id	sid	tid	token	lemma	pos
ap-1179	1	1	ap-3-10.dvi	ap-3-10.dvi	PROPN
ap-1179	1	2	acta	acta	PROPN
ap-1179	1	3	polytechnica	polytechnica	PROPN
ap-1179	1	4	vol	vol	NOUN
ap-1179	1	5	.	.	PROPN
ap-1179	2	1	50	50	NUM
ap-1179	2	2	no	no	NOUN
ap-1179	2	3	.	.	PUNCT
ap-1179	3	1	3/2010	3/2010	NUM
ap-1179	3	2	topics	topic	NOUN
ap-1179	3	3	on	on	ADP
ap-1179	3	4	n	n	CCONJ
ap-1179	3	5	-	-	PUNCT
ap-1179	3	6	ary	ary	ADJ
ap-1179	3	7	algebraic	algebraic	PROPN
ap-1179	3	8	structures	structure	NOUN
ap-1179	3	9	j.	j.	PROPN
ap-1179	3	10	a.	a.	PROPN
ap-1179	3	11	de	de	PROPN
ap-1179	3	12	azcárraga	azcárraga	PROPN
ap-1179	3	13	,	,	PUNCT
ap-1179	3	14	j.	j.	PROPN
ap-1179	3	15	m.	m.	PROPN
ap-1179	3	16	izquierdo	izquierdo	PROPN
ap-1179	3	17	abstract	abstract	NOUN
ap-1179	3	18	we	we	PRON
ap-1179	3	19	review	review	VERB
ap-1179	3	20	the	the	DET
ap-1179	3	21	basic	basic	ADJ
ap-1179	3	22	definitions	definition	NOUN
ap-1179	3	23	and	and	CCONJ
ap-1179	3	24	properties	property	NOUN
ap-1179	3	25	of	of	ADP
ap-1179	3	26	two	two	NUM
ap-1179	3	27	types	type	NOUN
ap-1179	3	28	of	of	ADP
ap-1179	3	29	n	n	CCONJ
ap-1179	3	30	-	-	PUNCT
ap-1179	3	31	ary	ary	PROPN
ap-1179	3	32	structures	structure	NOUN
ap-1179	3	33	,	,	PUNCT
ap-1179	3	34	the	the	DET
ap-1179	3	35	generalized	generalized	ADJ
ap-1179	3	36	lie	lie	NOUN
ap-1179	3	37	algebras	algebra	NOUN
ap-1179	3	38	(	(	PUNCT
ap-1179	3	39	gla	gla	PROPN
ap-1179	3	40	)	)	PUNCT
ap-1179	3	41	and	and	CCONJ
ap-1179	3	42	the	the	DET
ap-1179	3	43	filippov	filippov	NOUN
ap-1179	3	44	(	(	PUNCT
ap-1179	3	45	≡	≡	PROPN
ap-1179	3	46	n	n	CCONJ
ap-1179	3	47	-	-	PUNCT
ap-1179	3	48	lie	lie	NOUN
ap-1179	3	49	)	)	PUNCT
ap-1179	3	50	algebras	algebra	NOUN
ap-1179	3	51	(	(	PUNCT
ap-1179	3	52	fa	fa	NOUN
ap-1179	3	53	)	)	PUNCT
ap-1179	3	54	,	,	PUNCT
ap-1179	3	55	as	as	ADV
ap-1179	3	56	well	well	ADV
ap-1179	3	57	as	as	ADP
ap-1179	3	58	those	those	PRON
ap-1179	3	59	of	of	ADP
ap-1179	3	60	their	their	PRON
ap-1179	3	61	poisson	poisson	NOUN
ap-1179	3	62	counterparts	counterpart	NOUN
ap-1179	3	63	,	,	PUNCT
ap-1179	3	64	the	the	DET
ap-1179	3	65	generalized	generalized	ADJ
ap-1179	3	66	poisson	poisson	NOUN
ap-1179	3	67	(	(	PUNCT
ap-1179	3	68	gps	gps	PROPN
ap-1179	3	69	)	)	PUNCT
ap-1179	3	70	and	and	CCONJ
ap-1179	3	71	nambu	nambu	NOUN
ap-1179	3	72	-	-	PUNCT
ap-1179	3	73	poisson	poisson	NOUN
ap-1179	3	74	(	(	PUNCT
ap-1179	3	75	n	n	CCONJ
ap-1179	3	76	-	-	PUNCT
ap-1179	3	77	p	p	NOUN
ap-1179	3	78	)	)	PUNCT
ap-1179	3	79	structures	structure	NOUN
ap-1179	3	80	.	.	PUNCT
ap-1179	4	1	we	we	PRON
ap-1179	4	2	describe	describe	VERB
ap-1179	4	3	the	the	DET
ap-1179	4	4	filippov	filippov	ADJ
ap-1179	4	5	algebra	algebra	NOUN
ap-1179	4	6	cohomology	cohomology	NOUN
ap-1179	4	7	complexes	complexe	VERB
ap-1179	4	8	relevant	relevant	ADJ
ap-1179	4	9	for	for	ADP
ap-1179	4	10	the	the	DET
ap-1179	4	11	central	central	ADJ
ap-1179	4	12	extensions	extension	NOUN
ap-1179	4	13	and	and	CCONJ
ap-1179	4	14	infinitesimal	infinitesimal	ADJ
ap-1179	4	15	deformations	deformation	NOUN
ap-1179	4	16	of	of	ADP
ap-1179	4	17	fas	fas	NOUN
ap-1179	4	18	.	.	PUNCT
ap-1179	5	1	it	it	PRON
ap-1179	5	2	is	be	AUX
ap-1179	5	3	seen	see	VERB
ap-1179	5	4	that	that	SCONJ
ap-1179	5	5	semisimple	semisimple	PROPN
ap-1179	5	6	fas	fas	PROPN
ap-1179	5	7	do	do	AUX
ap-1179	5	8	not	not	PART
ap-1179	5	9	admit	admit	VERB
ap-1179	5	10	central	central	ADJ
ap-1179	5	11	extensions	extension	NOUN
ap-1179	5	12	and	and	CCONJ
ap-1179	5	13	,	,	PUNCT
ap-1179	5	14	moreover	moreover	ADV
ap-1179	5	15	,	,	PUNCT
ap-1179	5	16	that	that	SCONJ
ap-1179	5	17	they	they	PRON
ap-1179	5	18	are	be	AUX
ap-1179	5	19	rigid	rigid	ADJ
ap-1179	5	20	.	.	PUNCT
ap-1179	6	1	this	this	PRON
ap-1179	6	2	extends	extend	VERB
ap-1179	6	3	whitehead	whitehead	PROPN
ap-1179	6	4	’s	’s	PART
ap-1179	6	5	lemma	lemma	PROPN
ap-1179	6	6	to	to	ADP
ap-1179	6	7	all	all	DET
ap-1179	6	8	n	n	PRON
ap-1179	6	9	≥	≥	NUM
ap-1179	6	10	2	2	NUM
ap-1179	6	11	,	,	PUNCT
ap-1179	6	12	n	n	NOUN
ap-1179	6	13	=	=	SYM
ap-1179	6	14	2	2	NUM
ap-1179	6	15	being	be	AUX
ap-1179	6	16	the	the	DET
ap-1179	6	17	original	original	ADJ
ap-1179	6	18	lie	lie	NOUN
ap-1179	6	19	algebra	algebra	NOUN
ap-1179	6	20	case	case	NOUN
ap-1179	6	21	.	.	PUNCT
ap-1179	7	1	some	some	DET
ap-1179	7	2	comments	comment	NOUN
ap-1179	7	3	on	on	ADP
ap-1179	7	4	n	n	CCONJ
ap-1179	7	5	-	-	PUNCT
ap-1179	7	6	leibniz	leibniz	NOUN
ap-1179	7	7	algebras	algebras	PROPN
ap-1179	7	8	are	be	AUX
ap-1179	7	9	also	also	ADV
ap-1179	7	10	made	make	VERB
ap-1179	7	11	.	.	PUNCT
ap-1179	8	1	1	1	NUM
ap-1179	8	2	introduction	introduction	NOUN
ap-1179	8	3	the	the	DET
ap-1179	8	4	jacobi	jacobi	PROPN
ap-1179	8	5	identity	identity	NOUN
ap-1179	8	6	(	(	PUNCT
ap-1179	8	7	ji	ji	NOUN
ap-1179	8	8	)	)	PUNCT
ap-1179	8	9	for	for	ADP
ap-1179	8	10	lie	lie	NOUN
ap-1179	8	11	algebras	algebras	PROPN
ap-1179	8	12	g	g	PROPN
ap-1179	8	13	,	,	PUNCT
ap-1179	8	14	[	[	X
ap-1179	8	15	x	x	X
ap-1179	8	16	,	,	PUNCT
ap-1179	8	17	[	[	X
ap-1179	8	18	y	y	NOUN
ap-1179	8	19	,	,	PUNCT
ap-1179	8	20	z]]+	z]]+	PROPN
ap-1179	9	1	[	[	X
ap-1179	9	2	y	y	NOUN
ap-1179	9	3	,	,	PUNCT
ap-1179	9	4	[	[	X
ap-1179	9	5	z	z	X
ap-1179	9	6	,	,	PUNCT
ap-1179	9	7	x	x	X
ap-1179	9	8	]	]	X
ap-1179	9	9	]	]	PUNCT
ap-1179	10	1	+	+	CCONJ
ap-1179	11	1	[	[	X
ap-1179	11	2	z	z	X
ap-1179	11	3	,	,	PUNCT
ap-1179	11	4	[	[	X
ap-1179	11	5	x	x	X
ap-1179	11	6	,	,	PUNCT
ap-1179	11	7	y	y	PROPN
ap-1179	11	8	]	]	X
ap-1179	11	9	]	]	X
ap-1179	11	10	=	=	SYM
ap-1179	11	11	0	0	NUM
ap-1179	11	12	,	,	PUNCT
ap-1179	11	13	may	may	AUX
ap-1179	11	14	be	be	AUX
ap-1179	11	15	looked	look	VERB
ap-1179	11	16	at	at	ADP
ap-1179	11	17	in	in	ADP
ap-1179	11	18	two	two	NUM
ap-1179	11	19	ways	way	NOUN
ap-1179	11	20	.	.	PUNCT
ap-1179	12	1	first	first	ADV
ap-1179	12	2	,	,	PUNCT
ap-1179	12	3	one	one	PRON
ap-1179	12	4	may	may	AUX
ap-1179	12	5	see	see	VERB
ap-1179	12	6	it	it	PRON
ap-1179	12	7	as	as	ADP
ap-1179	12	8	a	a	DET
ap-1179	12	9	consequence	consequence	NOUN
ap-1179	12	10	of	of	ADP
ap-1179	12	11	the	the	DET
ap-1179	12	12	associativity	associativity	NOUN
ap-1179	12	13	of	of	ADP
ap-1179	12	14	the	the	DET
ap-1179	12	15	composition	composition	NOUN
ap-1179	12	16	of	of	ADP
ap-1179	12	17	generators	generator	NOUN
ap-1179	12	18	in	in	ADP
ap-1179	12	19	the	the	DET
ap-1179	12	20	lie	lie	NOUN
ap-1179	12	21	bracket	bracket	NOUN
ap-1179	12	22	.	.	PUNCT
ap-1179	13	1	secondly	secondly	ADV
ap-1179	13	2	,	,	PUNCT
ap-1179	13	3	it	it	PRON
ap-1179	13	4	may	may	AUX
ap-1179	13	5	be	be	AUX
ap-1179	13	6	viewed	view	VERB
ap-1179	13	7	as	as	ADP
ap-1179	13	8	the	the	DET
ap-1179	13	9	statement	statement	NOUN
ap-1179	13	10	that	that	SCONJ
ap-1179	13	11	the	the	DET
ap-1179	13	12	adjoint	adjoint	NOUN
ap-1179	13	13	map	map	NOUN
ap-1179	13	14	is	be	AUX
ap-1179	13	15	a	a	DET
ap-1179	13	16	derivation	derivation	NOUN
ap-1179	13	17	of	of	ADP
ap-1179	13	18	the	the	DET
ap-1179	13	19	lie	lie	NOUN
ap-1179	13	20	algebra	algebra	NOUN
ap-1179	13	21	,	,	PUNCT
ap-1179	13	22	adx	adx	X
ap-1179	13	23	[	[	X
ap-1179	13	24	y	y	PROPN
ap-1179	13	25	,	,	PUNCT
ap-1179	13	26	z	z	X
ap-1179	13	27	]	]	X
ap-1179	13	28	=	=	PUNCT
ap-1179	14	1	[	[	X
ap-1179	14	2	adx	adx	PROPN
ap-1179	14	3	y	y	PROPN
ap-1179	14	4	,	,	PUNCT
ap-1179	14	5	z	z	X
ap-1179	14	6	]	]	X
ap-1179	14	7	+	+	CCONJ
ap-1179	14	8	[	[	X
ap-1179	14	9	y	y	NOUN
ap-1179	14	10	,	,	PUNCT
ap-1179	14	11	adx	adx	PROPN
ap-1179	14	12	z	z	NOUN
ap-1179	14	13	]	]	X
ap-1179	14	14	.	.	PUNCT
ap-1179	15	1	a	a	DET
ap-1179	15	2	natural	natural	ADJ
ap-1179	15	3	problem	problem	NOUN
ap-1179	15	4	is	be	AUX
ap-1179	15	5	to	to	PART
ap-1179	15	6	consider	consider	VERB
ap-1179	15	7	n	n	CCONJ
ap-1179	15	8	-	-	PUNCT
ap-1179	15	9	ary	ary	NOUN
ap-1179	15	10	generalizations	generalization	NOUN
ap-1179	15	11	,	,	PUNCT
ap-1179	15	12	i.e.	i.e.	X
ap-1179	15	13	to	to	PART
ap-1179	15	14	look	look	VERB
