of	ADP
ap-1350	75	24	b.	b.	PROPN
ap-1350	75	25	set	set	VERB
ap-1350	75	26	λn	λn	NOUN
ap-1350	75	27	:	:	PUNCT
ap-1350	75	28	=	=	SYM
ap-1350	75	29	√	√	INTJ
ap-1350	75	30	(	(	PUNCT
ap-1350	75	31	q2n	q2n	ADV
ap-1350	75	32	−	−	PROPN
ap-1350	75	33	s)(q2n	s)(q2n	NUM
ap-1350	75	34	−	−	NOUN
ap-1350	75	35	1	1	NUM
ap-1350	75	36	)	)	PUNCT
ap-1350	75	37	and	and	CCONJ
ap-1350	75	38	λn(t	λn(t	NUM
ap-1350	75	39	)	)	PUNCT
ap-1350	75	40	:	:	PUNCT
ap-1350	76	1	=	=	X
ap-1350	76	2	√	√	INTJ
ap-1350	76	3	(	(	PUNCT
ap-1350	76	4	q2nt	q2nt	NOUN
ap-1350	76	5	−	−	PROPN
ap-1350	76	6	s)(q2nt	s)(q2nt	NOUN
ap-1350	76	7	−	−	NOUN
ap-1350	76	8	1	1	NUM
ap-1350	76	9	)	)	PUNCT
ap-1350	76	10	.	.	PUNCT
ap-1350	77	1	then	then	ADV
ap-1350	77	2	a	a	DET
ap-1350	77	3	list	list	NOUN
ap-1350	77	4	of	of	ADP
ap-1350	77	5	non	non	ADJ
ap-1350	77	6	-	-	ADJ
ap-1350	77	7	equivalent	equivalent	ADJ
ap-1350	77	8	*	*	PUNCT
ap-1350	77	9	-representations	-representation	NOUN
ap-1350	77	10	of	of	ADP
ap-1350	77	11	x	x	PRON
ap-1350	77	12	is	be	AUX
ap-1350	77	13	given	give	VERB
ap-1350	77	14	by	by	ADP
ap-1350	77	15	the	the	DET
ap-1350	77	16	following	follow	VERB
ap-1350	77	17	formulas	formula	NOUN
ap-1350	77	18	(	(	PUNCT
ap-1350	77	19	suppressing	suppress	VERB
ap-1350	77	20	the	the	DET
ap-1350	77	21	letter	letter	NOUN
ap-1350	77	22	π	π	PROPN
ap-1350	77	23	of	of	ADP
ap-1350	77	24	the	the	DET
ap-1350	77	25	representation	representation	NOUN
ap-1350	77	26	)	)	PUNCT
ap-1350	77	27	.	.	PUNCT
ap-1350	78	1	s	s	PART
ap-1350	79	1	∈	∈	PROPN
ap-1350	80	1	[	[	X
ap-1350	80	2	−1	−1	NOUN
ap-1350	80	3	,	,	PUNCT
ap-1350	80	4	1	1	NUM
ap-1350	80	5	)	)	PUNCT
ap-1350	80	6	:	:	PUNCT
ap-1350	80	7	xηn	xηn	PROPN
ap-1350	80	8	=	=	SYM
ap-1350	80	9	q−2nηn	q−2nηn	PROPN
ap-1350	80	10	,	,	PUNCT
ap-1350	80	11	yηn	yηn	PROPN
ap-1350	80	12	=	=	SYM
ap-1350	80	13	λ−(n+1)ηn+1	λ−(n+1)ηn+1	PROPN
ap-1350	80	14	on	on	ADP
ap-1350	80	15	h	h	NOUN
ap-1350	80	16	=	=	PROPN
ap-1350	80	17	⊕	⊕	PROPN
ap-1350	80	18	n∈n0	n∈n0	NOUN
ap-1350	80	19	h0	h0	PROPN
ap-1350	80	20	.	.	PUNCT
ap-1350	80	21	s	s	PART
ap-1350	80	22	∈	∈	PROPN
ap-1350	81	1	[	[	X
ap-1350	81	2	0	0	NUM
ap-1350	81	3	,	,	PUNCT
ap-1350	81	4	1	1	NUM
ap-1350	81	5	)	)	PUNCT
ap-1350	81	6	:	:	PUNCT
ap-1350	81	7	xηn	xηn	PROPN
ap-1350	81	8	=	=	SYM
ap-1350	82	1	−q2(n+1)aηn	−q2(n+1)aηn	PROPN
ap-1350	82	2	,	,	PUNCT
ap-1350	82	3	yηn	yηn	PROPN
ap-1350	82	4	=	=	PUNCT
ap-1350	83	1	λn(−a)ηn−1	λn(−a)ηn−1	PROPN
ap-1350	83	2	on	on	ADP
ap-1350	83	3	h	h	NOUN
ap-1350	83	4	=	=	PROPN
ap-1350	83	5	⊕	⊕	PROPN
ap-1350	83	6	n∈z	n∈z	PROPN
ap-1350	83	7	h0	h0	PROPN
ap-1350	83	8	.	.	PUNCT
ap-1350	84	1	s	s	PART
ap-1350	84	2	∈	∈	PROPN
ap-1350	84	3	(	(	PUNCT
ap-1350	84	4	0	0	NUM
ap-1350	84	5	,	,	PUNCT
ap-1350	84	6	1	1	NUM
ap-1350	84	7	)	)	PUNCT
ap-1350	84	8	:	:	PUNCT
ap-1350	84	9	xηn	xηn	PROPN
ap-1350	84	10	=	=	SYM
ap-1350	84	11	q2(n+1)sηn	q2(n+1)sηn	PROPN
ap-1350	84	12	,	,	PUNCT
ap-1350	84	13	yηn	yηn	PROPN
ap-1350	84	14	=	=	PRON
ap-1350	84	15	λn(s)ηn−1	λn(s)ηn−1	PROPN
ap-1350	84	16	on	on	ADP
ap-1350	84	17	h	h	NOUN
ap-1350	84	18	=	=	PROPN
ap-1350	84	19	⊕	⊕	PROPN
ap-1350	84	20	n∈n0	n∈n0	PROPN
ap-1350	84	21	h0	h0	PROPN
ap-1350	84	22	;	;	PUNCT
ap-1350	84	23	x	x	SYM
ap-1350	84	24	=	=	SYM
ap-1350	84	25	0	0	NUM
ap-1350	84	26	,	,	PUNCT
ap-1350	84	27	y	y	PROPN
ap-1350	84	28	=	=	SYM
ap-1350	84	29	su	su	PROPN
ap-1350	84	30	on	on	ADP
ap-1350	84	31	h0	h0	PROPN
ap-1350	84	32	.	.	PUNCT
ap-1350	85	1	s	s	PROPN
ap-1350	85	2	∈	∈	PROPN
ap-1350	85	3	(	(	PUNCT
ap-1350	85	4	q2	q2	NOUN
ap-1350	85	5	,	,	PUNCT
ap-1350	85	6	1	1	NUM
ap-1350	85	7	)	)	PUNCT
ap-1350	85	8	:	:	PUNCT
ap-1350	85	9	xηn	xηn	PROPN
ap-1350	85	10	=	=	SYM
ap-1350	85	11	q−2nsηn	q−2nsηn	NOUN
ap-1350	85	12	,	,	PUNCT
ap-1350	85	13	yηn	yηn	PROPN
ap-1350	85	14	=	=	SYM
ap-1350	85	15	λ−(n+1)(s)ηn+1	λ−(n+1)(s)ηn+1	PROPN
ap-1350	85	16	on	on	ADP
ap-1350	85	17	h	h	NOUN
ap-1350	85	18	=	=	PROPN
ap-1350	85	19	⊕	⊕	PROPN
ap-1350	85	20	n∈n0	n∈n0	PROPN
ap-1350	85	21	h0	h0	PROPN
ap-1350	85	22	;	;	PUNCT
ap-1350	85	23	xηn	xηn	PROPN
ap-1350	85	24	=	=	SYM
ap-1350	85	25	q2(n+1)ηn	q2(n+1)ηn	X
ap-1350	85	26	,	,	PUNCT
ap-1350	85	27	yηn	yηn	PROPN
ap-1350	85	28	=	=	PUNCT
ap-1350	86	1	λnηn−1	λnηn−1	PROPN
ap-1350	86	2	on	on	ADP
ap-1350	86	3	h	h	NOUN
ap-1350	86	4	=	=	PROPN
ap-1350	86	5	⊕	⊕	PROPN
ap-1350	86	6	n∈n0	n∈n0	PROPN
ap-1350	86	7	h0	h0	PROPN