ap-1179	15	15	for	for	ADP
ap-1179	15	16	the	the	DET
ap-1179	15	17	possible	possible	ADJ
ap-1179	15	18	characteristic	characteristic	ADJ
ap-1179	15	19	identities	identity	NOUN
ap-1179	15	20	that	that	SCONJ
ap-1179	15	21	a	a	DET
ap-1179	15	22	n	n	CCONJ
ap-1179	15	23	-	-	PUNCT
ap-1179	15	24	ary	ary	NOUN
ap-1179	15	25	bracket	bracket	NOUN
ap-1179	15	26	,	,	PUNCT
ap-1179	15	27	(	(	PUNCT
ap-1179	15	28	x1	x1	PROPN
ap-1179	15	29	,	,	PUNCT
ap-1179	15	30	.	.	PUNCT
ap-1179	15	31	.	.	PUNCT
ap-1179	15	32	.	.	PUNCT
ap-1179	16	1	,	,	PUNCT
ap-1179	16	2	xn	xn	X
ap-1179	16	3	)	)	PUNCT
ap-1179	16	4	∈	∈	PROPN
ap-1179	17	1	g×	g×	X
ap-1179	17	2	.	.	PUNCT
ap-1179	17	3	.	.	PUNCT
ap-1179	18	1	.×g	.×g	PROPN
ap-1179	18	2	�	�	PROPN
ap-1179	19	1	→	→	SYM
ap-1179	20	1	[	[	X
ap-1179	20	2	x1	x1	PROPN
ap-1179	20	3	,	,	PUNCT
ap-1179	20	4	.	.	PUNCT
ap-1179	20	5	.	.	PUNCT
ap-1179	21	1	.	.	PUNCT
ap-1179	22	1	,	,	PUNCT
ap-1179	22	2	xn	xn	X
ap-1179	22	3	]	]	X
ap-1179	22	4	∈	∈	PROPN
ap-1179	22	5	g	g	PROPN
ap-1179	22	6	,	,	PUNCT
ap-1179	22	7	(	(	PUNCT
ap-1179	22	8	1.1	1.1	NUM
ap-1179	22	9	)	)	PUNCT
ap-1179	22	10	antisymmetric	antisymmetric	VERB
ap-1179	22	11	in	in	ADP
ap-1179	22	12	its	its	PRON
ap-1179	22	13	arguments	argument	NOUN
ap-1179	22	14	(	(	PUNCT
ap-1179	22	15	this	this	PRON
ap-1179	22	16	may	may	AUX
ap-1179	22	17	be	be	AUX
ap-1179	22	18	relaxed	relax	VERB
ap-1179	22	19	;	;	PUNCT
ap-1179	22	20	see	see	VERB
ap-1179	22	21	last	last	ADJ
ap-1179	22	22	section	section	NOUN
ap-1179	22	23	)	)	PUNCT
ap-1179	22	24	,	,	PUNCT
ap-1179	22	25	may	may	AUX
ap-1179	22	26	satisfy	satisfy	VERB
ap-1179	22	27	.	.	PUNCT
ap-1179	23	1	when	when	SCONJ
ap-1179	23	2	n	n	X
ap-1179	23	3	>	>	SYM
ap-1179	23	4	2	2	NUM
ap-1179	23	5	two	two	NUM
ap-1179	23	6	generalizations	generalization	NOUN
ap-1179	23	7	of	of	ADP
ap-1179	23	8	the	the	DET
ap-1179	23	9	ji	ji	PROPN
ap-1179	23	10	suggest	suggest	VERB
ap-1179	23	11	themselves	themselves	PRON
ap-1179	23	12	.	.	PUNCT
ap-1179	24	1	these	these	PRON
ap-1179	24	2	are	be	AUX
ap-1179	24	3	:	:	PUNCT
ap-1179	24	4	(	(	PUNCT
ap-1179	24	5	a	a	X
ap-1179	24	6	)	)	PUNCT
ap-1179	24	7	higher	high	ADJ
ap-1179	24	8	order	order	NOUN
ap-1179	24	9	lie	lie	NOUN
ap-1179	24	10	algebras	algebra	NOUN
ap-1179	24	11	or	or	CCONJ
ap-1179	24	12	generalized	generalized	ADJ
ap-1179	24	13	lie	lie	NOUN
ap-1179	24	14	algebras	algebra	NOUN
ap-1179	24	15	(	(	PUNCT
ap-1179	24	16	gla	gla	PROPN
ap-1179	24	17	)	)	PUNCT
ap-1179	24	18	g	g	PROPN
ap-1179	24	19	,	,	PUNCT
ap-1179	24	20	proposed	propose	VERB
ap-1179	24	21	independently	independently	ADV
ap-1179	24	22	in	in	ADP
ap-1179	24	23	[	[	X
ap-1179	24	24	1	1	NUM
ap-1179	24	25	,	,	PUNCT
ap-1179	24	26	2	2	NUM
ap-1179	24	27	,	,	PUNCT
ap-1179	24	28	3	3	NUM
ap-1179	24	29	]	]	PUNCT
ap-1179	24	30	and	and	CCONJ
ap-1179	24	31	[	[	X
ap-1179	24	32	4	4	NUM
ap-1179	24	33	,	,	PUNCT
ap-1179	24	34	5	5	NUM
ap-1179	24	35	,	,	PUNCT
ap-1179	24	36	6	6	NUM
ap-1179	24	37	,	,	PUNCT
ap-1179	24	38	7	7	NUM
ap-1179	24	39	]	]	PUNCT
ap-1179	24	40	.	.	PUNCT
ap-1179	25	1	their	their	PRON
ap-1179	25	2	bracket	bracket	NOUN
ap-1179	25	3	is	be	AUX
ap-1179	25	4	defined	define	VERB
ap-1179	25	5	by	by	ADP
ap-1179	25	6	the	the	DET
ap-1179	25	7	full	full	ADJ
ap-1179	25	8	antisymmetrization	antisymmetrization	NOUN
ap-1179	26	1	[	[	X
ap-1179	26	2	xi1	xi1	PROPN
ap-1179	26	3	,	,	PUNCT
ap-1179	26	4	.	.	PUNCT
ap-1179	26	5	.	.	PUNCT
ap-1179	26	6	.	.	PUNCT
ap-1179	27	1	,	,	PUNCT
ap-1179	27	2	xin	xin	PROPN
ap-1179	27	3	]	]	PUNCT
ap-1179	28	1	:	:	PUNCT
ap-1179	28	2	=	=	NUM
ap-1179	28	3	∑	∑	PUNCT
ap-1179	28	4	σ∈sn	σ∈sn	PROPN
ap-1179	28	5	(	(	PUNCT
ap-1179	28	6	−1)π(σ)xiσ(1	−1)π(σ)xiσ(1	PROPN
ap-1179	28	7	)	)	PUNCT
ap-1179	28	8	.	.	PUNCT
ap-1179	28	9	.	.	PUNCT
ap-1179	28	10	.	.	PUNCT
ap-1179	29	1	xiσ(n	xiσ(n	X
ap-1179	29	2	)	)	PUNCT
ap-1179	29	3	.	.	PUNCT
ap-1179	30	1	(	(	PUNCT
ap-1179	30	2	1.2	1.2	NUM
ap-1179	30	3	)	)	PUNCT
ap-1179	30	4	for	for	ADP
ap-1179	30	5	n	n	PRON
ap-1179	30	6	even	even	ADV
ap-1179	30	7	,	,	PUNCT
ap-1179	30	8	this	this	DET
ap-1179	30	9	definition	definition	NOUN
ap-1179	30	10	implies	imply	VERB
ap-1179	30	11	the	the	DET
ap-1179	30	12	generalized	generalized	ADJ
ap-1179	30	13	jacobi	jacobi	NOUN
ap-1179	30	14	identity	identity	NOUN
ap-1179	30	15	(	(	PUNCT
ap-1179	30	16	gji)∑	gji)∑	PROPN
ap-1179	30	17	σ∈s2n−1	σ∈s2n−1	PROPN
ap-1179	30	18	(	(	PUNCT
ap-1179	30	19	−1)π(σ	−1)π(σ	NOUN
ap-1179	30	20	)	)	PUNCT
ap-1179	30	21	[	[	PUNCT
ap-1179	30	22	[	[	X
ap-1179	30	23	xiσ(1	xiσ(1	NOUN
ap-1179	30	24	)	)	PUNCT
ap-1179	30	25	,	,	PUNCT
ap-1179	30	26	.	.	PUNCT
ap-1179	30	27	.	.	PUNCT
ap-1179	31	1	.	.	PUNCT
ap-1179	32	1	,	,	PUNCT
ap-1179	32	2	xiσ(n	xiσ(n	X
ap-1179	32	3	)	)	PUNCT
ap-1179	32	4	]	]	PUNCT
ap-1179	32	5	,	,	PUNCT
ap-1179	32	6	xiσ(n+1	xiσ(n+1	PROPN
ap-1179	32	7	)	)	PUNCT
ap-1179	32	8	.	.	PUNCT
ap-1179	32	9	.	.	PUNCT
ap-1179	33	1	.	.	PUNCT
ap-1179	34	1	,	,	PUNCT
ap-1179	34	2	xiσ(2n−1	xiσ(2n−1	PROPN
ap-1179	34	3	)	)	PUNCT
ap-1179	34	4	]	]	PUNCT
ap-1179	35	1	=	=	PUNCT
ap-1179	35	2	0	0	PUNCT
ap-1179	35	3	(	(	PUNCT
ap-1179	35	4	1.3	1.3	NUM
ap-1179	35	5	)	)	PUNCT
ap-1179	35	6	which	which	PRON
ap-1179	35	7	follows	follow	VERB
ap-1179	35	8	from	from	ADP
ap-1179	35	9	the	the	DET
ap-1179	35	10	associtivity	associtivity	NOUN
ap-1179	35	11	of	of	ADP
ap-1179	35	12	the	the	DET
ap-1179	35	13	products	product	NOUN
ap-1179	35	14	in	in	ADP
ap-1179	35	15	(	(	PUNCT
ap-1179	35	16	1.2	1.2	NUM
ap-1179	35	17	)	)	PUNCT
ap-1179	35	18	(	(	PUNCT
ap-1179	35	19	for	for	ADP
ap-1179	35	20	n	n	PRON
ap-1179	35	21	odd	odd	ADJ
ap-1179	35	22	,	,	PUNCT
ap-1179	35	23	the	the	DET
ap-1179	35	24	r	r	NOUN
ap-1179	35	25	·	·	PUNCT
ap-1179	35	26	h	h	NOUN
ap-1179	35	27	·	·	PUNCT
ap-1179	35	28	s	s	PART
ap-1179	35	29	is	be	AUX
ap-1179	35	30	n!(n−	n!(n−	ADJ
ap-1179	35	31	1)![xi1	1)![xi1	NUM
ap-1179	35	32	,	,	PUNCT
ap-1179	35	33	.	.	PUNCT
ap-1179	35	34	.	.	PUNCT
ap-1179	35	35	.	.	PUNCT
ap-1179	36	1	,	,	PUNCT
ap-1179	36	2	xi2n−1	xi2n−1	PUNCT
ap-1179	36	3	]	]	PUNCT
ap-1179	36	4	rather	rather	ADV
ap-1179	36	5	than	than	ADP
ap-1179	36	6	zero	zero	NUM
ap-1179	36	7	)	)	PUNCT
ap-1179	36	8	.	.	PUNCT
ap-1179	37	1	chosen	choose	VERB
ap-1179	37	2	a	a	DET
ap-1179	37	3	basis	basis	NOUN
ap-1179	37	4	of	of	ADP
ap-1179	37	5	g	g	NOUN
ap-1179	37	6	,	,	PUNCT
ap-1179	37	7	the	the	DET
ap-1179	37	8	bracket	bracket	NOUN
ap-1179	37	9	may	may	AUX
ap-1179	37	10	be	be	AUX
ap-1179	37	11	written	write	VERB
ap-1179	37	12	as	as	ADP
ap-1179	37	13	[	[	X
ap-1179	37	14	xi1	xi1	PROPN
ap-1179	37	15	,	,	PUNCT
ap-1179	37	16	.	.	PUNCT
ap-1179	37	17	.	.	PUNCT
ap-1179	37	18	.	.	PUNCT
ap-1179	38	1	,	,	PUNCT
ap-1179	38	2	xi2p	xi2p	X
ap-1179	38	3	]	]	X
ap-1179	39	1	=	=	PUNCT
ap-1179	39	2	ωi1	ωi1	PROPN
ap-1179	39	3	...	...	PUNCT
ap-1179	39	4	i2p	i2p	PROPN
ap-1179	39	5	jxj	jxj	PROPN
ap-1179	39	6	,	,	PUNCT
ap-1179	39	7	where	where	SCONJ
ap-1179	39	8	the	the	DET
ap-1179	39	9	ωi1	ωi1	PROPN
ap-1179	39	10	...	...	PUNCT
ap-1179	39	11	i2p	i2p	PROPN
ap-1179	39	12	j	j	PROPN
ap-1179	39	13	are	be	AUX
ap-1179	39	14	the	the	DET
ap-1179	39	15	structure	structure	NOUN
ap-1179	39	16	constants	constant	NOUN
ap-1179	39	17	of	of	ADP
ap-1179	39	18	the	the	DET
ap-1179	39	19	gla	gla	PROPN
ap-1179	39	20	.	.	PUNCT
ap-1179	40	1	(	(	PUNCT
ap-1179	40	2	b	b	X
ap-1179	40	3	)	)	PUNCT
ap-1179	40	4	n	n	CCONJ
ap-1179	40	5	-	-	PUNCT
ap-1179	40	6	lie	lie	NOUN
ap-1179	40	7	or	or	CCONJ
ap-1179	40	8	filippov	filippov	NOUN
ap-1179	40	9	algebras	algebra	NOUN
ap-1179	40	10	(	(	PUNCT
ap-1179	40	11	fa	fa	NOUN
ap-1179	40	12	)	)	PUNCT
ap-1179	40	13	g.	g.	NOUN
ap-1179	40	14	the	the	DET
ap-1179	40	15	characteristic	characteristic	ADJ
ap-1179	40	16	identity	identity	NOUN
ap-1179	40	17	that	that	PRON
ap-1179	40	18	generalizes	generalize	VERB
ap-1179	40	19	the	the	DET
ap-1179	40	20	n	n	NOUN
ap-1179	40	21	=	=	SYM
ap-1179	40	22	2	2	NUM
ap-1179	40	23	ji	ji	NOUN
ap-1179	40	24	is	be	AUX
ap-1179	40	25	the	the	DET
ap-1179	40	26	filippov	filippov	ADJ
ap-1179	40	27	identity	identity	NOUN
ap-1179	40	28	(	(	PUNCT
ap-1179	40	29	fi	fi	NOUN
ap-1179	40	30	)	)	PUNCT
ap-1179	41	1	[	[	X
ap-1179	41	2	8	8	NUM
ap-1179	41	3	]	]	PUNCT
ap-1179	42	1	[	[	X
ap-1179	42	2	x1	x1	X
ap-1179	42	3	,	,	PUNCT
ap-1179	42	4	.	.	PUNCT
ap-1179	42	5	.	.	PUNCT
ap-1179	43	1	.	.	PUNCT
ap-1179	44	1	,	,	PUNCT
ap-1179	44	2	xn−1	xn−1	PROPN
ap-1179	44	3	,	,	PUNCT
ap-1179	44	4	[	[	X
ap-1179	44	5	y1	y1	X
ap-1179	44	6	,	,	PUNCT
ap-1179	44	7	.	.	PUNCT
ap-1179	44	8	.	.	PUNCT
ap-1179	44	9	.	.	PUNCT
ap-1179	45	1	yn	yn	PRON
ap-1179	45	2	]	]	X
ap-1179	45	3	]	]	X
ap-1179	45	4	=	=	SYM
ap-1179	45	5	n∑	n∑	X
ap-1179	45	6	a=1	a=1	X
ap-1179	46	1	[	[	X
ap-1179	46	2	y1	y1	NOUN
ap-1179	46	3	,	,	PUNCT
ap-1179	46	4	.	.	PUNCT
ap-1179	46	5	.	.	PUNCT
ap-1179	46	6	.	.	PUNCT
ap-1179	47	1	ya−1	ya−1	NOUN
ap-1179	47	2	,	,	PUNCT
ap-1179	47	3	[	[	X
ap-1179	47	4	x1	x1	X
ap-1179	47	5	,	,	PUNCT
ap-1179	47	6	.	.	PUNCT
ap-1179	47	7	.	.	PUNCT
ap-1179	47	8	.	.	PUNCT
ap-1179	48	1	,	,	PUNCT
ap-1179	48	2	xn−1	xn−1	PROPN
ap-1179	48	3	,	,	PUNCT
ap-1179	48	4	ya	ya	PROPN
ap-1179	48	5	]	]	X
ap-1179	48	6	,	,	PUNCT
ap-1179	48	7	ya+1	ya+1	PROPN
ap-1179	48	8	,	,	PUNCT
ap-1179	48	9	.	.	PUNCT
ap-1179	48	10	.	.	PUNCT
ap-1179	48	11	.	.	PUNCT
ap-1179	49	1	yn	yn	X
ap-1179	49	2	]	]	PUNCT
ap-1179	49	3	.	.	PUNCT
ap-1179	50	1	(	(	PUNCT
ap-1179	50	2	1.4	1.4	NUM
ap-1179	50	3	)	)	PUNCT
ap-1179	50	4	if	if	SCONJ
ap-1179	50	5	we	we	PRON
ap-1179	50	6	introduce	introduce	VERB
ap-1179	50	7	fundamental	fundamental	ADJ
ap-1179	50	8	objects	object	NOUN
ap-1179	50	9	x	x	PUNCT
ap-1179	50	10	=	=	SYM
ap-1179	50	11	(	(	PUNCT
ap-1179	50	12	x1	x1	PROPN
ap-1179	50	13	,	,	PUNCT
ap-1179	50	14	.	.	PUNCT
ap-1179	50	15	.	.	PUNCT
ap-1179	50	16	.	.	PUNCT
ap-1179	51	1	,	,	PUNCT
ap-1179	51	2	xn−1	xn−1	PROPN
ap-1179	51	3	)	)	PUNCT
ap-1179	51	4	antisymmetric	antisymmetric	VERB
ap-1179	51	5	in	in	ADP
ap-1179	51	6	their	their	PRON
ap-1179	51	7	(	(	PUNCT
ap-1179	51	8	n−1	n−1	PROPN
ap-1179	51	9	)	)	PUNCT
ap-1179	51	10	entries	entry	NOUN
ap-1179	51	11	and	and	CCONJ
ap-1179	51	12	acting	act	VERB
ap-1179	51	13	on	on	ADP
ap-1179	51	14	g	g	PROPN
ap-1179	51	15	as	as	SCONJ
ap-1179	51	16	x	x	X
ap-1179	51	17	·	·	PUNCT
ap-1179	51	18	z	z	PROPN
ap-1179	51	19	≡	≡	PROPN
ap-1179	51	20	adxz	adxz	VERB
ap-1179	51	21	:	:	PUNCT
ap-1179	51	22	=	=	PUNCT
ap-1179	52	1	[	[	X
ap-1179	52	2	x1	x1	X
ap-1179	52	3	,	,	PUNCT
ap-1179	52	4	.	.	PUNCT
ap-1179	52	5	.	.	PUNCT
ap-1179	53	1	.	.	PUNCT
ap-1179	54	1	,	,	PUNCT
ap-1179	54	2	xn−1	xn−1	PROPN
ap-1179	54	3	,	,	PUNCT
ap-1179	54	4	z	z	NOUN
ap-1179	54	5	]	]	X
ap-1179	54	6	(	(	PUNCT
ap-1179	54	7	1.5	1.5	NUM
ap-1179	54	8	)	)	PUNCT
ap-1179	54	9	∀z	∀z	NOUN
ap-1179	54	10	∈	∈	PROPN
ap-1179	54	11	g	g	PROPN
ap-1179	54	12	,	,	PUNCT
ap-1179	54	13	then	then	ADV
ap-1179	54	14	the	the	DET
ap-1179	54	15	fi	fi	NOUN
ap-1179	54	16	just	just	ADV
ap-1179	54	17	expresses	express	VERB
ap-1179	54	18	that	that	SCONJ
ap-1179	54	19	adx	adx	PROPN
ap-1179	54	20	is	be	AUX
ap-1179	54	21	a	a	DET
ap-1179	54	22	derivation	derivation	NOUN
ap-1179	54	23	of	of	ADP
ap-1179	54	24	the	the	DET
ap-1179	54	25	bracket	bracket	NOUN
ap-1179	54	26	,	,	PUNCT
ap-1179	54	27	adx[y1	adx[y1	PROPN
ap-1179	54	28	,	,	PUNCT
ap-1179	54	29	.	.	PUNCT
ap-1179	54	30	.	.	PUNCT
ap-1179	55	1	.	.	PUNCT
ap-1179	56	1	,	,	PUNCT
ap-1179	56	2	yn	yn	X
ap-1179	56	3	]	]	X
ap-1179	56	4	=	=	SYM
ap-1179	56	5	n∑	n∑	NOUN
ap-1179	56	6	a=1	a=1	X
ap-1179	57	1	[	[	X
ap-1179	57	2	y1	y1	NOUN
ap-1179	57	3	,	,	PUNCT
ap-1179	57	4	.	.	PUNCT
ap-1179	57	5	.	.	PUNCT
ap-1179	57	6	.	.	PUNCT
ap-1179	58	1	,	,	PUNCT
ap-1179	58	2	adxya	adxya	ADJ
ap-1179	58	3	,	,	PUNCT
ap-1179	58	4	.	.	PUNCT
ap-1179	58	5	.	.	PUNCT
ap-1179	59	1	.	.	PUNCT
ap-1179	60	1	,	,	PUNCT
ap-1179	60	2	yn	yn	X
ap-1179	60	3	]	]	PUNCT
ap-1179	60	4	.	.	PUNCT
ap-1179	61	1	(	(	PUNCT
ap-1179	61	2	1.6	1.6	NUM
ap-1179	61	3	)	)	PUNCT
ap-1179	61	4	chosen	choose	VERB
ap-1179	61	5	a	a	DET
ap-1179	61	6	basis	basis	NOUN
ap-1179	61	7	,	,	PUNCT
ap-1179	61	8	a	a	DET
ap-1179	61	9	fa	fa	NOUN
ap-1179	61	10	may	may	AUX
ap-1179	61	11	be	be	AUX
ap-1179	61	12	defined	define	VERB
ap-1179	61	13	through	through	ADP
ap-1179	61	14	its	its	PRON
ap-1179	61	15	structure	structure	NOUN
ap-1179	61	16	constants	constant	NOUN
ap-1179	61	17	,	,	PUNCT
ap-1179	62	1	[	[	X
ap-1179	62	2	xa1	xa1	X
ap-1179	62	3	.	.	PUNCT
ap-1179	62	4	.	.	PUNCT
ap-1179	62	5	.	.	PUNCT
ap-1179	63	1	xan	xan	PROPN
ap-1179	63	2	]	]	PUNCT
ap-1179	64	1	=	=	PUNCT
ap-1179	64	2	fa1	fa1	NOUN
ap-1179	64	3	...	...	PUNCT
ap-1179	64	4	an	an	PRON
ap-1179	65	1	d	d	NOUN
ap-1179	65	2	xd	xd	INTJ
ap-1179	65	3	,	,	PUNCT
ap-1179	65	4	(	(	PUNCT
ap-1179	65	5	1.7	1.7	NUM
ap-1179	65	6	)	)	PUNCT
ap-1179	65	7	and	and	CCONJ
ap-1179	65	8	the	the	DET
ap-1179	65	9	fi	fi	NOUN
ap-1179	65	10	is	be	AUX
ap-1179	65	11	written	write	VERB
ap-1179	65	12	as	as	ADP
ap-1179	65	13	fb1	fb1	NOUN
ap-1179	65	14	...	...	PUNCT
ap-1179	65	15	bn	bn	ADP
ap-1179	65	16	l	l	NOUN
ap-1179	65	17	fa1	fa1	NOUN
ap-1179	65	18	...	...	PUNCT
ap-1179	65	19	an−1l	an−1l	PROPN
ap-1179	65	20	s	s	PART
ap-1179	65	21	=	=	PUNCT
ap-1179	65	22	n∑	n∑	ADJ
ap-1179	65	23	k=1	k=1	X
ap-1179	65	24	fa1	fa1	NOUN
ap-1179	65	25	...	...	PUNCT
ap-1179	65	26	an−1bk	an−1bk	NUM
ap-1179	65	27	l	l	NOUN
ap-1179	65	28	fb1	fb1	NOUN
ap-1179	65	29	...	...	PUNCT
ap-1179	65	30	bk−1lbk+1	bk−1lbk+1	VERB
ap-1179	65	31	...	...	PUNCT
ap-1179	65	32	bn	bn	NOUN
ap-1179	65	33	s	s	PROPN
ap-1179	65	34	.	.	PUNCT
ap-1179	66	1	(	(	PUNCT
ap-1179	66	2	1.8	1.8	NUM
ap-1179	66	3	)	)	SYM
ap-1179	66	4	2	2	NUM
ap-1179	66	5	some	some	DET
ap-1179	66	6	definitions	definition	NOUN
ap-1179	66	7	and	and	CCONJ
ap-1179	66	8	properties	property	NOUN
ap-1179	66	9	of	of	ADP
ap-1179	66	10	fa	fa	NOUN
ap-1179	66	11	the	the	DET
ap-1179	66	12	definitions	definition	NOUN
ap-1179	66	13	of	of	ADP
ap-1179	66	14	ideals	ideal	NOUN
ap-1179	66	15	,	,	PUNCT
ap-1179	66	16	solvable	solvable	ADJ
ap-1179	66	17	ideals	ideal	NOUN
ap-1179	66	18	and	and	CCONJ
ap-1179	66	19	semisimple	semisimple	NOUN
ap-1179	66	20	algebras	algebra	NOUN
ap-1179	66	21	can	can	AUX
ap-1179	66	22	be	be	AUX
ap-1179	66	23	extended	extend	VERB
ap-1179	66	24	to	to	ADP
ap-1179	66	25	the	the	DET
ap-1179	66	26	n	n	NOUN
ap-1179	66	27	>	>	SYM
ap-1179	66	28	2	2	NUM
ap-1179	66	29	case	case	NOUN
ap-1179	66	30	as	as	SCONJ
ap-1179	66	31	follows	follow	VERB
ap-1179	66	32	[	[	X
ap-1179	66	33	9	9	NUM
ap-1179	66	34	]	]	PUNCT
ap-1179	66	35	.	.	PUNCT
ap-1179	67	1	a	a	DET
ap-1179	67	2	subalgebra	subalgebra	NOUN
ap-1179	67	3	i	i	PRON
ap-1179	67	4	of	of	ADP
ap-1179	67	5	g	g	PROPN
ap-1179	67	6	is	be	AUX
ap-1179	67	7	an	an	DET
ap-1179	67	8	ideal	ideal	NOUN
ap-1179	67	9	of	of	ADP
ap-1179	67	10	g	g	NOUN
ap-1179	67	11	if	if	SCONJ
ap-1179	67	12	[	[	X
ap-1179	67	13	x1	x1	X
ap-1179	67	14	,	,	PUNCT
ap-1179	67	15	.	.	PUNCT
ap-1179	67	16	.	.	PUNCT
ap-1179	67	17	.	.	PUNCT
ap-1179	68	1	,	,	PUNCT
ap-1179	68	2	xn−1	xn−1	PROPN
ap-1179	68	3	,	,	PUNCT
ap-1179	68	4	z	z	X
ap-1179	68	5	]	]	X
ap-1179	69	1	⊂	⊂	PROPN
ap-1179	69	2	i	i	PRON
ap-1179	69	3	(	(	PUNCT
ap-1179	69	4	2.9	2.9	NUM
ap-1179	69	5	)	)	PUNCT
ap-1179	69	6	∀x1	∀x1	NOUN
ap-1179	69	7	,	,	PUNCT
ap-1179	69	8	.	.	PUNCT
ap-1179	69	9	.	.	PUNCT
ap-1179	69	10	.	.	PUNCT
ap-1179	70	1	,	,	PUNCT
ap-1179	70	2	xn−1	xn−1	PROPN
ap-1179	70	3	∈	∈	PROPN
ap-1179	70	4	g	g	PROPN
ap-1179	70	5	,	,	PUNCT
ap-1179	70	6	∀z	∀z	PROPN
ap-1179	70	7	∈	∈	PROPN
ap-1179	71	1	i	i	PRON
ap-1179	71	2	.	.	PUNCT
ap-1179	72	1	to	to	PART
ap-1179	72	2	appear	appear	VERB
ap-1179	72	3	in	in	ADP
ap-1179	72	4	the	the	DET
ap-1179	72	5	proceedings	proceeding	NOUN
ap-1179	72	6	of	of	ADP
ap-1179	72	7	the	the	DET
ap-1179	72	8	meeting	meeting	NOUN