ap-1350	86	8	;	;	PUNCT
ap-1350	86	9	xηn	xηn	PROPN
ap-1350	86	10	=	=	SYM
ap-1350	86	11	q2(n+1)bηn	q2(n+1)bηn	PROPN
ap-1350	86	12	,	,	PUNCT
ap-1350	86	13	yηn	yηn	NOUN
ap-1350	86	14	=	=	PUNCT
ap-1350	86	15	λn(b)ηn−1	λn(b)ηn−1	ADJ
ap-1350	86	16	on	on	ADP
ap-1350	86	17	h	h	NOUN
ap-1350	86	18	=	=	PROPN
ap-1350	86	19	⊕	⊕	PROPN
ap-1350	86	20	n∈z	n∈z	PROPN
ap-1350	86	21	h0	h0	PROPN
ap-1350	86	22	.	.	PUNCT
ap-1350	86	23	s	s	PART
ap-1350	87	1	=	=	PROPN
ap-1350	87	2	q2	q2	NOUN
ap-1350	87	3	:	:	PUNCT
ap-1350	87	4	x	x	X
ap-1350	87	5	=	=	SYM
ap-1350	87	6	q2	q2	PROPN
ap-1350	87	7	,	,	PUNCT
ap-1350	87	8	y	y	PROPN
ap-1350	87	9	=	=	NOUN
ap-1350	87	10	0	0	NUM
ap-1350	87	11	on	on	ADP
ap-1350	87	12	h0	h0	PROPN
ap-1350	87	13	.	.	PUNCT
ap-1350	87	14	s	s	PART
ap-1350	88	1	=	=	NOUN
ap-1350	88	2	0	0	PUNCT
ap-1350	88	3	:	:	PUNCT
ap-1350	88	4	x	x	X
ap-1350	88	5	=	=	PUNCT
ap-1350	88	6	y	y	PROPN
ap-1350	88	7	=	=	SYM
ap-1350	88	8	0	0	NUM
ap-1350	88	9	on	on	ADP
ap-1350	88	10	h0	h0	PROPN
ap-1350	88	11	.	.	PUNCT
ap-1350	88	12	s	s	PART
ap-1350	89	1	∈	∈	PROPN
ap-1350	90	1	[	[	X
ap-1350	90	2	−1	−1	NOUN
ap-1350	90	3	,	,	PUNCT
ap-1350	90	4	0	0	NUM
ap-1350	90	5	)	)	PUNCT
ap-1350	90	6	:	:	PUNCT
ap-1350	90	7	xηn	xηn	PROPN
ap-1350	90	8	=	=	SYM
ap-1350	90	9	q−2nsηn	q−2nsηn	NOUN
ap-1350	90	10	,	,	PUNCT
ap-1350	90	11	yηn	yηn	PROPN
ap-1350	90	12	=	=	SYM
ap-1350	90	13	λ−(n+1)(s)ηn+1	λ−(n+1)(s)ηn+1	PROPN
ap-1350	90	14	on	on	ADP
ap-1350	90	15	h	h	NOUN
ap-1350	90	16	=	=	PROPN
ap-1350	90	17	⊕	⊕	PROPN
ap-1350	90	18	n∈n0	n∈n0	PROPN
ap-1350	90	19	h0	h0	PROPN
ap-1350	90	20	.	.	PUNCT
ap-1350	91	1	the	the	DET
ap-1350	91	2	domain	domain	NOUN
ap-1350	91	3	d	d	NOUN
ap-1350	91	4	of	of	ADP
ap-1350	91	5	the	the	DET
ap-1350	91	6	representation	representation	NOUN
ap-1350	91	7	can	can	AUX
ap-1350	91	8	be	be	AUX
ap-1350	91	9	chosen	choose	VERB
ap-1350	91	10	,	,	PUNCT
ap-1350	91	11	for	for	ADP
ap-1350	91	12	instance	instance	NOUN
ap-1350	91	13	,	,	PUNCT
ap-1350	91	14	to	to	PART
ap-1350	91	15	be	be	AUX
ap-1350	91	16	the	the	DET
ap-1350	91	17	linear	linear	ADJ
ap-1350	91	18	span	span	NOUN
ap-1350	91	19	of	of	ADP
ap-1350	91	20	the	the	DET
ap-1350	91	21	ηn	ηn	NOUN
ap-1350	91	22	’s	’s	NOUN
ap-1350	91	23	.	.	PUNCT
ap-1350	92	1	if	if	SCONJ
ap-1350	92	2	one	one	PRON
ap-1350	92	3	imposes	impose	VERB
ap-1350	92	4	some	some	DET
ap-1350	92	5	well	well	ADJ
ap-1350	92	6	-	-	PUNCT
ap-1350	92	7	behavedness	behavedness	NOUN
ap-1350	92	8	conditions	condition	NOUN
ap-1350	92	9	,	,	PUNCT
ap-1350	92	10	for	for	ADP
ap-1350	92	11	instance	instance	NOUN
ap-1350	92	12	that	that	SCONJ
ap-1350	92	13	x̄	x̄	PRON
ap-1350	92	14	is	be	AUX
ap-1350	92	15	self	self	NOUN
ap-1350	92	16	-	-	PUNCT
ap-1350	92	17	adjoint	adjoint	NOUN
ap-1350	92	18	and	and	CCONJ
ap-1350	92	19	that	that	DET
ap-1350	92	20	yf(x̄	yf(x̄	AUX
ap-1350	92	21	)	)	PUNCT
ap-1350	92	22	⊂	⊂	PROPN
ap-1350	92	23	f(x̄)y	f(x̄)y	PROPN
ap-1350	92	24	for	for	ADP
ap-1350	92	25	all	all	DET
ap-1350	92	26	bounded	bounded	ADJ
ap-1350	92	27	measurable	measurable	ADJ
ap-1350	92	28	functions	function	NOUN
ap-1350	92	29	(	(	PUNCT
ap-1350	92	30	with	with	ADP
ap-1350	92	31	respect	respect	NOUN
ap-1350	92	32	to	to	ADP
ap-1350	92	33	the	the	DET
ap-1350	92	34	spectral	spectral	ADJ
ap-1350	92	35	measure	measure	NOUN
ap-1350	92	36	of	of	ADP
ap-1350	92	37	x̄	x̄	PROPN
ap-1350	92	38	)	)	PUNCT
ap-1350	92	39	,	,	PUNCT
ap-1350	92	40	then	then	ADV
ap-1350	92	41	this	this	DET
ap-1350	92	42	list	list	NOUN
ap-1350	92	43	is	be	AUX
ap-1350	92	44	complete	complete	ADJ
ap-1350	92	45	in	in	ADP
ap-1350	92	46	the	the	DET
ap-1350	92	47	sense	sense	NOUN
ap-1350	92	48	that	that	SCONJ
ap-1350	92	49	each	each	DET
ap-1350	92	50	well	well	ADV
ap-1350	92	51	-	-	PUNCT
ap-1350	92	52	behaved	behave	VERB
ap-1350	92	53	representation	representation	NOUN
ap-1350	92	54	is	be	AUX
ap-1350	92	55	a	a	DET
ap-1350	92	56	direct	direct	ADJ
ap-1350	92	57	sum	sum	NOUN
ap-1350	92	58	of	of	ADP
ap-1350	92	59	representations	representation	NOUN
ap-1350	92	60	from	from	ADP
ap-1350	92	61	the	the	DET
ap-1350	92	62	above	above	ADJ
ap-1350	92	63	list	list	NOUN
ap-1350	92	64	.	.	PUNCT
ap-1350	93	1	a	a	DET
ap-1350	93	2	single	single	ADJ
ap-1350	93	3	representation	representation	NOUN
ap-1350	93	4	is	be	AUX
ap-1350	93	5	irreducible	irreducible	ADJ
ap-1350	93	6	if	if	SCONJ