ap-1179	72	9	selected	select	VERB
ap-1179	72	10	topics	topic	NOUN
ap-1179	72	11	in	in	ADP
ap-1179	72	12	mathematical	mathematical	ADJ
ap-1179	72	13	and	and	CCONJ
ap-1179	72	14	particle	particle	NOUN
ap-1179	72	15	physics	physics	NOUN
ap-1179	72	16	,	,	PUNCT
ap-1179	72	17	may	may	AUX
ap-1179	72	18	5–7	5–7	NUM
ap-1179	72	19	2009	2009	NUM
ap-1179	72	20	(	(	PUNCT
ap-1179	72	21	niederlefest	niederlef	ADJ
ap-1179	72	22	)	)	PUNCT
ap-1179	72	23	,	,	PUNCT
ap-1179	72	24	held	hold	VERB
ap-1179	72	25	in	in	ADP
ap-1179	72	26	prague	prague	NOUN
ap-1179	72	27	on	on	ADP
ap-1179	72	28	occasion	occasion	NOUN
ap-1179	72	29	of	of	ADP
ap-1179	72	30	the	the	DET
ap-1179	72	31	70th	70th	ADJ
ap-1179	72	32	birthday	birthday	NOUN
ap-1179	72	33	of	of	ADP
ap-1179	72	34	professor	professor	PROPN
ap-1179	72	35	j.	j.	PROPN
ap-1179	72	36	niederle	niederle	PROPN
ap-1179	72	37	.	.	PUNCT
ap-1179	73	1	7	7	NUM
ap-1179	73	2	acta	acta	PROPN
ap-1179	73	3	polytechnica	polytechnica	PROPN
ap-1179	73	4	vol	vol	NOUN
ap-1179	73	5	.	.	PROPN
ap-1179	74	1	50	50	NUM
ap-1179	74	2	no	no	NOUN
ap-1179	74	3	.	.	PUNCT
ap-1179	75	1	3/2010	3/2010	NUM
ap-1179	75	2	an	an	DET
ap-1179	75	3	ideal	ideal	NOUN
ap-1179	75	4	i	i	PRON
ap-1179	75	5	is	be	AUX
ap-1179	75	6	(	(	PUNCT
ap-1179	75	7	n-)solvable	n-)solvable	ADJ
ap-1179	75	8	if	if	SCONJ
ap-1179	75	9	the	the	DET
ap-1179	75	10	series	series	NOUN
ap-1179	75	11	i(0	i(0	PROPN
ap-1179	75	12	)	)	PUNCT
ap-1179	75	13	:	:	PUNCT
ap-1179	76	1	=	=	PUNCT
ap-1179	76	2	i	i	PROPN
ap-1179	76	3	,	,	PUNCT
ap-1179	76	4	i(1	i(1	PROPN
ap-1179	76	5	)	)	PUNCT
ap-1179	76	6	:	:	PUNCT
ap-1179	77	1	=	=	X
ap-1179	78	1	[	[	X
ap-1179	78	2	i(0	i(0	PROPN
ap-1179	78	3	)	)	PUNCT
ap-1179	78	4	,	,	PUNCT
ap-1179	78	5	.	.	PUNCT
ap-1179	78	6	.	.	PUNCT
ap-1179	79	1	.	.	PUNCT
ap-1179	80	1	,	,	PUNCT
ap-1179	80	2	i(0	i(0	PROPN
ap-1179	80	3	)	)	PUNCT
ap-1179	80	4	]	]	PUNCT
ap-1179	80	5	,	,	PUNCT
ap-1179	80	6	.	.	PUNCT
ap-1179	80	7	.	.	PUNCT
ap-1179	81	1	.	.	PUNCT
ap-1179	82	1	,	,	PUNCT
ap-1179	82	2	i(s	i(s	PROPN
ap-1179	82	3	)	)	PUNCT
ap-1179	82	4	:	:	PUNCT
ap-1179	82	5	=	=	X
ap-1179	83	1	[	[	X
ap-1179	83	2	i(s−1	i(s−1	NOUN
ap-1179	83	3	)	)	PUNCT
ap-1179	83	4	,	,	PUNCT
ap-1179	83	5	.	.	PUNCT
ap-1179	83	6	.	.	PUNCT
ap-1179	84	1	.	.	PUNCT
ap-1179	85	1	,	,	PUNCT
ap-1179	85	2	i(s−1	i(s−1	NOUN
ap-1179	85	3	)	)	PUNCT
ap-1179	85	4	]	]	PUNCT
ap-1179	85	5	,	,	PUNCT
ap-1179	85	6	.	.	PUNCT
ap-1179	85	7	.	.	PUNCT
ap-1179	86	1	.	.	PUNCT
ap-1179	87	1	(	(	PUNCT
ap-1179	87	2	2.10	2.10	NUM
ap-1179	87	3	)	)	PUNCT
ap-1179	87	4	ends	end	VERB
ap-1179	87	5	.	.	PUNCT
ap-1179	88	1	a	a	DET
ap-1179	88	2	fa	fa	NOUN
ap-1179	88	3	is	be	AUX
ap-1179	88	4	then	then	ADV
ap-1179	88	5	semisimple	semisimple	ADJ
ap-1179	88	6	if	if	SCONJ
ap-1179	88	7	it	it	PRON
ap-1179	88	8	does	do	AUX
ap-1179	88	9	not	not	PART
ap-1179	88	10	have	have	VERB
ap-1179	88	11	solvable	solvable	ADJ
ap-1179	88	12	ideals	ideal	NOUN
ap-1179	88	13	,	,	PUNCT
ap-1179	88	14	and	and	CCONJ
ap-1179	88	15	simple	simple	ADJ
ap-1179	88	16	if	if	SCONJ
ap-1179	88	17	[	[	X
ap-1179	88	18	g	g	NOUN
ap-1179	88	19	,	,	PUNCT
ap-1179	88	20	.	.	PUNCT
ap-1179	88	21	.	.	PUNCT
ap-1179	88	22	.	.	PUNCT
ap-1179	89	1	,	,	PUNCT
ap-1179	89	2	g	g	X
ap-1179	89	3	]	]	X
ap-1179	89	4	�	�	X
ap-1179	89	5	=	=	SYM
ap-1179	89	6	{	{	PUNCT
ap-1179	89	7	0	0	NUM
ap-1179	89	8	}	}	PUNCT
ap-1179	89	9	and	and	CCONJ
ap-1179	89	10	does	do	AUX
ap-1179	89	11	not	not	PART
ap-1179	89	12	contain	contain	VERB
ap-1179	89	13	non	non	ADJ
ap-1179	89	14	-	-	ADJ
ap-1179	89	15	trivial	trivial	ADJ
ap-1179	89	16	ideals	ideal	NOUN
ap-1179	89	17	.	.	PUNCT
ap-1179	90	1	there	there	PRON
ap-1179	90	2	is	be	VERB
ap-1179	90	3	also	also	ADV
ap-1179	90	4	a	a	DET
ap-1179	90	5	cartanlike	cartanlike	ADJ
ap-1179	90	6	criterion	criterion	NOUN
ap-1179	90	7	for	for	ADP
ap-1179	90	8	semisimplicity	semisimplicity	NOUN
ap-1179	90	9	[	[	X
ap-1179	90	10	10	10	NUM
ap-1179	90	11	]	]	PUNCT
ap-1179	90	12	.	.	PUNCT
ap-1179	91	1	namely	namely	ADV
ap-1179	91	2	,	,	PUNCT
ap-1179	91	3	a	a	DET
ap-1179	91	4	fa	fa	NOUN
ap-1179	91	5	is	be	AUX
ap-1179	91	6	semisimple	semisimple	NOUN
ap-1179	91	7	if	if	SCONJ
ap-1179	91	8	k(x	k(x	PROPN
ap-1179	91	9	,	,	PUNCT
ap-1179	91	10	y	y	PROPN
ap-1179	91	11	)	)	PUNCT
ap-1179	91	12	=	=	PUNCT
ap-1179	91	13	k(x1	k(x1	NOUN
ap-1179	91	14	,	,	PUNCT
ap-1179	91	15	.	.	PUNCT
ap-1179	91	16	.	.	PUNCT
ap-1179	92	1	.	.	PUNCT
ap-1179	93	1	,	,	PUNCT
ap-1179	93	2	xn−1	xn−1	PROPN
ap-1179	93	3	,	,	PUNCT
ap-1179	93	4	y1	y1	PROPN
ap-1179	93	5	,	,	PUNCT
ap-1179	93	6	.	.	PUNCT
ap-1179	93	7	.	.	PUNCT
ap-1179	93	8	.	.	PUNCT
ap-1179	94	1	,	,	PUNCT
ap-1179	94	2	yn−1	yn−1	PROPN
ap-1179	94	3	)	)	PUNCT
ap-1179	94	4	:	:	PUNCT
ap-1179	95	1	=	=	SYM
ap-1179	95	2	tr(adxady	tr(adxady	ADJ
ap-1179	95	3	)	)	PUNCT
ap-1179	95	4	(	(	PUNCT
ap-1179	95	5	2.11	2.11	NUM
ap-1179	95	6	)	)	PUNCT
ap-1179	95	7	is	be	AUX
ap-1179	95	8	non	non	ADJ
ap-1179	95	9	-	-	ADJ
ap-1179	95	10	degenerate	degenerate	ADJ
ap-1179	95	11	in	in	ADP
ap-1179	95	12	the	the	DET
ap-1179	95	13	sense	sense	NOUN
ap-1179	95	14	that	that	SCONJ
ap-1179	95	15	k(z	k(z	PROPN
ap-1179	95	16	,	,	PUNCT
ap-1179	95	17	g	g	PROPN
ap-1179	95	18	,	,	PUNCT
ap-1179	95	19	n−2	n−2	PROPN
ap-1179	95	20	.	.	PUNCT
ap-1179	95	21	.	.	PUNCT
ap-1179	96	1	.	.	PUNCT
ap-1179	97	1	,	,	PUNCT
ap-1179	97	2	g	g	NOUN
ap-1179	97	3	,	,	PUNCT
ap-1179	97	4	g	g	PROPN
ap-1179	97	5	,	,	PUNCT
ap-1179	97	6	n−1	n−1	PROPN
ap-1179	97	7	.	.	PUNCT
ap-1179	97	8	.	.	PUNCT
ap-1179	97	9	.	.	PUNCT
ap-1179	98	1	,	,	PUNCT
ap-1179	98	2	g	g	NOUN
ap-1179	98	3	)	)	PUNCT
ap-1179	98	4	=	=	SYM
ap-1179	99	1	0⇒	0⇒	NOUN
ap-1179	99	2	z	z	NOUN
ap-1179	100	1	=	=	SYM
ap-1179	100	2	0	0	PROPN
ap-1179	100	3	.	.	PUNCT
ap-1179	101	1	(	(	PUNCT
ap-1179	101	2	2.12	2.12	NUM
ap-1179	101	3	)	)	PUNCT
ap-1179	101	4	it	it	PRON
ap-1179	101	5	can	can	AUX
ap-1179	101	6	also	also	ADV
ap-1179	101	7	be	be	AUX
ap-1179	101	8	shown	show	VERB
ap-1179	101	9	[	[	PUNCT
ap-1179	101	10	11	11	NUM
ap-1179	101	11	]	]	PUNCT
ap-1179	101	12	that	that	SCONJ
ap-1179	101	13	a	a	DET
ap-1179	101	14	semisimple	semisimple	NOUN
ap-1179	101	15	fa	fa	PROPN
ap-1179	101	16	is	be	AUX
ap-1179	101	17	the	the	DET
ap-1179	101	18	sum	sum	NOUN
ap-1179	101	19	of	of	ADP
ap-1179	101	20	simple	simple	ADJ
ap-1179	101	21	ideals	ideal	NOUN
ap-1179	101	22	,	,	PUNCT
ap-1179	101	23	g	g	NOUN
ap-1179	101	24	=	=	SYM
ap-1179	101	25	k⊕	k⊕	NOUN
ap-1179	101	26	s=1	s=1	X
ap-1179	101	27	gs	gs	NOUN
ap-1179	101	28	=	=	SYM
ap-1179	101	29	g(1	g(1	PROPN
ap-1179	101	30	)	)	PUNCT
ap-1179	101	31	⊕	⊕	PROPN
ap-1179	101	32	.	.	PUNCT
ap-1179	101	33	.	.	PUNCT
ap-1179	102	1	.⊕g(k	.⊕g(k	NOUN
ap-1179	102	2	)	)	PUNCT
ap-1179	103	1	(	(	PUNCT
ap-1179	103	2	2.13	2.13	NUM
ap-1179	103	3	)	)	PUNCT
ap-1179	103	4	the	the	DET
ap-1179	103	5	derivations	derivation	NOUN
ap-1179	103	6	of	of	ADP
ap-1179	103	7	a	a	DET
ap-1179	103	8	fa	fa	NOUN
ap-1179	103	9	g	g	NOUN
ap-1179	103	10	generate	generate	VERB
ap-1179	103	11	a	a	DET
ap-1179	103	12	lie	lie	NOUN
ap-1179	103	13	algebra	algebra	NOUN
ap-1179	103	14	.	.	PUNCT
ap-1179	104	1	to	to	PART
ap-1179	104	2	see	see	VERB
ap-1179	104	3	it	it	PRON
ap-1179	104	4	,	,	PUNCT
ap-1179	104	5	introduce	introduce	VERB
ap-1179	104	6	first	first	ADV
ap-1179	104	7	the	the	DET
ap-1179	104	8	composition	composition	NOUN
ap-1179	104	9	of	of	ADP
ap-1179	104	10	fundamental	fundamental	ADJ
ap-1179	104	11	objects	object	NOUN
ap-1179	104	12	,	,	PUNCT
ap-1179	104	13	x	x	X
ap-1179	104	14	·	·	PUNCT
ap-1179	104	15	y	y	X
ap-1179	104	16	:	:	PUNCT
ap-1179	105	1	=	=	SYM
ap-1179	105	2	n−1∑	n−1∑	NUM
ap-1179	105	3	a=1	a=1	X
ap-1179	105	4	(	(	PUNCT
ap-1179	105	5	y1	y1	NOUN
ap-1179	105	6	,	,	PUNCT
ap-1179	105	7	.	.	PUNCT
ap-1179	105	8	.	.	PUNCT
ap-1179	105	9	.	.	PUNCT
ap-1179	106	1	,	,	PUNCT
ap-1179	106	2	ya−1	ya−1	NOUN
ap-1179	106	3	,	,	PUNCT
ap-1179	106	4	[	[	X