ap-1350	93	7	and	and	CCONJ
ap-1350	93	8	only	only	ADV
ap-1350	93	9	if	if	SCONJ
ap-1350	93	10	h0	h0	PROPN
ap-1350	93	11	=	=	PROPN
ap-1350	93	12	c.	c.	PROPN
ap-1350	93	13	in	in	ADP
ap-1350	93	14	this	this	DET
ap-1350	93	15	case	case	NOUN
ap-1350	93	16	a	a	PRON
ap-1350	93	17	,	,	PUNCT
ap-1350	93	18	b	b	NOUN
ap-1350	93	19	and	and	CCONJ
ap-1350	93	20	u	u	NOUN
ap-1350	93	21	become	become	VERB
ap-1350	93	22	complex	complex	ADJ
ap-1350	93	23	numbers	number	NOUN
ap-1350	93	24	such	such	ADJ
ap-1350	93	25	that	that	SCONJ
ap-1350	93	26	a	a	DET
ap-1350	93	27	∈	∈	PROPN
ap-1350	93	28	(	(	PUNCT
ap-1350	93	29	q2	q2	NOUN
ap-1350	93	30	,	,	PUNCT
ap-1350	93	31	1	1	NUM
ap-1350	93	32	]	]	PUNCT
ap-1350	93	33	,	,	PUNCT
ap-1350	93	34	b	b	X
ap-1350	93	35	∈	∈	PROPN
ap-1350	93	36	(	(	PUNCT
ap-1350	93	37	q2	q2	NOUN
ap-1350	93	38	,	,	PUNCT
ap-1350	93	39	s	s	PART
ap-1350	93	40	)	)	PUNCT
ap-1350	93	41	and	and	CCONJ
ap-1350	93	42	|u	|u	ADJ
ap-1350	93	43	|	|	NOUN
ap-1350	93	44	=	=	NOUN
ap-1350	93	45	1	1	X
ap-1350	93	46	.	.	X
ap-1350	94	1	for	for	ADP
ap-1350	94	2	the	the	DET
ap-1350	94	3	proof	proof	NOUN
ap-1350	94	4	of	of	ADP
ap-1350	94	5	these	these	DET
ap-1350	94	6	claims	claim	NOUN
ap-1350	94	7	,	,	PUNCT
ap-1350	94	8	see	see	VERB
ap-1350	94	9	[	[	X
ap-1350	94	10	4	4	NUM
ap-1350	94	11	]	]	PUNCT
ap-1350	94	12	.	.	PUNCT
ap-1350	95	1	given	give	VERB
ap-1350	95	2	a	a	DET
ap-1350	95	3	*	*	PUNCT
ap-1350	95	4	-representation	-representation	NOUN
ap-1350	95	5	such	such	ADJ
ap-1350	95	6	that	that	SCONJ
ap-1350	95	7	x	x	PRON
ap-1350	95	8	is	be	AUX
ap-1350	95	9	invertible	invertible	ADJ
ap-1350	95	10	in	in	ADP
ap-1350	95	11	l+(d	l+(d	PROPN
ap-1350	95	12	)	)	PUNCT
ap-1350	95	13	,	,	PUNCT
ap-1350	95	14	set	set	VERB
ap-1350	95	15	e	e	NOUN
ap-1350	95	16	:	:	PUNCT
ap-1350	95	17	=	=	SYM
ap-1350	96	1	q−1/2(q	q−1/2(q	ADJ
ap-1350	96	2	−	−	PROPN
ap-1350	96	3	q−1)−1x−1y	q−1)−1x−1y	ADJ
ap-1350	96	4	,	,	PUNCT
ap-1350	96	5	f	f	X
ap-1350	96	6	:	:	PUNCT
ap-1350	97	1	=	=	SYM
ap-1350	97	2	−q1/2(q	−q1/2(q	NUM
ap-1350	97	3	−	−	PROPN
ap-1350	97	4	q−1)−1y∗	q−1)−1y∗	PROPN
ap-1350	97	5	,	,	PUNCT
ap-1350	97	6	k	k	PROPN
ap-1350	97	7	:	:	PUNCT
ap-1350	97	8	=	=	SYM
ap-1350	97	9	qx−1	qx−1	VERB
ap-1350	97	10	.	.	PUNCT
ap-1350	98	1	direct	direct	ADJ
ap-1350	98	2	computations	computation	NOUN
ap-1350	98	3	show	show	VERB
ap-1350	98	4	that	that	SCONJ
ap-1350	98	5	k	k	PROPN
ap-1350	98	6	�	�	PROPN
ap-1350	98	7	z	z	PROPN
ap-1350	98	8	=	=	SYM
ap-1350	98	9	kzk−1	kzk−1	PROPN
ap-1350	98	10	,	,	PUNCT
ap-1350	98	11	e	e	X
ap-1350	98	12	�	�	PROPN
ap-1350	98	13	z	z	PROPN
ap-1350	98	14	=	=	SYM
ap-1350	98	15	ez	ez	PROPN
ap-1350	98	16	−	−	PROPN
ap-1350	98	17	kzk−1e	kzk−1e	PROPN
ap-1350	98	18	,	,	PUNCT
ap-1350	98	19	f	f	PROPN
ap-1350	98	20	�	�	PROPN
ap-1350	98	21	z	z	PROPN
ap-1350	98	22	=	=	PUNCT
ap-1350	98	23	fzk	fzk	NOUN
ap-1350	98	24	−	−	PROPN
ap-1350	98	25	zfk	zfk	NOUN
ap-1350	98	26	(	(	PUNCT
ap-1350	98	27	8)	8)	NUM
ap-1350	98	28	for	for	ADP
ap-1350	98	29	z	z	NOUN
ap-1350	98	30	=	=	SYM
ap-1350	98	31	x	x	PROPN
ap-1350	98	32	,	,	PUNCT
ap-1350	98	33	y	y	PROPN
ap-1350	98	34	,	,	PUNCT
ap-1350	98	35	y∗.	y∗.	NUM
ap-1350	98	36	using	use	VERB
ap-1350	98	37	the	the	DET
ap-1350	98	38	relations	relation	NOUN
ap-1350	98	39	ke	ke	NOUN
ap-1350	98	40	=	=	PUNCT
ap-1350	98	41	q2ek	q2ek	X
ap-1350	98	42	,	,	PUNCT
ap-1350	98	43	fk	fk	INTJ
ap-1350	98	44	=	=	PUNCT
ap-1350	98	45	q2kf	q2kf	X
ap-1350	98	46	,	,	PUNCT
ap-1350	98	47	ef	ef	PROPN
ap-1350	98	48	−	−	PROPN
ap-1350	98	49	fe	fe	X
ap-1350	98	50	=	=	PUNCT
ap-1350	98	51	(	(	PUNCT
ap-1350	98	52	q	q	NOUN
ap-1350	98	53	−	−	PROPN
ap-1350	98	54	q−1)−1(sk	q−1)−1(sk	X
ap-1350	98	55	−	−	PROPN
ap-1350	98	56	k−1	k−1	PROPN
ap-1350	98	57	)	)	PUNCT
ap-1350	98	58	,	,	PUNCT
ap-1350	98	59	(	(	PUNCT
ap-1350	98	60	9	9	X
ap-1350	98	61	)	)	PUNCT
ap-1350	98	62	one	one	NOUN
ap-1350	98	63	easily	easily	ADV
ap-1350	98	64	proves	prove	VERB
ap-1350	98	65	that	that	SCONJ
ap-1350	98	66	(	(	PUNCT
ap-1350	98	67	8)	8)	NUM
ap-1350	98	68	defines	define	VERB
ap-1350	98	69	a	a	DET
ap-1350	98	70	u	u	NOUN
ap-1350	98	71	-	-	NOUN
ap-1350	98	72	action	action	NOUN
ap-1350	98	73	on	on	ADP
ap-1350	98	74	l+(d	l+(d	PROPN
ap-1350	98	75	)	)	PUNCT
ap-1350	98	76	turning	turn	VERB
ap-1350	98	77	it	it	PRON
ap-1350	98	78	into	into	ADP
ap-1350	98	79	a	a	DET
ap-1350	98	80	left	left	ADJ
ap-1350	98	81	u	u	NOUN
ap-1350	98	82	-	-	NOUN
ap-1350	98	83	module	module	NOUN
ap-1350	98	84	*	*	PUNCT
ap-1350	98	85	-algebra	-algebra	NOUN
ap-1350	98	86	.	.	PUNCT
ap-1350	99	1	with	with	ADP
ap-1350	99	2	a	a	DET
ap-1350	99	3	being	be	AUX
ap-1350	99	4	the	the	DET
ap-1350	99	5	*	*	PUNCT
ap-1350	99	6	-subalgebra	-subalgebra	NOUN
ap-1350	99	7	of	of	ADP
ap-1350	99	8	l+(d	l+(d	PROPN
ap-1350	99	9	)	)	PUNCT
ap-1350	99	10	generated	generate	VERB
ap-1350	99	11	by	by	ADP
ap-1350	99	12	y	y	PROPN
ap-1350	99	13	,	,	PUNCT
ap-1350	99	14	y∗	y∗	PROPN
ap-1350	99	15	,	,	PUNCT
ap-1350	99	16	x	x	PUNCT
ap-1350	99	17	and	and	CCONJ
ap-1350	99	18	x−1	x−1	PROPN
ap-1350	99	19	,	,	PUNCT
ap-1350	99	20	the	the	DET
ap-1350	99	21	*	*	PUNCT
ap-1350	99	22	-algebra	-algebra	PROPN
ap-1350	99	23	s(a	s(a	NOUN
ap-1350	99	24	)	)	PUNCT
ap-1350	99	25	defined	define	VERB
ap-1350	99	26	in	in	ADP
ap-1350	99	27	(	(	PUNCT
ap-1350	99	28	4	4	NUM
ap-1350	99	29	)	)	PUNCT
ap-1350	99	30	becomes	become	VERB
ap-1350	99	31	a	a	DET
ap-1350	99	32	left	left	ADJ
ap-1350	99	33	u	u	NOUN
ap-1350	99	34	-	-	NOUN
ap-1350	99	35	module	module	NOUN
ap-1350	99	36	*	*	PUNCT
ap-1350	99	37	-subalgebra	-subalgebra	NOUN
ap-1350	99	38	of	of	ADP
ap-1350	99	39	l+(d	l+(d	PROPN
ap-1350	99	40	)	)	PUNCT
ap-1350	99	41	.	.	PUNCT
ap-1350	100	1	since	since	SCONJ
ap-1350	100	2	the	the	DET
ap-1350	100	3	traces	trace	NOUN
ap-1350	100	4	of	of	ADP
ap-1350	100	5	elements	element	NOUN
ap-1350	100	6	from	from	ADP
ap-1350	100	7	s(a	s(a	PROPN
ap-1350	100	8	)	)	PUNCT
ap-1350	100	9	are	be	AUX
ap-1350	100	10	welldefined	welldefine	VERB
ap-1350	100	11	,	,	PUNCT
ap-1350	100	12	we	we	PRON
ap-1350	100	13	can	can	AUX
ap-1350	100	14	state	state	VERB
ap-1350	100	15	the	the	DET
ap-1350	100	16	following	follow	VERB
ap-1350	100	17	proposition	proposition	NOUN
ap-1350	100	18	:	:	PUNCT
ap-1350	100	19	proposition	proposition	NOUN
ap-1350	100	20	2	2	NUM
ap-1350	100	21	if	if	SCONJ
ap-1350	100	22	±x	±x	PROPN
ap-1350	100	23	is	be	AUX
ap-1350	100	24	a	a	DET
ap-1350	100	25	non	non	ADJ
ap-1350	100	26	-	-	ADJ
ap-1350	100	27	negative	negative	ADJ
ap-1350	100	28	selfadjoint	selfadjoint	NOUN
ap-1350	100	29	operator	operator	NOUN
ap-1350	100	30	,	,	PUNCT
ap-1350	100	31	then	then	ADV
ap-1350	100	32	h(f	h(f	PROPN
ap-1350	100	33	)	)	PUNCT
ap-1350	100	34	:	:	PUNCT
ap-1350	100	35	=	=	SYM
ap-1350	100	36	±tr(k−1f	±tr(k−1f	NOUN
ap-1350	100	37	)	)	PUNCT
ap-1350	100	38	defines	define	VERB
ap-1350	100	39	an	an	DET
ap-1350	100	40	invariant	invariant	ADJ
ap-1350	100	41	integral	integral	NOUN
ap-1350	100	42	on	on	ADP
ap-1350	100	43	s(a	s(a	PROPN
ap-1350	100	44	)	)	PUNCT
ap-1350	100	45	.	.	PUNCT
ap-1350	101	1	proof	proof	NOUN
ap-1350	101	2	.	.	PUNCT
ap-1350	102	1	the	the	DET
ap-1350	102	2	invariance	invariance	NOUN
ap-1350	102	3	follows	follow	VERB
ap-1350	102	4	from	from	ADP
ap-1350	102	5	the	the	DET
ap-1350	102	6	trace	trace	NOUN
ap-1350	102	7	property	property	NOUN
ap-1350	102	8	tr(af	tr(af	PROPN
ap-1350	102	9	)	)	PUNCT
ap-1350	102	10	=	=	SYM
ap-1350	102	11	tr(fa	tr(fa	PROPN
ap-1350	102	12	)	)	PUNCT
ap-1350	102	13	for	for	ADP
ap-1350	102	14	all	all	DET
ap-1350	102	15	f	f	PROPN
ap-1350	102	16	∈	∈	PROPN
ap-1350	102	17	s(a	s(a	PROPN
ap-1350	102	18	)	)	PUNCT
ap-1350	102	19	and	and	CCONJ
ap-1350	102	20	a	a	DET
ap-1350	102	21	∈	∈	NOUN
ap-1350	102	22	a.	a.	NOUN
ap-1350	102	23	as	as	ADP
ap-1350	102	24	an	an	DET
ap-1350	102	25	example	example	NOUN
ap-1350	102	26	,	,	PUNCT
ap-1350	102	27	we	we	PRON
ap-1350	102	28	show	show	VERB
ap-1350	102	29	the	the	DET
ap-1350	102	30	invariance	invariance	NOUN
ap-1350	102	31	with	with	ADP
ap-1350	102	32	respect	respect	NOUN
ap-1350	102	33	to	to	ADP
ap-1350	102	34	e	e	NOUN
ap-1350	102	35	,	,	PUNCT
ap-1350	102	36	h(e	h(e	PROPN
ap-1350	102	37	�	�	PROPN
ap-1350	102	38	z	z	PROPN
ap-1350	102	39	)	)	PUNCT
ap-1350	102	40	=	=	PUNCT
ap-1350	102	41	±tr(k−1ez	±tr(k−1ez	ADP
ap-1350	102	42	−	−	PROPN
ap-1350	102	43	zk−1e	zk−1e	NUM
ap-1350	102	44	)	)	PUNCT
ap-1350	103	1	=	=	PUNCT
ap-1350	103	2	±tr(k−1ez	±tr(k−1ez	ADP
ap-1350	103	3	−	−	NOUN
ap-1350	103	4	k−1ez	k−1ez	NOUN
ap-1350	103	5	)	)	PUNCT
ap-1350	103	6	=	=	SYM
ap-1350	103	7	0	0	PUNCT
ap-1350	104	1	=	=	SYM
ap-1350	104	2	ε(e)h(z	ε(e)h(z	PROPN
ap-1350	104	3	)	)	PUNCT
ap-1350	104	4	.	.	PUNCT
ap-1350	105	1	the	the	DET