ap-1179	106	5	x1	x1	X
ap-1179	106	6	,	,	PUNCT
ap-1179	106	7	.	.	PUNCT
ap-1179	106	8	.	.	PUNCT
ap-1179	107	1	.	.	PUNCT
ap-1179	108	1	,	,	PUNCT
ap-1179	108	2	xn−1	xn−1	PROPN
ap-1179	108	3	,	,	PUNCT
ap-1179	108	4	ya	ya	PROPN
ap-1179	108	5	]	]	X
ap-1179	108	6	,	,	PUNCT
ap-1179	108	7	ya+1	ya+1	PROPN
ap-1179	108	8	,	,	PUNCT
ap-1179	108	9	.	.	PUNCT
ap-1179	108	10	.	.	PUNCT
ap-1179	108	11	.	.	PUNCT
ap-1179	109	1	,	,	PUNCT
ap-1179	109	2	yn−1	yn−1	PROPN
ap-1179	109	3	)	)	PUNCT
ap-1179	109	4	(	(	PUNCT
ap-1179	109	5	2.14	2.14	NUM
ap-1179	109	6	)	)	PUNCT
ap-1179	109	7	which	which	PRON
ap-1179	109	8	reflects	reflect	VERB
ap-1179	109	9	that	that	SCONJ
ap-1179	109	10	x	x	PRON
ap-1179	109	11	acts	act	VERB
ap-1179	109	12	as	as	ADP
ap-1179	109	13	a	a	DET
ap-1179	109	14	derivation	derivation	NOUN
ap-1179	109	15	.	.	PUNCT
ap-1179	110	1	it	it	PRON
ap-1179	110	2	is	be	AUX
ap-1179	110	3	then	then	ADV
ap-1179	110	4	seen	see	VERB
ap-1179	110	5	that	that	SCONJ
ap-1179	110	6	fi	fi	NOUN
ap-1179	110	7	implies	imply	VERB
ap-1179	110	8	that	that	SCONJ
ap-1179	110	9	x	x	SYM
ap-1179	110	10	·	·	PUNCT
ap-1179	110	11	(	(	PUNCT
ap-1179	110	12	y	y	PROPN
ap-1179	110	13	·	·	PUNCT
ap-1179	110	14	z)−	z)−	PROPN
ap-1179	110	15	y	y	PROPN
ap-1179	110	16	·	·	PUNCT
ap-1179	110	17	(	(	PUNCT
ap-1179	110	18	x	x	X
ap-1179	110	19	·	·	SYM
ap-1179	110	20	z	z	NOUN
ap-1179	110	21	)	)	PUNCT
ap-1179	110	22	=	=	SYM
ap-1179	110	23	(	(	PUNCT
ap-1179	110	24	x	x	X
ap-1179	110	25	·	·	PUNCT
ap-1179	110	26	y	y	X
ap-1179	110	27	)	)	PUNCT
ap-1179	110	28	·	·	PUNCT
ap-1179	110	29	z	z	X
ap-1179	110	30	,	,	PUNCT
ap-1179	110	31	(	(	PUNCT
ap-1179	110	32	2.15	2.15	NUM
ap-1179	110	33	)	)	PUNCT
ap-1179	110	34	∀x	∀x	NUM
ap-1179	110	35	,	,	PUNCT
ap-1179	110	36	y	y	PROPN
ap-1179	110	37	,	,	PUNCT
ap-1179	110	38	z	z	PROPN
ap-1179	110	39	∈	∈	PROPN
ap-1179	110	40	∧n−1	∧n−1	PROPN
ap-1179	110	41	g	g	PROPN
ap-1179	110	42	adxadyz	adxadyz	ADV
ap-1179	110	43	−	−	PROPN
ap-1179	110	44	adyadxz	adyadxz	NOUN
ap-1179	110	45	=	=	SYM
ap-1179	110	46	adx·yz	adx·yz	PROPN
ap-1179	110	47	,	,	PUNCT
ap-1179	110	48	(	(	PUNCT
ap-1179	110	49	2.16	2.16	NUM
ap-1179	110	50	)	)	PUNCT
ap-1179	110	51	∀x	∀x	NUM
ap-1179	110	52	,	,	PUNCT
ap-1179	110	53	y	y	PROPN
ap-1179	110	54	∈	∈	PROPN
ap-1179	110	55	∧n−1	∧n−1	PROPN
ap-1179	110	56	g	g	PROPN
ap-1179	110	57	,	,	PUNCT
ap-1179	110	58	∀z	∀z	PROPN
ap-1179	110	59	∈	∈	PROPN
ap-1179	110	60	g	g	PROPN
ap-1179	110	61	,	,	PUNCT
ap-1179	110	62	which	which	PRON
ap-1179	110	63	means	mean	VERB
ap-1179	110	64	that	that	SCONJ
ap-1179	110	65	adx	adx	PROPN
ap-1179	110	66	∈	∈	PROPN
ap-1179	110	67	endg	endg	NOUN
ap-1179	110	68	satisfies	satisfy	VERB
ap-1179	110	69	adx·y	adx·y	PROPN
ap-1179	111	1	=	=	SYM
ap-1179	111	2	−ady·x	−ady·x	PROPN
ap-1179	111	3	.	.	PUNCT
ap-1179	112	1	these	these	DET
ap-1179	112	2	two	two	NUM
ap-1179	112	3	identities	identity	NOUN
ap-1179	112	4	show	show	VERB
ap-1179	112	5	that	that	SCONJ
ap-1179	112	6	the	the	DET
ap-1179	112	7	inner	inner	ADJ
ap-1179	112	8	derivations	derivation	NOUN
ap-1179	112	9	adx	adx	NOUN
ap-1179	112	10	associated	associate	VERB
ap-1179	112	11	with	with	ADP
ap-1179	112	12	the	the	DET
ap-1179	112	13	fundamental	fundamental	ADJ
ap-1179	112	14	objects	object	NOUN
ap-1179	112	15	x	x	PUNCT
ap-1179	112	16	generate	generate	VERB
ap-1179	112	17	(	(	PUNCT
ap-1179	112	18	the	the	DET
ap-1179	112	19	ad	ad	NOUN
ap-1179	112	20	map	map	NOUN
ap-1179	112	21	is	be	AUX
ap-1179	112	22	not	not	PART
ap-1179	112	23	necessarily	necessarily	ADV
ap-1179	112	24	injective	injective	ADJ
ap-1179	112	25	)	)	PUNCT
ap-1179	112	26	an	an	DET
ap-1179	112	27	ordinary	ordinary	ADJ
ap-1179	112	28	lie	lie	NOUN
ap-1179	112	29	algebra	algebra	NOUN
ap-1179	112	30	,	,	PUNCT
ap-1179	112	31	the	the	DET
ap-1179	112	32	lie	lie	NOUN
ap-1179	112	33	algebra	algebra	NOUN
ap-1179	112	34	associated	associate	VERB
ap-1179	112	35	with	with	ADP
ap-1179	112	36	the	the	DET
ap-1179	112	37	fa	fa	PROPN
ap-1179	112	38	g.	g.	PROPN
ap-1179	112	39	an	an	DET
ap-1179	112	40	important	important	ADJ
ap-1179	112	41	type	type	NOUN
ap-1179	112	42	of	of	ADP
ap-1179	112	43	fas	fas	NOUN
ap-1179	112	44	,	,	PUNCT
ap-1179	112	45	because	because	SCONJ
ap-1179	112	46	of	of	ADP
ap-1179	112	47	its	its	PRON
ap-1179	112	48	relevance	relevance	NOUN
ap-1179	112	49	in	in	ADP
ap-1179	112	50	physical	physical	ADJ
ap-1179	112	51	applications	application	NOUN
ap-1179	112	52	where	where	SCONJ
ap-1179	112	53	a	a	DET
ap-1179	112	54	scalar	scalar	ADJ
ap-1179	112	55	product	product	NOUN
ap-1179	112	56	is	be	AUX
ap-1179	112	57	usually	usually	ADV
ap-1179	112	58	needed	need	VERB
ap-1179	112	59	(	(	PUNCT
ap-1179	112	60	as	as	ADP
ap-1179	112	61	in	in	ADP
ap-1179	112	62	the	the	DET
ap-1179	112	63	bagger	bagger	NOUN
ap-1179	112	64	-	-	PUNCT
ap-1179	112	65	lambert	lambert	PROPN
ap-1179	112	66	-	-	PUNCT
ap-1179	112	67	gustavsson	gustavsson	PROPN
ap-1179	112	68	model	model	NOUN
ap-1179	112	69	in	in	ADP
ap-1179	112	70	m	m	NOUN
ap-1179	112	71	-	-	NOUN
ap-1179	112	72	theory	theory	NOUN
ap-1179	112	73	)	)	PUNCT
ap-1179	112	74	,	,	PUNCT
ap-1179	112	75	is	be	AUX
ap-1179	112	76	the	the	DET
ap-1179	112	77	class	class	NOUN
ap-1179	112	78	of	of	ADP
ap-1179	112	79	metric	metric	ADJ
ap-1179	112	80	filippov	filippov	NOUN
ap-1179	112	81	algebras	algebra	NOUN
ap-1179	112	82	.	.	PUNCT
ap-1179	113	1	these	these	PRON
ap-1179	113	2	are	be	AUX
ap-1179	113	3	endowed	endow	VERB
ap-1179	113	4	with	with	ADP
ap-1179	113	5	a	a	DET
ap-1179	113	6	metric	metric	ADJ
ap-1179	113	7	〈	〈	NOUN
ap-1179	113	8	,	,	PUNCT
ap-1179	113	9	〉	〉	NOUN
ap-1179	113	10	on	on	ADP
ap-1179	113	11	g	g	NOUN
ap-1179	113	12	,	,	PUNCT
ap-1179	113	13	〈	〈	PROPN
ap-1179	113	14	y	y	PROPN
ap-1179	113	15	,	,	PUNCT
ap-1179	113	16	z	z	PROPN
ap-1179	113	17	〉	〉	NUM
ap-1179	113	18	=	=	SYM
ap-1179	113	19	gaby	gaby	PROPN
ap-1179	113	20	a	a	DET
ap-1179	113	21	zb	zb	NOUN
ap-1179	113	22	,	,	PUNCT
ap-1179	113	23	∀	∀	X
ap-1179	113	24	y	y	NOUN
ap-1179	113	25	,	,	PUNCT
ap-1179	113	26	z	z	NOUN
ap-1179	113	27	∈	∈	PROPN
ap-1179	113	28	g	g	PROPN
ap-1179	113	29	that	that	PRON
ap-1179	113	30	is	be	AUX
ap-1179	113	31	invariant	invariant	ADJ
ap-1179	113	32	i.e.	i.e.	ADV
ap-1179	113	33	,	,	PUNCT
ap-1179	113	34	x	x	X
ap-1179	113	35	·	·	PUNCT
ap-1179	113	36	〈	〈	PROPN
ap-1179	113	37	y	y	PROPN
ap-1179	113	38	,	,	PUNCT
ap-1179	113	39	z	z	NOUN
ap-1179	113	40	〉	〉	NOUN
ap-1179	113	41	=	=	SYM
ap-1179	113	42	〈	〈	PROPN
ap-1179	113	43	x	x	X
ap-1179	113	44	·	·	PUNCT
ap-1179	113	45	y	y	PROPN
ap-1179	113	46	,	,	PUNCT
ap-1179	113	47	z〉+	z〉+	PROPN
ap-1179	113	48	〈	〈	PROPN
ap-1179	113	49	y	y	PROPN
ap-1179	113	50	,	,	PUNCT
ap-1179	113	51	x	x	X
ap-1179	113	52	·	·	PUNCT
ap-1179	114	1	z	z	X
ap-1179	114	2	〉	〉	NOUN
ap-1179	114	3	=	=	SYM
ap-1179	114	4	〈	〈	PROPN
ap-1179	114	5	[	[	X
ap-1179	114	6	x1	x1	PROPN
ap-1179	114	7	,	,	PUNCT
ap-1179	114	8	.	.	PUNCT
ap-1179	114	9	.	.	PUNCT
ap-1179	115	1	.	.	PUNCT
ap-1179	116	1	,	,	PUNCT
ap-1179	116	2	xn−1	xn−1	PROPN
ap-1179	116	3	,	,	PUNCT
ap-1179	116	4	y	y	PROPN
ap-1179	116	5	]	]	PUNCT
ap-1179	116	6	,	,	PUNCT
ap-1179	116	7	z〉+	z〉+	X
ap-1179	116	8	(	(	PUNCT
ap-1179	116	9	2.17	2.17	NUM
ap-1179	116	10	)	)	PUNCT
ap-1179	116	11	〈	〈	PROPN
ap-1179	116	12	y	y	PROPN
ap-1179	116	13	,	,	PUNCT
ap-1179	116	14	[	[	X
ap-1179	116	15	x1	x1	X
ap-1179	116	16	,	,	PUNCT
ap-1179	116	17	.	.	PUNCT
ap-1179	116	18	.	.	PUNCT
ap-1179	116	19	.	.	PUNCT
ap-1179	117	1	,	,	PUNCT
ap-1179	117	2	xn−1	xn−1	PROPN
ap-1179	117	3	,	,	PUNCT
ap-1179	117	4	z	z	NOUN
ap-1179	117	5	]	]	X
ap-1179	117	6	〉	〉	NUM
ap-1179	117	7	=	=	NOUN
ap-1179	117	8	0	0	PROPN
ap-1179	117	9	.	.	PUNCT
ap-1179	118	1	this	this	PRON
ap-1179	118	2	means	mean	VERB
ap-1179	118	3	that	that	SCONJ
ap-1179	118	4	the	the	DET
ap-1179	118	5	structure	structure	NOUN
ap-1179	118	6	constants	constant	VERB
ap-1179	118	7	with	with	ADP