ap-1350	105	2	positivity	positivity	NOUN
ap-1350	105	3	of	of	ADP
ap-1350	105	4	h	h	NOUN
ap-1350	105	5	is	be	AUX
ap-1350	105	6	clear	clear	ADJ
ap-1350	105	7	by	by	ADP
ap-1350	105	8	the	the	DET
ap-1350	105	9	positivity	positivity	NOUN
ap-1350	105	10	of	of	ADP
ap-1350	105	11	±k−1	±k−1	NOUN
ap-1350	105	12	=	=	SYM
ap-1350	105	13	±q−1x	±q−1x	PROPN
ap-1350	105	14	.	.	PUNCT
ap-1350	105	15	�	�	PROPN
ap-1350	105	16	note	note	VERB
ap-1350	105	17	that	that	SCONJ
ap-1350	105	18	equation	equation	NOUN
ap-1350	105	19	(	(	PUNCT
ap-1350	105	20	8)	8)	NUM
ap-1350	105	21	is	be	AUX
ap-1350	105	22	invariant	invariant	ADJ
ap-1350	105	23	under	under	ADP
ap-1350	105	24	the	the	DET
ap-1350	105	25	rescaling	rescaling	NOUN
ap-1350	105	26	k	k	PROPN
ap-1350	105	27	�	�	PROPN
ap-1350	105	28	→	→	SYM
ap-1350	105	29	tk	tk	PROPN
ap-1350	105	30	and	and	CCONJ
ap-1350	105	31	f	f	PROPN
ap-1350	105	32	�	�	PROPN
ap-1350	105	33	→	→	SYM
ap-1350	105	34	t−1f	t−1f	X
ap-1350	105	35	.	.	PUNCT
ap-1350	106	1	if	if	SCONJ
ap-1350	106	2	t	t	PROPN
ap-1350	106	3	∈	∈	PROPN
ap-1350	106	4	r	r	NOUN
ap-1350	106	5	\	\	PUNCT
ap-1350	106	6	{	{	PUNCT
ap-1350	106	7	0	0	NUM
ap-1350	106	8	}	}	PUNCT
ap-1350	106	9	,	,	PUNCT
ap-1350	106	10	the	the	DET
ap-1350	106	11	rescaling	rescaling	NOUN
ap-1350	106	12	does	do	AUX
ap-1350	106	13	not	not	PART
ap-1350	106	14	affect	affect	VERB
ap-1350	106	15	the	the	DET
ap-1350	106	16	involution	involution	NOUN
ap-1350	106	17	,	,	PUNCT
ap-1350	106	18	i.e.	i.e.	X
ap-1350	106	19	,	,	PUNCT
ap-1350	106	20	we	we	PRON
ap-1350	106	21	have	have	VERB
ap-1350	106	22	k∗	k∗	NOUN
ap-1350	106	23	=	=	PUNCT
ap-1350	106	24	k	k	PROPN
ap-1350	106	25	and	and	CCONJ
ap-1350	106	26	e∗	e∗	PROPN
ap-1350	106	27	=	=	SYM
ap-1350	106	28	−kf	−kf	PROPN
ap-1350	106	29	.	.	PUNCT
ap-1350	107	1	from	from	ADP
ap-1350	107	2	(	(	PUNCT
ap-1350	107	3	9	9	NUM
ap-1350	107	4	)	)	PUNCT
ap-1350	107	5	,	,	PUNCT
ap-1350	107	6	it	it	PRON
ap-1350	107	7	follows	follow	VERB
ap-1350	107	8	that	that	SCONJ
ap-1350	107	9	ρ(k	ρ(k	PROPN
ap-1350	107	10	)	)	PUNCT
ap-1350	108	1	=	=	SYM
ap-1350	108	2	s1/2k	s1/2k	NOUN
ap-1350	108	3	,	,	PUNCT
ap-1350	108	4	ρ(e	ρ(e	PROPN
ap-1350	108	5	)	)	PUNCT
ap-1350	108	6	=	=	SYM
ap-1350	109	1	e	e	X
ap-1350	109	2	,	,	PUNCT
ap-1350	109	3	ρ(f	ρ(f	NOUN
ap-1350	109	4	)	)	PUNCT
ap-1350	109	5	=	=	SYM
ap-1350	110	1	s−1/2f	s−1/2f	PROPN
ap-1350	110	2	defines	define	VERB
ap-1350	110	3	a	a	DET
ap-1350	110	4	moment	moment	NOUN
ap-1350	110	5	map	map	NOUN
ap-1350	110	6	ρ	ρ	NOUN
ap-1350	110	7	:	:	PUNCT
ap-1350	110	8	u	u	PROPN
ap-1350	110	9	→	→	PUNCT
ap-1350	110	10	a	a	DET
ap-1350	110	11	if	if	NOUN
ap-1350	110	12	and	and	CCONJ
ap-1350	110	13	only	only	ADV
ap-1350	110	14	if	if	SCONJ
ap-1350	110	15	s	s	X
ap-1350	110	16	∈	∈	PROPN
ap-1350	110	17	(	(	PUNCT
ap-1350	110	18	0	0	NUM
ap-1350	110	19	,	,	PUNCT
ap-1350	110	20	1	1	NUM
ap-1350	110	21	)	)	PUNCT
ap-1350	110	22	.	.	PUNCT
ap-1350	111	1	in	in	ADP
ap-1350	111	2	this	this	DET
ap-1350	111	3	situation	situation	NOUN
ap-1350	111	4	,	,	PUNCT
ap-1350	111	5	proposition	proposition	NOUN
ap-1350	111	6	2	2	NUM
ap-1350	111	7	is	be	AUX
ap-1350	111	8	an	an	DET
ap-1350	111	9	immediate	immediate	ADJ
ap-1350	111	10	consequence	consequence	NOUN
ap-1350	111	11	of	of	ADP
ap-1350	111	12	theorem	theorem	NOUN
ap-1350	111	13	1	1	NUM
ap-1350	111	14	together	together	ADV
ap-1350	111	15	with	with	ADP
ap-1350	111	16	the	the	DET
ap-1350	111	17	formula	formula	NOUN
ap-1350	111	18	of	of	ADP
ap-1350	111	19	the	the	DET
ap-1350	111	20	quantum	quantum	NOUN
ap-1350	111	21	trace	trace	NOUN
ap-1350	111	22	.	.	PUNCT
ap-1350	112	1	however	however	ADV
ap-1350	112	2	,	,	PUNCT
ap-1350	112	3	we	we	PRON
ap-1350	112	4	emphasize	emphasize	VERB
ap-1350	112	5	that	that	SCONJ
ap-1350	112	6	proposition	proposition	NOUN
ap-1350	112	7	2	2	NUM
ap-1350	112	8	holds	hold	VERB
ap-1350	112	9	for	for	ADP
ap-1350	112	10	all	all	DET
ap-1350	112	11	s	s	PART
ap-1350	112	12	∈	∈	NOUN
ap-1350	113	1	[	[	X
ap-1350	113	2	−1	−1	NOUN
ap-1350	113	3	,	,	PUNCT
ap-1350	113	4	0	0	NUM
ap-1350	113	5	)	)	PUNCT
ap-1350	113	6	,	,	PUNCT
ap-1350	113	7	even	even	ADV
ap-1350	113	8	if	if	SCONJ
ap-1350	113	9	the	the	DET
ap-1350	113	10	operators	operator	NOUN
ap-1350	113	11	k	k	X
ap-1350	113	12	,	,	PUNCT
ap-1350	113	13	e	e	PROPN
ap-1350	113	14	and	and	CCONJ
ap-1350	113	15	f	f	PROPN
ap-1350	113	16	do	do	AUX
ap-1350	113	17	not	not	PART
ap-1350	113	18	satisfy	satisfy	VERB
ap-1350	113	19	the	the	DET
ap-1350	113	20	defining	define	VERB
ap-1350	113	21	relations	relation	NOUN
ap-1350	113	22	of	of	ADP
ap-1350	113	23	uq(su1,1	uq(su1,1	PROPN
ap-1350	113	24	)	)	PUNCT
ap-1350	113	25	.	.	PUNCT
ap-1350	114	1	this	this	PRON
ap-1350	114	2	shows	show	VERB
ap-1350	114	3	that	that	SCONJ
ap-1350	114	4	the	the	DET
ap-1350	114	5	operator	operator	NOUN
ap-1350	114	6	-	-	PUNCT
ap-1350	114	7	theoretic	theoretic	NOUN
ap-1350	114	8	approach	approach	NOUN
ap-1350	114	9	to	to	ADP
ap-1350	114	10	invariant	invariant	ADJ
ap-1350	114	11	integration	integration	NOUN
ap-1350	114	12	theory	theory	NOUN
ap-1350	114	13	is	be	AUX
ap-1350	114	14	more	more	ADV
ap-1350	114	15	general	general	ADJ
ap-1350	114	16	than	than	ADP
ap-1350	114	17	the	the	DET
ap-1350	114	18	method	method	NOUN
ap-1350	114	19	based	base	VERB
ap-1350	114	20	on	on	ADP
ap-1350	114	21	a	a	DET
ap-1350	114	22	quantum	quantum	ADJ
ap-1350	114	23	moment	moment	NOUN
ap-1350	114	24	map	map	NOUN
ap-1350	114	25	.	.	PUNCT
ap-1350	115	1	we	we	PRON
ap-1350	115	2	also	also	ADV
ap-1350	115	3	would	would	AUX
ap-1350	115	4	like	like	VERB
ap-1350	115	5	to	to	PART
ap-1350	115	6	point	point	VERB
ap-1350	115	7	out	out	ADP
ap-1350	115	8	that	that	SCONJ
ap-1350	115	9	our	our	PRON
ap-1350	115	10	approach	approach	NOUN
ap-1350	115	11	works	work	VERB
ap-1350	115	12	for	for	ADP
ap-1350	115	13	all	all	DET
ap-1350	115	14	representations	representation	NOUN
ap-1350	115	15	from	from	ADP
ap-1350	115	16	the	the	DET
ap-1350	115	17	above	above	ADJ
ap-1350	115	18	list	list	NOUN
ap-1350	115	19	where	where	SCONJ
ap-1350	115	20	x	x	SYM
ap-1350	115	21	�	�	PROPN
ap-1350	115	22	=	=	SYM
ap-1350	115	23	0	0	NUM
ap-1350	115	24	,	,	PUNCT
ap-1350	115	25	even	even	ADV
ap-1350	115	26	for	for	ADP
ap-1350	115	27	those	those	PRON
ap-1350	115	28	where	where	SCONJ
ap-1350	115	29	x	x	PRON
ap-1350	115	30	has	have	VERB
ap-1350	115	31	a	a	DET
ap-1350	115	32	continuous	continuous	ADJ
ap-1350	115	33	spectrum	spectrum	NOUN
ap-1350	115	34	,	,	PUNCT
ap-1350	115	35	whereas	whereas	SCONJ
ap-1350	115	36	in	in	ADP
ap-1350	115	37	the	the	DET
ap-1350	115	38	algebraic	algebraic	ADJ
ap-1350	115	39	approach	approach	NOUN
ap-1350	115	40	,	,	PUNCT
ap-1350	115	41	one	one	PRON
ap-1350	115	42	usually	usually	ADV
ap-1350	115	43	considers	consider	VERB
ap-1350	115	44	functions	function	NOUN
ap-1350	115	45	in	in	ADP
ap-1350	115	46	x	x	PUNCT
ap-1350	115	47	which	which	PRON
ap-1350	115	48	are	be	AUX
ap-1350	115	49	supported	support	VERB
ap-1350	115	50	on	on	ADP
ap-1350	115	51	a	a	DET
ap-1350	115	52	discrete	discrete	ADJ
ap-1350	115	53	set	set	NOUN
ap-1350	115	54	[	[	X
ap-1350	115	55	2	2	NUM
ap-1350	115	56	,	,	PUNCT
ap-1350	115	57	7	7	NUM
ap-1350	115	58	]	]	PUNCT
ap-1350	115	59	.	.	PUNCT
ap-1350	116	1	references	reference	NOUN
ap-1350	116	2	[	[	X
ap-1350	116	3	1	1	NUM
ap-1350	116	4	]	]	X
ap-1350	116	5	klimyk	klimyk	NOUN
ap-1350	116	6	,	,	PUNCT
ap-1350	116	7	a.	a.	NOUN
ap-1350	116	8	u.	u.	PROPN
ap-1350	116	9	,	,	PUNCT
ap-1350	116	10	schmüdgen	schmüdgen	PROPN
ap-1350	116	11	,	,	PUNCT
ap-1350	116	12	k.	k.	NOUN
ap-1350	116	13	:	:	PUNCT
ap-1350	116	14	quantum	quantum	ADJ
ap-1350	116	15	groups	group	NOUN
ap-1350	116	16	and	and	CCONJ
ap-1350	116	17	their	their	PRON
ap-1350	116	18	representations	representation	NOUN
ap-1350	116	19	.	.	PUNCT
ap-1350	117	1	berlin	berlin	PROPN
ap-1350	117	2	:	:	PUNCT
ap-1350	117	3	springerverlag	springerverlag	PROPN
ap-1350	117	4	,	,	PUNCT
ap-1350	117	5	1997	1997	NUM
ap-1350	117	6	.	.	PUNCT
ap-1350	118	1	31	31	NUM
ap-1350	118	2	acta	acta	PROPN
ap-1350	118	3	polytechnica	polytechnica	PROPN
ap-1350	118	4	vol	vol	NOUN
ap-1350	118	5	.	.	PUNCT
ap-1350	119	1	51	51	NUM
ap-1350	119	2	no	no	INTJ
ap-1350	119	3	.	.	PUNCT
ap-1350	120	1	1/2011	1/2011	NUM
ap-1350	121	1	[	[	X
ap-1350	121	2	2	2	NUM
ap-1350	121	3	]	]	X
ap-1350	121	4	korogodsky	korogodsky	ADJ
ap-1350	121	5	,	,	PUNCT
ap-1350	121	6	l.	l.	PROPN
ap-1350	121	7	i.	i.	PROPN
ap-1350	121	8	:	:	PUNCT
ap-1350	121	9	representation	representation	NOUN
ap-1350	121	10	of	of	ADP
ap-1350	121	11	quantum	quantum	NOUN
ap-1350	121	12	algebras	algebra	NOUN
ap-1350	121	13	arising	arise	VERB
ap-1350	121	14	from	from	ADP
ap-1350	121	15	non	non	ADJ