ap-1179	118	8	all	all	DET
ap-1179	118	9	indices	index	NOUN
ap-1179	118	10	down	down	ADP
ap-1179	118	11	fa1	fa1	NOUN
ap-1179	118	12	...	...	PUNCT
ap-1179	118	13	an−1bc	an−1bc	NUM
ap-1179	118	14	are	be	AUX
ap-1179	118	15	completely	completely	ADV
ap-1179	118	16	antisymmetric	antisymmetric	ADJ
ap-1179	118	17	since	since	SCONJ
ap-1179	118	18	the	the	DET
ap-1179	118	19	invariance	invariance	NOUN
ap-1179	118	20	of	of	ADP
ap-1179	118	21	g	g	NOUN
ap-1179	118	22	above	above	ADV
ap-1179	118	23	implies	imply	VERB
ap-1179	118	24	fa1	fa1	NOUN
ap-1179	118	25	...	...	PUNCT
ap-1179	118	26	an−1b	an−1b	PUNCT
ap-1179	119	1	l	l	X
ap-1179	119	2	glc+	glc+	ADJ
ap-1179	119	3	fa1	fa1	NOUN
ap-1179	119	4	...	...	PUNCT
ap-1179	119	5	an−1c	an−1c	PROPN
ap-1179	119	6	l	l	NOUN
ap-1179	119	7	gbl	gbl	X
ap-1179	119	8	=	=	SYM
ap-1179	119	9	0	0	PROPN
ap-1179	119	10	.	.	PUNCT
ap-1179	120	1	the	the	DET
ap-1179	120	2	fa1	fa1	NOUN
ap-1179	120	3	...	...	PUNCT
ap-1179	120	4	an+1	an+1	AUX
ap-1179	120	5	define	define	VERB
ap-1179	120	6	a	a	DET
ap-1179	120	7	skewsymmetric	skewsymmetric	ADJ
ap-1179	120	8	invariant	invariant	ADJ
ap-1179	120	9	tensor	tensor	NOUN
ap-1179	120	10	under	under	ADP
ap-1179	120	11	the	the	DET
ap-1179	120	12	action	action	NOUN
ap-1179	120	13	of	of	ADP
ap-1179	120	14	x	x	PRON
ap-1179	120	15	,	,	PUNCT
ap-1179	120	16	since	since	SCONJ
ap-1179	120	17	the	the	DET
ap-1179	120	18	fi	fi	NOUN
ap-1179	120	19	implies	imply	VERB
ap-1179	120	20	n+1∑	n+1∑	PROPN
ap-1179	120	21	i=1	i=1	PROPN
ap-1179	120	22	fa1	fa1	NOUN
ap-1179	120	23	...	...	PUNCT
ap-1179	120	24	an−1bi	an−1bi	NUM
ap-1179	120	25	l	l	NOUN
ap-1179	120	26	fb1	fb1	NOUN
ap-1179	120	27	...	...	PUNCT
ap-1179	120	28	bi−1lbi+1	bi−1lbi+1	NOUN
ap-1179	120	29	...	...	PUNCT
ap-1179	120	30	bn+1	bn+1	NUM
ap-1179	120	31	=	=	SYM
ap-1179	120	32	0	0	NUM
ap-1179	120	33	or	or	CCONJ
ap-1179	120	34	lx	lx	ADP
ap-1179	120	35	.f	.f	PROPN
ap-1179	120	36	=	=	PUNCT
ap-1179	120	37	0	0	PUNCT
ap-1179	120	38	.	.	PUNCT
ap-1179	121	1	(	(	PUNCT
ap-1179	121	2	2.18	2.18	NUM
ap-1179	121	3	)	)	PUNCT
ap-1179	121	4	3	3	NUM
ap-1179	121	5	examples	example	NOUN
ap-1179	121	6	of	of	ADP
ap-1179	121	7	n	n	CCONJ
ap-1179	121	8	-	-	PUNCT
ap-1179	121	9	ary	ary	NOUN
ap-1179	121	10	structures	structure	NOUN
ap-1179	121	11	3.1	3.1	NUM
ap-1179	121	12	examples	example	NOUN
ap-1179	121	13	of	of	ADP
ap-1179	121	14	glas	gla	NOUN
ap-1179	121	15	let	let	VERB
ap-1179	121	16	n	n	NOUN
ap-1179	121	17	=	=	NOUN
ap-1179	121	18	2p	2p	NOUN
ap-1179	121	19	.	.	PUNCT
ap-1179	122	1	we	we	PRON
ap-1179	122	2	look	look	VERB
ap-1179	122	3	for	for	ADP
ap-1179	122	4	structure	structure	NOUN
ap-1179	122	5	constants	constant	NOUN
ap-1179	122	6	ωi1	ωi1	PROPN
ap-1179	122	7	...	...	PUNCT
ap-1179	122	8	i2p	i2p	PROPN
ap-1179	122	9	j	j	PROPN
ap-1179	123	1	that	that	PRON
ap-1179	123	2	satisfy	satisfy	VERB
ap-1179	123	3	the	the	DET
ap-1179	123	4	gji	gji	NOUN
ap-1179	123	5	(	(	PUNCT
ap-1179	123	6	1.3	1.3	NUM
ap-1179	123	7	)	)	PUNCT
ap-1179	123	8	i.e.	i.e.	X
ap-1179	123	9	,	,	PUNCT
ap-1179	123	10	such	such	ADJ
ap-1179	123	11	that	that	SCONJ
ap-1179	123	12	ω[j1	ω[j1	NOUN
ap-1179	123	13	...	...	PUNCT
ap-1179	123	14	j2p	j2p	PROPN
ap-1179	123	15	lωj2p+1	lωj2p+1	PROPN
ap-1179	123	16	...	...	PUNCT
ap-1179	123	17	j4p−1]l	j4p−1]l	PROPN
ap-1179	123	18	s	s	PART
ap-1179	123	19	=	=	NOUN
ap-1179	123	20	0	0	PROPN
ap-1179	123	21	.	.	PUNCT
ap-1179	124	1	(	(	PUNCT
ap-1179	124	2	3.19	3.19	NUM
ap-1179	124	3	)	)	PUNCT
ap-1179	124	4	it	it	PRON
ap-1179	124	5	turns	turn	VERB
ap-1179	124	6	out	out	ADP
ap-1179	124	7	[	[	X
ap-1179	124	8	3	3	NUM
ap-1179	124	9	,	,	PUNCT
ap-1179	124	10	2	2	NUM
ap-1179	124	11	]	]	PUNCT
ap-1179	124	12	that	that	PRON
ap-1179	124	13	given	give	VERB
ap-1179	124	14	a	a	DET
ap-1179	124	15	simple	simple	ADJ
ap-1179	124	16	compact	compact	ADJ
ap-1179	124	17	lie	lie	NOUN
ap-1179	124	18	algebra	algebra	NOUN
ap-1179	124	19	,	,	PUNCT
ap-1179	124	20	the	the	DET
ap-1179	124	21	coordinates	coordinate	NOUN
ap-1179	124	22	of	of	ADP
ap-1179	124	23	the	the	DET
ap-1179	124	24	(	(	PUNCT
ap-1179	124	25	odd	odd	ADJ
ap-1179	124	26	)	)	PUNCT
ap-1179	124	27	cocyles	cocyle	NOUN
ap-1179	124	28	for	for	ADP
ap-1179	124	29	the	the	DET
ap-1179	124	30	lie	lie	NOUN
ap-1179	124	31	algebra	algebra	NOUN
ap-1179	124	32	cohomology	cohomology	NOUN
ap-1179	124	33	satisfy	satisfy	VERB
ap-1179	124	34	the	the	DET
ap-1179	124	35	gji	gji	NOUN
ap-1179	124	36	identity	identity	NOUN
ap-1179	124	37	(	(	PUNCT
ap-1179	124	38	1.2	1.2	NUM
ap-1179	124	39	)	)	PUNCT
ap-1179	124	40	.	.	PUNCT
ap-1179	125	1	these	these	PRON
ap-1179	125	2	provide	provide	VERB
ap-1179	125	3	the	the	DET
ap-1179	125	4	structure	structure	NOUN
ap-1179	125	5	constants	constant	NOUN
ap-1179	125	6	of	of	ADP
ap-1179	125	7	an	an	DET
ap-1179	125	8	infinity	infinity	NOUN
ap-1179	125	9	of	of	ADP
ap-1179	125	10	glas	gla	NOUN
ap-1179	125	11	,	,	PUNCT
ap-1179	125	12	with	with	ADP
ap-1179	125	13	brackets	bracket	NOUN
ap-1179	125	14	with	with	ADP
ap-1179	125	15	n	n	NOUN
ap-1179	125	16	=	=	SYM
ap-1179	125	17	2(mi−1	2(mi−1	NUM
ap-1179	125	18	)	)	PUNCT
ap-1179	125	19	entries	entry	NOUN
ap-1179	125	20	(	(	PUNCT
ap-1179	125	21	where	where	SCONJ
ap-1179	125	22	i	i	PRON
ap-1179	125	23	=	=	NOUN
ap-1179	125	24	1	1	NUM
ap-1179	125	25	,	,	PUNCT
ap-1179	125	26	.	.	PUNCT
ap-1179	125	27	.	.	PUNCT
ap-1179	125	28	.	.	PUNCT
ap-1179	126	1	,	,	PUNCT
ap-1179	126	2	l	l	NOUN
ap-1179	126	3	and	and	CCONJ
ap-1179	126	4	l	l	NOUN
ap-1179	126	5	is	be	AUX
ap-1179	126	6	the	the	DET
ap-1179	126	7	rank	rank	NOUN
ap-1179	126	8	of	of	ADP
ap-1179	126	9	the	the	DET
ap-1179	126	10	algebra	algebra	NOUN
ap-1179	126	11	)	)	PUNCT
ap-1179	126	12	,	,	PUNCT
ap-1179	126	13	according	accord	VERB
ap-1179	126	14	to	to	ADP
ap-1179	126	15	the	the	DET
ap-1179	126	16	table	table	NOUN
ap-1179	126	17	below	below	ADV
ap-1179	126	18	:	:	PUNCT
ap-1179	126	19	g	g	PROPN
ap-1179	126	20	dim	dim	VERB
ap-1179	126	21	g	g	PROPN
ap-1179	126	22	orders	order	NOUN
ap-1179	126	23	mi	mi	PROPN
ap-1179	126	24	of	of	ADP
ap-1179	126	25	invariants	invariant	NOUN
ap-1179	126	26	(	(	PUNCT
ap-1179	126	27	and	and	CCONJ
ap-1179	126	28	casimirs	casimirs	PROPN
ap-1179	126	29	)	)	PUNCT
ap-1179	126	30	orders	order	NOUN
ap-1179	126	31	2mi	2mi	ADJ
ap-1179	126	32	−	−	ADP
ap-1179	126	33	1	1	NUM
ap-1179	126	34	of	of	ADP
ap-1179	126	35	g	g	NOUN
ap-1179	126	36	-	-	PUNCT
ap-1179	126	37	cocycles	cocycle	NOUN
ap-1179	126	38	al	al	PROPN
ap-1179	126	39	(	(	PUNCT
ap-1179	126	40	l	l	PROPN
ap-1179	127	1	+	+	PROPN
ap-1179	127	2	1)2	1)2	NUM
ap-1179	127	3	−	−	NOUN
ap-1179	127	4	1	1	NUM
ap-1179	128	1	[	[	X
ap-1179	128	2	l	l	X
ap-1179	128	3	≥	≥	NUM
ap-1179	128	4	1	1	NUM
ap-1179	128	5	]	]	SYM
ap-1179	128	6	2	2	NUM
ap-1179	128	7	,	,	PUNCT
ap-1179	128	8	3	3	NUM
ap-1179	128	9	,	,	PUNCT
ap-1179	128	10	.	.	PUNCT
ap-1179	128	11	.	.	PUNCT
ap-1179	128	12	.	.	PUNCT
ap-1179	129	1	,	,	PUNCT
ap-1179	129	2	l+	l+	PUNCT
ap-1179	129	3	1	1	NUM
ap-1179	129	4	3	3	NUM
ap-1179	129	5	,	,	PUNCT
ap-1179	129	6	5	5	NUM
ap-1179	129	7	,	,	PUNCT
ap-1179	129	8	.	.	PUNCT
ap-1179	129	9	.	.	PUNCT
ap-1179	130	1	.	.	PUNCT
ap-1179	131	1	,	,	PUNCT
ap-1179	131	2	2l	2l	NOUN
ap-1179	131	3	+	+	CCONJ
ap-1179	131	4	1	1	NUM
ap-1179	131	5	bl	bl	NOUN
ap-1179	131	6	l(2l+	l(2l+	NOUN
ap-1179	131	7	1	1	NUM
ap-1179	131	8	)	)	PUNCT
ap-1179	132	1	[	[	X
ap-1179	132	2	l	l	X
ap-1179	132	3	≥	≥	NOUN
ap-1179	132	4	2	2	NUM
ap-1179	132	5	]	]	SYM
ap-1179	132	6	2	2	NUM
ap-1179	132	7	,	,	PUNCT
ap-1179	132	8	4	4	NUM
ap-1179	132	9	,	,	PUNCT
ap-1179	132	10	.	.	PUNCT
ap-1179	132	11	.	.	PUNCT
ap-1179	133	1	.	.	PUNCT
ap-1179	134	1	,	,	PUNCT
ap-1179	134	2	2l	2l	PROPN
ap-1179	134	3	3	3	NUM
ap-1179	134	4	,	,	PUNCT
ap-1179	134	5	7	7	NUM
ap-1179	134	6	,	,	PUNCT
ap-1179	134	7	.	.	PUNCT
ap-1179	134	8	.	.	PUNCT
ap-1179	134	9	.	.	PUNCT
ap-1179	135	1	,	,	PUNCT