ap-1350	121	16	-	-	ADJ
ap-1350	121	17	compact	compact	ADJ
ap-1350	121	18	quantum	quantum	ADJ
ap-1350	121	19	groups	group	NOUN
ap-1350	121	20	:	:	PUNCT
ap-1350	121	21	quantum	quantum	NOUN
ap-1350	121	22	orbit	orbit	NOUN
ap-1350	121	23	method	method	NOUN
ap-1350	121	24	and	and	CCONJ
ap-1350	121	25	super	super	ADJ
ap-1350	121	26	-	-	ADJ
ap-1350	121	27	tensor	tensor	NOUN
ap-1350	121	28	products	product	NOUN
ap-1350	121	29	,	,	PUNCT
ap-1350	121	30	ph.d	ph.d	PROPN
ap-1350	121	31	.	.	PUNCT
ap-1350	122	1	thesis	thesis	PROPN
ap-1350	122	2	,	,	PUNCT
ap-1350	122	3	massachusetts	massachusetts	PROPN
ap-1350	122	4	institute	institute	PROPN
ap-1350	122	5	of	of	ADP
ap-1350	122	6	technology	technology	PROPN
ap-1350	122	7	,	,	PUNCT
ap-1350	122	8	dept	dept	NOUN
ap-1350	122	9	.	.	PROPN
ap-1350	122	10	of	of	ADP
ap-1350	122	11	math	math	NOUN
ap-1350	122	12	.	.	PUNCT
ap-1350	122	13	,	,	PUNCT
ap-1350	122	14	1996	1996	NUM
ap-1350	122	15	.	.	PUNCT
ap-1350	123	1	complimentary	complimentary	ADJ
ap-1350	123	2	series	series	NOUN
ap-1350	123	3	representations	representation	NOUN
ap-1350	123	4	and	and	CCONJ
ap-1350	123	5	quantum	quantum	NOUN
ap-1350	123	6	orbit	orbit	NOUN
ap-1350	123	7	method	method	NOUN
ap-1350	123	8	.	.	PUNCT
ap-1350	124	1	arxiv	arxiv	NOUN
ap-1350	124	2	:	:	PUNCT
ap-1350	124	3	q	q	NOUN
ap-1350	124	4	-	-	PUNCT
ap-1350	124	5	alg/9708026v1	alg/9708026v1	VERB
ap-1350	124	6	.	.	PUNCT
ap-1350	125	1	[	[	X
ap-1350	125	2	3	3	NUM
ap-1350	125	3	]	]	X
ap-1350	125	4	kürsten	kürsten	ADJ
ap-1350	125	5	,	,	PUNCT
ap-1350	125	6	k.-d	k.-d	PROPN
ap-1350	125	7	.	.	PROPN
ap-1350	125	8	,	,	PUNCT
ap-1350	125	9	wagner	wagner	PROPN
ap-1350	125	10	,	,	PUNCT
ap-1350	125	11	e.	e.	PROPN
ap-1350	125	12	:	:	PUNCT
ap-1350	125	13	an	an	DET
ap-1350	125	14	operatortheoretic	operatortheoretic	ADJ
ap-1350	125	15	approach	approach	NOUN
ap-1350	125	16	to	to	ADP
ap-1350	125	17	invariant	invariant	ADJ
ap-1350	125	18	integrals	integral	NOUN
ap-1350	125	19	on	on	ADP
ap-1350	125	20	quantum	quantum	PROPN
ap-1350	125	21	homogeneous	homogeneous	ADJ
ap-1350	125	22	sun,1	sun,1	NOUN
ap-1350	125	23	-	-	PUNCT
ap-1350	125	24	spaces	space	NOUN
ap-1350	125	25	.	.	PUNCT
ap-1350	126	1	publ	publ	NOUN
ap-1350	126	2	.	.	PUNCT
ap-1350	127	1	res	re	NOUN
ap-1350	127	2	.	.	PROPN
ap-1350	127	3	inst	inst	PROPN
ap-1350	127	4	.	.	PUNCT
ap-1350	128	1	math	math	NOUN
ap-1350	128	2	.	.	PUNCT
ap-1350	129	1	sci	sci	PROPN
ap-1350	129	2	.	.	PROPN
ap-1350	130	1	43	43	NUM
ap-1350	130	2	(	(	PUNCT
ap-1350	130	3	1	1	NUM
ap-1350	130	4	)	)	PUNCT
ap-1350	130	5	,	,	PUNCT
ap-1350	130	6	2007	2007	NUM
ap-1350	130	7	,	,	PUNCT
ap-1350	130	8	p.	p.	NOUN
ap-1350	130	9	1–37	1–37	PROPN
ap-1350	130	10	.	.	PUNCT
ap-1350	131	1	[	[	X
ap-1350	131	2	4	4	NUM
ap-1350	131	3	]	]	PUNCT
ap-1350	131	4	lucio	lucio	PROPN
ap-1350	131	5	peña	peña	PROPN
ap-1350	131	6	,	,	PUNCT
ap-1350	131	7	p.	p.	PROPN
ap-1350	131	8	c.	c.	PROPN
ap-1350	131	9	,	,	PUNCT
ap-1350	131	10	osuna	osuna	PROPN
ap-1350	131	11	castro	castro	PROPN
ap-1350	131	12	,	,	PUNCT
ap-1350	131	13	o.	o.	PROPN
ap-1350	131	14	,	,	PUNCT
ap-1350	131	15	wagner	wagner	PROPN
ap-1350	131	16	,	,	PUNCT
ap-1350	131	17	e.	e.	PROPN
ap-1350	131	18	:	:	PUNCT
ap-1350	131	19	invariant	invariant	ADJ
ap-1350	131	20	integration	integration	NOUN
ap-1350	131	21	theory	theory	NOUN
ap-1350	131	22	on	on	ADP
ap-1350	131	23	the	the	DET
ap-1350	131	24	quantum	quantum	ADJ
ap-1350	131	25	hyperboloid	hyperboloid	NOUN
ap-1350	131	26	,	,	PUNCT
ap-1350	131	27	in	in	ADP
ap-1350	131	28	preparation	preparation	NOUN
ap-1350	131	29	.	.	PUNCT
ap-1350	132	1	[	[	X
ap-1350	132	2	5	5	NUM
ap-1350	132	3	]	]	X
ap-1350	132	4	osuna	osuna	PROPN
ap-1350	132	5	castro	castro	PROPN
ap-1350	132	6	,	,	PUNCT
ap-1350	132	7	o.	o.	PROPN
ap-1350	132	8	,	,	PUNCT
ap-1350	132	9	wagner	wagner	PROPN
ap-1350	132	10	,	,	PUNCT
ap-1350	132	11	e.	e.	PROPN
ap-1350	132	12	:	:	PUNCT
ap-1350	132	13	an	an	DET
ap-1350	132	14	operatortheoretic	operatortheoretic	ADJ
ap-1350	132	15	approach	approach	NOUN
ap-1350	132	16	to	to	ADP
ap-1350	132	17	invariant	invariant	ADJ
ap-1350	132	18	integrals	integral	NOUN
ap-1350	132	19	on	on	ADP
ap-1350	132	20	quantum	quantum	ADJ
ap-1350	132	21	homogeneous	homogeneous	ADJ
ap-1350	132	22	sl(n	sl(n	PUNCT
ap-1350	132	23	+	+	NOUN
ap-1350	132	24	1	1	NUM
ap-1350	132	25	,	,	PUNCT