ap-1179	135	2	4l	4l	NOUN
ap-1179	135	3	−	−	NOUN
ap-1179	135	4	1	1	NUM
ap-1179	135	5	cl	cl	NOUN
ap-1179	135	6	l(2l+	l(2l+	NOUN
ap-1179	135	7	1	1	NUM
ap-1179	135	8	)	)	PUNCT
ap-1179	136	1	[	[	X
ap-1179	136	2	l	l	X
ap-1179	136	3	≥	≥	NOUN
ap-1179	136	4	3	3	NUM
ap-1179	136	5	]	]	SYM
ap-1179	136	6	2	2	NUM
ap-1179	136	7	,	,	PUNCT
ap-1179	136	8	4	4	NUM
ap-1179	136	9	,	,	PUNCT
ap-1179	136	10	.	.	PUNCT
ap-1179	136	11	.	.	PUNCT
ap-1179	137	1	.	.	PUNCT
ap-1179	138	1	,	,	PUNCT
ap-1179	138	2	2l	2l	PROPN
ap-1179	138	3	3	3	NUM
ap-1179	138	4	,	,	PUNCT
ap-1179	138	5	7	7	NUM
ap-1179	138	6	,	,	PUNCT
ap-1179	138	7	.	.	PUNCT
ap-1179	138	8	.	.	PUNCT
ap-1179	138	9	.	.	PUNCT
ap-1179	139	1	,	,	PUNCT
ap-1179	139	2	4l	4l	NOUN
ap-1179	139	3	−	−	PROPN
ap-1179	139	4	1	1	NUM
ap-1179	139	5	dl	dl	PROPN
ap-1179	139	6	l(2l−	l(2l−	PROPN
ap-1179	139	7	1	1	NUM
ap-1179	139	8	)	)	PUNCT
ap-1179	140	1	[	[	X
ap-1179	140	2	l	l	X
ap-1179	140	3	≥	≥	NOUN
ap-1179	140	4	4	4	NUM
ap-1179	140	5	]	]	SYM
ap-1179	140	6	2	2	NUM
ap-1179	140	7	,	,	PUNCT
ap-1179	140	8	4	4	NUM
ap-1179	140	9	,	,	PUNCT
ap-1179	140	10	.	.	PUNCT
ap-1179	140	11	.	.	PUNCT
ap-1179	141	1	.	.	PUNCT
ap-1179	142	1	,	,	PUNCT
ap-1179	142	2	2l−	2l−	NUM
ap-1179	142	3	2	2	NUM
ap-1179	142	4	,	,	PUNCT
ap-1179	142	5	l	l	NOUN
ap-1179	142	6	3	3	NUM
ap-1179	142	7	,	,	PUNCT
ap-1179	142	8	7	7	NUM
ap-1179	142	9	,	,	PUNCT
ap-1179	142	10	.	.	PUNCT
ap-1179	142	11	.	.	PUNCT
ap-1179	142	12	.	.	PUNCT
ap-1179	143	1	,	,	PUNCT
ap-1179	143	2	4l	4l	NOUN
ap-1179	143	3	−	−	PROPN
ap-1179	143	4	5	5	NUM
ap-1179	143	5	,	,	PUNCT
ap-1179	143	6	2l−	2l−	NUM
ap-1179	143	7	1	1	NUM
ap-1179	143	8	g2	g2	PROPN
ap-1179	143	9	14	14	NUM
ap-1179	143	10	2	2	NUM
ap-1179	143	11	,	,	PUNCT
ap-1179	143	12	6	6	NUM
ap-1179	143	13	3	3	NUM
ap-1179	143	14	,	,	PUNCT
ap-1179	143	15	11	11	NUM
ap-1179	143	16	f4	f4	NUM
ap-1179	143	17	52	52	NUM
ap-1179	143	18	2	2	NUM
ap-1179	143	19	,	,	PUNCT
ap-1179	143	20	6	6	NUM
ap-1179	143	21	,	,	PUNCT
ap-1179	143	22	8	8	NUM
ap-1179	143	23	,	,	PUNCT
ap-1179	143	24	12	12	NUM
ap-1179	143	25	3	3	NUM
ap-1179	143	26	,	,	PUNCT
ap-1179	143	27	11	11	NUM
ap-1179	143	28	,	,	PUNCT
ap-1179	143	29	15	15	NUM
ap-1179	143	30	,	,	PUNCT
ap-1179	143	31	23	23	NUM
ap-1179	143	32	e6	e6	NOUN
ap-1179	143	33	78	78	NUM
ap-1179	143	34	2	2	NUM
ap-1179	143	35	,	,	PUNCT
ap-1179	143	36	5	5	NUM
ap-1179	143	37	,	,	PUNCT
ap-1179	143	38	6	6	NUM
ap-1179	143	39	,	,	PUNCT
ap-1179	143	40	8	8	NUM
ap-1179	143	41	,	,	PUNCT
ap-1179	143	42	9	9	NUM
ap-1179	143	43	,	,	PUNCT
ap-1179	143	44	12	12	NUM
ap-1179	143	45	3	3	NUM
ap-1179	143	46	,	,	PUNCT
ap-1179	143	47	9	9	NUM
ap-1179	143	48	,	,	PUNCT
ap-1179	143	49	11	11	NUM
ap-1179	143	50	,	,	PUNCT
ap-1179	143	51	15	15	NUM
ap-1179	143	52	,	,	PUNCT
ap-1179	143	53	17	17	NUM
ap-1179	143	54	,	,	PUNCT
ap-1179	143	55	23	23	NUM
ap-1179	143	56	e7	e7	PROPN
ap-1179	143	57	133	133	NUM
ap-1179	143	58	2	2	NUM
ap-1179	143	59	,	,	PUNCT
ap-1179	143	60	6	6	NUM
ap-1179	143	61	,	,	PUNCT
ap-1179	143	62	8	8	NUM
ap-1179	143	63	,	,	PUNCT
ap-1179	143	64	10	10	NUM
ap-1179	143	65	,	,	PUNCT
ap-1179	143	66	12	12	NUM
ap-1179	143	67	,	,	PUNCT
ap-1179	143	68	14	14	NUM
ap-1179	143	69	,	,	PUNCT
ap-1179	143	70	18	18	NUM
ap-1179	143	71	3	3	NUM
ap-1179	143	72	,	,	PUNCT
ap-1179	143	73	11	11	NUM
ap-1179	143	74	,	,	PUNCT
ap-1179	143	75	15	15	NUM
ap-1179	143	76	,	,	PUNCT
ap-1179	143	77	19	19	NUM
ap-1179	143	78	,	,	PUNCT
ap-1179	143	79	23	23	NUM
ap-1179	143	80	,	,	PUNCT
ap-1179	143	81	27	27	NUM
ap-1179	143	82	,	,	PUNCT
ap-1179	143	83	35	35	NUM
ap-1179	143	84	e8	e8	PROPN
ap-1179	143	85	248	248	NUM
ap-1179	143	86	2	2	NUM
ap-1179	143	87	,	,	PUNCT
ap-1179	143	88	8	8	NUM
ap-1179	143	89	,	,	PUNCT
ap-1179	143	90	12	12	NUM
ap-1179	143	91	,	,	PUNCT
ap-1179	143	92	14	14	NUM
ap-1179	143	93	,	,	PUNCT
ap-1179	143	94	18	18	NUM
ap-1179	143	95	,	,	PUNCT
ap-1179	143	96	20	20	NUM
ap-1179	143	97	,	,	PUNCT
ap-1179	143	98	24	24	NUM
ap-1179	143	99	,	,	PUNCT
ap-1179	143	100	30	30	NUM
ap-1179	143	101	3	3	NUM
ap-1179	143	102	,	,	PUNCT
ap-1179	143	103	15	15	NUM
ap-1179	143	104	,	,	PUNCT
ap-1179	143	105	23	23	NUM
ap-1179	143	106	,	,	PUNCT
ap-1179	143	107	27	27	NUM
ap-1179	143	108	,	,	PUNCT
ap-1179	143	109	35	35	NUM
ap-1179	143	110	,	,	PUNCT
ap-1179	143	111	39	39	NUM
ap-1179	143	112	,	,	PUNCT
ap-1179	143	113	47	47	NUM
ap-1179	143	114	,	,	PUNCT
ap-1179	143	115	59	59	NUM
ap-1179	143	116	8	8	NUM
ap-1179	143	117	acta	acta	PROPN
ap-1179	143	118	polytechnica	polytechnica	PROPN
ap-1179	143	119	vol	vol	NOUN
ap-1179	143	120	.	.	PROPN
ap-1179	144	1	50	50	NUM
ap-1179	144	2	no	no	NOUN
ap-1179	144	3	.	.	PUNCT
ap-1179	145	1	3/2010	3/2010	NUM
ap-1179	145	2	3.2	3.2	NUM
ap-1179	145	3	examples	example	NOUN
ap-1179	145	4	of	of	ADP
ap-1179	145	5	fas	fas	PROPN
ap-1179	145	6	an	an	DET
ap-1179	145	7	important	important	ADJ
ap-1179	145	8	example	example	NOUN
ap-1179	145	9	of	of	ADP
ap-1179	145	10	finite	finite	ADJ
ap-1179	145	11	filippov	filippov	PROPN
ap-1179	145	12	algebras	algebras	PROPN
ap-1179	145	13	is	be	AUX
ap-1179	145	14	provided	provide	VERB
ap-1179	145	15	by	by	ADP
ap-1179	145	16	the	the	DET
ap-1179	145	17	real	real	ADJ
ap-1179	145	18	euclidean	euclidean	ADJ
ap-1179	145	19	simple	simple	ADJ
ap-1179	145	20	n	n	CCONJ
ap-1179	145	21	-	-	PUNCT
ap-1179	145	22	lie	lie	NOUN
ap-1179	145	23	algebras	algebra	NOUN
ap-1179	145	24	an+1	an+1	VERB
ap-1179	145	25	defined	define	VERB
ap-1179	145	26	on	on	ADP
ap-1179	145	27	an	an	DET
ap-1179	145	28	euclidean	euclidean	NOUN
ap-1179	145	29	(	(	PUNCT
ap-1179	145	30	n+1)-dimensional	n+1)-dimensional	ADJ
ap-1179	145	31	vector	vector	NOUN
ap-1179	145	32	space	space	NOUN
ap-1179	145	33	.	.	PUNCT
ap-1179	146	1	let	let	VERB
ap-1179	146	2	us	we	PRON
ap-1179	146	3	fix	fix	VERB
ap-1179	146	4	a	a	DET
ap-1179	146	5	basis	basis	NOUN
ap-1179	146	6	{	{	PUNCT
ap-1179	146	7	ei	ei	NOUN
ap-1179	146	8	}	}	PUNCT
ap-1179	146	9	(	(	PUNCT
ap-1179	146	10	i	i	NOUN
ap-1179	146	11	=	=	NOUN
ap-1179	146	12	1	1	NUM
ap-1179	146	13	,	,	PUNCT
ap-1179	146	14	.	.	PUNCT
ap-1179	146	15	.	.	PUNCT
ap-1179	147	1	.	.	PUNCT
ap-1179	148	1	,	,	PUNCT
ap-1179	148	2	n	n	PROPN
ap-1179	148	3	+	+	NOUN
ap-1179	148	4	1	1	NUM
ap-1179	148	5	)	)	PUNCT
ap-1179	148	6	.	.	PUNCT
ap-1179	149	1	the	the	DET
ap-1179	149	2	basic	basic	ADJ
ap-1179	149	3	commutators	commutator	NOUN
ap-1179	149	4	are	be	AUX
ap-1179	149	5	given	give	VERB
ap-1179	149	6	by	by	ADP
ap-1179	149	7	[	[	X
ap-1179	149	8	e1	e1	NOUN
ap-1179	149	9	.	.	PUNCT
ap-1179	149	10	.	.	PUNCT
ap-1179	149	11	.	.	PUNCT
ap-1179	150	1	êi	êi	PROPN
ap-1179	150	2	.	.	PUNCT
ap-1179	150	3	.	.	PUNCT
ap-1179	150	4	.	.	PUNCT
ap-1179	151	1	en+1	en+1	PUNCT
ap-1179	151	2	]	]	X
ap-1179	151	3	=	=	SYM
ap-1179	151	4	(	(	PUNCT
ap-1179	151	5	−1)n+1ei	−1)n+1ei	PROPN
ap-1179	151	6	or	or	CCONJ
ap-1179	151	7	[	[	X
ap-1179	151	8	ei1	ei1	X
ap-1179	151	9	.	.	PUNCT
ap-1179	151	10	.	.	PUNCT
ap-1179	151	11	.	.	PUNCT
ap-1179	152	1	ein	ein	NOUN
ap-1179	152	2	]	]	PUNCT
ap-1179	152	3	=	=	PUNCT
ap-1179	152	4	(	(	PUNCT
ap-1179	152	5	−1)n	−1)n	PUNCT
ap-1179	152	6	n+1∑	n+1∑	PROPN
ap-1179	152	7	i=1	i=1	PROPN
ap-1179	153	1	εi1	εi1	PROPN
ap-1179	153	2	...	...	PUNCT
ap-1179	153	3	in	in	ADP
ap-1179	153	4	iei	iei	PROPN
ap-1179	153	5	.	.	PUNCT
ap-1179	154	1	(	(	PUNCT
ap-1179	154	2	3.20	3.20	NUM
ap-1179	154	3	)	)	PUNCT
ap-1179	154	4	there	there	PRON
ap-1179	154	5	are	be	VERB
ap-1179	154	6	also	also	ADV
ap-1179	154	7	infinite	infinite	ADJ
ap-1179	154	8	-	-	PUNCT
ap-1179	154	9	dimensional	dimensional	ADJ
ap-1179	154	10	fas	fas	NOUN
ap-1179	154	11	that	that	PRON
ap-1179	154	12	generalize	generalize	VERB
ap-1179	154	13	the	the	DET
ap-1179	154	14	ordinary	ordinary	ADJ
ap-1179	154	15	poisson	poisson	NOUN
ap-1179	154	16	algebra	algebra	NOUN
ap-1179	154	17	by	by	ADP
ap-1179	154	18	means	mean	NOUN
ap-1179	154	19	of	of	ADP
ap-1179	154	20	the	the	DET