ap-1350	132	26	r)-spaces	r)-spaces	PROPN
ap-1350	132	27	.	.	PUNCT
ap-1350	133	1	arxiv	arxiv	NOUN
ap-1350	133	2	:	:	PUNCT
ap-1350	133	3	math.qa/0904.0669v1	math.qa/0904.0669v1	X
ap-1350	133	4	.	.	PUNCT
ap-1350	134	1	[	[	X
ap-1350	134	2	6	6	NUM
ap-1350	134	3	]	]	PUNCT
ap-1350	134	4	schmüdgen	schmüdgen	X
ap-1350	134	5	,	,	PUNCT
ap-1350	134	6	k.	k.	PROPN
ap-1350	134	7	,	,	PUNCT
ap-1350	134	8	wagner	wagner	PROPN
ap-1350	134	9	,	,	PUNCT
ap-1350	134	10	e.	e.	PROPN
ap-1350	134	11	:	:	PUNCT
ap-1350	134	12	hilbert	hilbert	NOUN
ap-1350	134	13	space	space	NOUN
ap-1350	134	14	representations	representation	NOUN
ap-1350	134	15	of	of	ADP
ap-1350	134	16	cross	cross	NOUN
ap-1350	134	17	product	product	NOUN
ap-1350	134	18	algebras	algebra	NOUN
ap-1350	134	19	.	.	PUNCT
ap-1350	135	1	j.	j.	PROPN
ap-1350	135	2	funct	funct	PROPN
ap-1350	135	3	.	.	PUNCT
ap-1350	136	1	anal	anal	PROPN
ap-1350	136	2	.	.	PUNCT
ap-1350	137	1	200	200	NUM
ap-1350	137	2	(	(	PUNCT
ap-1350	137	3	2	2	NUM
ap-1350	137	4	)	)	PUNCT
ap-1350	137	5	,	,	PUNCT
ap-1350	137	6	2003	2003	NUM
ap-1350	137	7	,	,	PUNCT
ap-1350	137	8	p.	p.	NOUN
ap-1350	137	9	451–493	451–493	NUM
ap-1350	137	10	.	.	PUNCT
ap-1350	138	1	[	[	X
ap-1350	138	2	7	7	NUM
ap-1350	138	3	]	]	X
ap-1350	138	4	shklyarov	shklyarov	NOUN
ap-1350	138	5	,	,	PUNCT
ap-1350	138	6	d.	d.	PROPN
ap-1350	138	7	l.	l.	PROPN
ap-1350	138	8	,	,	PUNCT
ap-1350	138	9	sinel’shchikov	sinel’shchikov	PROPN
ap-1350	138	10	,	,	PUNCT
ap-1350	138	11	s.	s.	PROPN
ap-1350	138	12	d.	d.	PROPN
ap-1350	138	13	,	,	PUNCT
ap-1350	138	14	vaksman	vaksman	NOUN
ap-1350	138	15	,	,	PUNCT
ap-1350	138	16	l.	l.	PROPN
ap-1350	138	17	l.	l.	PROPN
ap-1350	138	18	:	:	PUNCT
ap-1350	138	19	integral	integral	ADJ
ap-1350	138	20	representations	representation	NOUN
ap-1350	138	21	of	of	ADP
ap-1350	138	22	functions	function	NOUN
ap-1350	138	23	in	in	ADP
ap-1350	138	24	the	the	DET
ap-1350	138	25	quantum	quantum	NOUN
ap-1350	138	26	disk	disk	NOUN
ap-1350	138	27	.	.	PUNCT
ap-1350	139	1	i.	i.	PROPN
ap-1350	139	2	(	(	PUNCT
ap-1350	139	3	russian	russian	ADJ
ap-1350	139	4	)	)	PUNCT
ap-1350	139	5	mat	mat	PROPN
ap-1350	139	6	.	.	PUNCT
ap-1350	139	7	fiz	fiz	PROPN
ap-1350	139	8	.	.	PUNCT
ap-1350	140	1	anal	anal	PROPN
ap-1350	140	2	.	.	PUNCT
ap-1350	141	1	geom	geom	PROPN
ap-1350	141	2	.	.	PUNCT
ap-1350	142	1	4	4	NUM
ap-1350	142	2	(	(	PUNCT
ap-1350	142	3	3	3	NUM
ap-1350	142	4	)	)	PUNCT
ap-1350	142	5	,	,	PUNCT
ap-1350	142	6	1997	1997	NUM
ap-1350	142	7	,	,	PUNCT
ap-1350	142	8	p.	p.	NOUN
ap-1350	142	9	286–308	286–308	NUM
ap-1350	142	10	.	.	PUNCT
ap-1350	142	11	quantum	quantum	ADJ
ap-1350	142	12	matrix	matrix	NOUN
ap-1350	142	13	balls	ball	NOUN
ap-1350	142	14	:	:	PUNCT
ap-1350	142	15	differential	differential	ADJ
ap-1350	142	16	and	and	CCONJ
ap-1350	142	17	integral	integral	ADJ
ap-1350	142	18	calculi	calculi	NOUN
ap-1350	142	19	.	.	PUNCT
ap-1350	143	1	arxiv	arxiv	NOUN
ap-1350	143	2	:	:	PUNCT
ap-1350	144	1	math.qa/9905035	math.qa/9905035	PROPN
ap-1350	144	2	.	.	PUNCT
ap-1350	145	1	osvaldo	osvaldo	PROPN
ap-1350	145	2	osuna	osuna	PROPN
ap-1350	145	3	castro	castro	PROPN
ap-1350	145	4	e	e	NOUN
ap-1350	145	5	-	-	NOUN
ap-1350	145	6	mail	mail	NOUN
ap-1350	145	7	:	:	PUNCT
ap-1350	145	8	osvaldo@ifm.umich.mx	osvaldo@ifm.umich.mx	PROPN
ap-1350	145	9	department	department	PROPN
ap-1350	145	10	of	of	ADP
ap-1350	145	11	physics	physics	PROPN
ap-1350	145	12	and	and	CCONJ
ap-1350	145	13	mathematics	mathematics	PROPN
ap-1350	145	14	university	university	PROPN
ap-1350	145	15	of	of	ADP
ap-1350	145	16	michoacan	michoacan	PROPN
ap-1350	145	17	morelia	morelia	PROPN
ap-1350	145	18	,	,	PUNCT
ap-1350	145	19	mexico	mexico	PROPN
ap-1350	145	20	elmar	elmar	PROPN
ap-1350	145	21	wagner	wagner	PROPN
ap-1350	145	22	e	e	PROPN
ap-1350	145	23	-	-	NOUN
ap-1350	145	24	mail	mail	NOUN
ap-1350	145	25	:	:	PUNCT
ap-1350	145	26	elmar@ifm.umich.mx	elmar@ifm.umich.mx	PROPN
ap-1350	145	27	department	department	PROPN
ap-1350	145	28	of	of	ADP
ap-1350	145	29	physics	physics	PROPN
ap-1350	145	30	and	and	CCONJ
ap-1350	145	31	mathematics	mathematics	PROPN
ap-1350	145	32	university	university	PROPN
ap-1350	145	33	of	of	ADP
ap-1350	145	34	michoacan	michoacan	PROPN
ap-1350	145	35	morelia	morelia	PROPN
ap-1350	145	36	,	,	PUNCT
ap-1350	145	37	mexico	mexico	PROPN
ap-1350	145	38	32	32	NUM