ap-1179	154	21	bracket	bracket	NOUN
ap-1179	154	22	of	of	ADP
ap-1179	154	23	n	n	NOUN
ap-1179	154	24	functions	function	NOUN
ap-1179	154	25	fi	fi	NOUN
ap-1179	154	26	=	=	NOUN
ap-1179	155	1	fi	fi	NOUN
ap-1179	155	2	(	(	PUNCT
ap-1179	155	3	x1	x1	PROPN
ap-1179	155	4	,	,	PUNCT
ap-1179	155	5	x2	x2	PROPN
ap-1179	155	6	,	,	PUNCT
ap-1179	155	7	.	.	PUNCT
ap-1179	155	8	.	.	PUNCT
ap-1179	155	9	.	.	PUNCT
ap-1179	156	1	,	,	PUNCT
ap-1179	156	2	xn	xn	X
ap-1179	156	3	)	)	PUNCT
ap-1179	156	4	defined	define	VERB
ap-1179	156	5	by	by	ADP
ap-1179	156	6	[	[	X
ap-1179	156	7	f1	f1	NOUN
ap-1179	156	8	,	,	PUNCT
ap-1179	156	9	f2	f2	PROPN
ap-1179	156	10	,	,	PUNCT
ap-1179	156	11	.	.	PUNCT
ap-1179	156	12	.	.	PUNCT
ap-1179	157	1	.	.	PUNCT
ap-1179	158	1	,	,	PUNCT
ap-1179	158	2	fn	fn	NOUN
ap-1179	158	3	]	]	X
ap-1179	158	4	:	:	PUNCT
ap-1179	159	1	=	=	SYM
ap-1179	159	2	εi1	εi1	NOUN
ap-1179	159	3	...	...	PUNCT
ap-1179	159	4	in	in	ADP
ap-1179	159	5	1	1	NUM
ap-1179	159	6	...	...	SYM
ap-1179	159	7	n	n	CCONJ
ap-1179	159	8	∂i1f	∂i1f	ADP
ap-1179	159	9	1	1	NUM
ap-1179	159	10	.	.	PUNCT
ap-1179	159	11	.	.	PUNCT
ap-1179	159	12	.	.	PUNCT
ap-1179	160	1	∂infn	∂infn	PROPN
ap-1179	160	2	=	=	SYM
ap-1179	160	3	∣∣∣∣	∣∣∣∣	PROPN
ap-1179	160	4	∂(f1	∂(f1	PROPN
ap-1179	160	5	,	,	PUNCT
ap-1179	160	6	f2	f2	PROPN
ap-1179	160	7	,	,	PUNCT
ap-1179	160	8	.	.	PUNCT
ap-1179	160	9	.	.	PUNCT
ap-1179	161	1	.	.	PUNCT
ap-1179	162	1	,	,	PUNCT
ap-1179	162	2	fn	fn	NOUN
ap-1179	162	3	)	)	PUNCT
ap-1179	162	4	∂(x1	∂(x1	PROPN
ap-1179	162	5	,	,	PUNCT
ap-1179	162	6	x2	x2	PROPN
ap-1179	162	7	,	,	PUNCT
ap-1179	162	8	.	.	PUNCT
ap-1179	162	9	.	.	PUNCT
ap-1179	162	10	.	.	PUNCT
ap-1179	163	1	,	,	PUNCT
ap-1179	163	2	xn	xn	X
ap-1179	163	3	)	)	PUNCT
ap-1179	163	4	∣∣∣∣	∣∣∣∣	NOUN
ap-1179	163	5	,	,	PUNCT
ap-1179	163	6	(	(	PUNCT
ap-1179	163	7	3.21	3.21	NUM
ap-1179	163	8	)	)	PUNCT
ap-1179	163	9	considered	consider	VERB
ap-1179	163	10	by	by	ADP
ap-1179	163	11	nambu	nambu	NOUN
ap-1179	163	12	[	[	X
ap-1179	163	13	12	12	NUM
ap-1179	163	14	]	]	X
ap-1179	163	15	specially	specially	ADV
ap-1179	163	16	for	for	ADP
ap-1179	163	17	n	n	NOUN
ap-1179	163	18	=	=	SYM
ap-1179	163	19	3	3	X
ap-1179	163	20	.	.	PUNCT
ap-1179	164	1	the	the	DET
ap-1179	164	2	conmmutators	conmmutator	NOUN
ap-1179	164	3	in	in	ADP
ap-1179	164	4	(	(	PUNCT
ap-1179	164	5	3.20	3.20	NUM
ap-1179	164	6	)	)	PUNCT
ap-1179	164	7	and	and	CCONJ
ap-1179	164	8	the	the	DET
ap-1179	164	9	above	above	ADJ
ap-1179	164	10	jacobian	jacobian	ADJ
ap-1179	164	11	nbracket	nbracket	NOUN
ap-1179	164	12	satisfy	satisfy	VERB
ap-1179	164	13	the	the	DET
ap-1179	164	14	fi	fi	NOUN
ap-1179	164	15	,	,	PUNCT
ap-1179	164	16	which	which	PRON
ap-1179	164	17	can	can	AUX
ap-1179	164	18	be	be	AUX
ap-1179	164	19	checked	check	VERB
ap-1179	164	20	by	by	ADP
ap-1179	164	21	using	use	VERB
ap-1179	164	22	the	the	DET
ap-1179	164	23	schouten	schouten	ADJ
ap-1179	164	24	identities	identity	NOUN
ap-1179	164	25	technique	technique	NOUN
ap-1179	164	26	.	.	PUNCT
ap-1179	165	1	all	all	DET
ap-1179	165	2	these	these	DET
ap-1179	165	3	examples	example	NOUN
ap-1179	165	4	are	be	AUX
ap-1179	165	5	also	also	ADV
ap-1179	165	6	metric	metric	ADJ
ap-1179	165	7	fas	fas	NOUN
ap-1179	165	8	.	.	PROPN
ap-1179	165	9	4	4	NUM
ap-1179	165	10	n	n	CCONJ
ap-1179	165	11	-	-	PUNCT
ap-1179	165	12	ary	ary	NOUN
ap-1179	165	13	poisson	poisson	NOUN
ap-1179	165	14	generalizations	generalization	NOUN
ap-1179	165	15	both	both	CCONJ
ap-1179	165	16	glas	glas	PROPN
ap-1179	165	17	and	and	CCONJ
ap-1179	165	18	fas	fas	PROPN
ap-1179	165	19	have	have	VERB
ap-1179	165	20	n	n	CCONJ
ap-1179	165	21	-	-	PUNCT
ap-1179	165	22	ary	ary	ADJ
ap-1179	165	23	poisson	poisson	PROPN
ap-1179	165	24	structure	structure	NOUN
ap-1179	165	25	counterparts	counterpart	NOUN
ap-1179	165	26	.	.	PUNCT
ap-1179	166	1	these	these	PRON
ap-1179	166	2	satisfy	satisfy	VERB
ap-1179	166	3	the	the	DET
ap-1179	166	4	associated	associated	ADJ
ap-1179	166	5	gji	gji	NOUN
ap-1179	166	6	and	and	CCONJ
ap-1179	166	7	fi	fi	NOUN
ap-1179	166	8	characteristic	characteristic	ADJ
ap-1179	166	9	identities	identity	NOUN
ap-1179	166	10	,	,	PUNCT
ap-1179	166	11	to	to	PART
ap-1179	166	12	which	which	PRON
ap-1179	166	13	leibniz	leibniz	PROPN
ap-1179	166	14	’s	’s	PART
ap-1179	166	15	rule	rule	NOUN
ap-1179	166	16	is	be	AUX
ap-1179	166	17	added	add	VERB
ap-1179	166	18	.	.	PUNCT
ap-1179	167	1	4.1	4.1	NUM
ap-1179	167	2	generalized	generalize	VERB
ap-1179	167	3	poisson	poisson	NOUN
ap-1179	167	4	structures	structure	NOUN
ap-1179	167	5	(	(	PUNCT
ap-1179	167	6	gps	gps	PROPN
ap-1179	167	7	)	)	PUNCT
ap-1179	167	8	the	the	DET
ap-1179	167	9	generalized	generalize	VERB
ap-1179	167	10	poisson	poisson	NOUN
ap-1179	167	11	structures	structure	NOUN
ap-1179	167	12	[	[	X
ap-1179	167	13	2	2	NUM
ap-1179	167	14	]	]	PUNCT
ap-1179	167	15	(	(	PUNCT
ap-1179	167	16	gps	gps	PROPN
ap-1179	167	17	,	,	PUNCT
ap-1179	167	18	n	n	CCONJ
ap-1179	167	19	even	even	ADV
ap-1179	167	20	)	)	PUNCT
ap-1179	167	21	are	be	AUX
ap-1179	167	22	defined	define	VERB
ap-1179	167	23	by	by	ADP
ap-1179	167	24	brackets	bracket	NOUN
ap-1179	167	25	{	{	PUNCT
ap-1179	167	26	f1	f1	NOUN
ap-1179	167	27	,	,	PUNCT
ap-1179	167	28	.	.	PUNCT
ap-1179	167	29	.	.	PUNCT
ap-1179	167	30	.	.	PUNCT
ap-1179	168	1	,	,	PUNCT
ap-1179	168	2	fn	fn	NOUN
ap-1179	168	3	}	}	PUNCT
ap-1179	168	4	where	where	SCONJ
ap-1179	168	5	the	the	DET
ap-1179	168	6	fi	fi	NOUN
ap-1179	168	7	,	,	PUNCT
ap-1179	168	8	i	i	NOUN
ap-1179	168	9	=	=	NOUN
ap-1179	168	10	1	1	NUM
ap-1179	168	11	,	,	PUNCT
ap-1179	168	12	.	.	PUNCT
ap-1179	168	13	.	.	PUNCT
ap-1179	168	14	.	.	PUNCT
ap-1179	169	1	,	,	PUNCT
ap-1179	169	2	n	n	CCONJ
ap-1179	169	3	,	,	PUNCT
ap-1179	169	4	are	be	AUX
ap-1179	169	5	functions	function	NOUN
ap-1179	169	6	on	on	ADP
ap-1179	169	7	a	a	DET
ap-1179	169	8	manifold	manifold	NOUN
ap-1179	169	9	.	.	PUNCT
ap-1179	170	1	they	they	PRON
ap-1179	170	2	are	be	AUX
ap-1179	170	3	skewsymmtric	skewsymmtric	ADJ
ap-1179	170	4	{	{	PUNCT
ap-1179	170	5	f1	f1	NOUN
ap-1179	170	6	,	,	PUNCT
ap-1179	170	7	.	.	PUNCT
ap-1179	170	8	.	.	PUNCT
ap-1179	170	9	.	.	PUNCT
ap-1179	171	1	,	,	PUNCT
ap-1179	171	2	fi	fi	NOUN
ap-1179	171	3	,	,	PUNCT
ap-1179	171	4	.	.	PUNCT
ap-1179	171	5	.	.	PUNCT
ap-1179	171	6	.	.	PUNCT
ap-1179	172	1	,	,	PUNCT
ap-1179	172	2	fj	fj	INTJ
ap-1179	172	3	,	,	PUNCT
ap-1179	172	4	.	.	PUNCT
ap-1179	172	5	.	.	PUNCT
ap-1179	172	6	.	.	PUNCT
ap-1179	173	1	,	,	PUNCT
ap-1179	173	2	fn	fn	NOUN
ap-1179	173	3	}	}	PUNCT
ap-1179	173	4	=	=	SYM
ap-1179	173	5	−{f1	−{f1	NOUN
ap-1179	173	6	,	,	PUNCT
ap-1179	173	7	.	.	PUNCT
ap-1179	173	8	.	.	PUNCT
ap-1179	173	9	.	.	PUNCT
ap-1179	174	1	,	,	PUNCT
ap-1179	174	2	fj	fj	INTJ
ap-1179	174	3	,	,	PUNCT
ap-1179	174	4	.	.	PUNCT
ap-1179	174	5	.	.	PUNCT
ap-1179	174	6	.	.	PUNCT
ap-1179	175	1	,	,	PUNCT
ap-1179	175	2	fi	fi	NOUN
ap-1179	175	3	,	,	PUNCT
ap-1179	175	4	.	.	PUNCT
ap-1179	175	5	.	.	PUNCT
ap-1179	176	1	.	.	PUNCT
ap-1179	177	1	,	,	PUNCT
ap-1179	177	2	fn	fn	NOUN
ap-1179	177	3	}	}	PUNCT
ap-1179	177	4	,	,	PUNCT
ap-1179	177	5	(	(	PUNCT
ap-1179	177	6	4.22	4.22	NUM
ap-1179	177	7	)	)	PUNCT
ap-1179	177	8	satisfy	satisfy	VERB
ap-1179	177	9	the	the	DET
ap-1179	177	10	leibniz	leibniz	NOUN
ap-1179	177	11	identity	identity	NOUN
ap-1179	177	12	,	,	PUNCT
ap-1179	177	13	{	{	PUNCT
ap-1179	177	14	f1	f1	NOUN
ap-1179	177	15	,	,	PUNCT
ap-1179	177	16	.	.	PUNCT
ap-1179	177	17	.	.	PUNCT
ap-1179	178	1	.	.	PUNCT
ap-1179	179	1	,	,	PUNCT
ap-1179	179	2	fn−1	fn−1	PROPN
ap-1179	179	3	,	,	PUNCT
ap-1179	179	4	gh	gh	PROPN
ap-1179	179	5	}	}	PUNCT
ap-1179	179	6	=	=	PUNCT
ap-1179	179	7	g{f1	g{f1	NUM
ap-1179	179	8	,	,	PUNCT
ap-1179	179	9	.	.	PUNCT
ap-1179	179	10	.	.	PUNCT
ap-1179	180	1	.	.	PUNCT
ap-1179	181	1	,	,	PUNCT
ap-1179	181	2	fn−1	fn−1	PROPN
ap-1179	181	3	,	,	PUNCT
ap-1179	181	4	h}+	h}+	X
ap-1179	181	5	{	{	PUNCT
ap-1179	181	6	f1	f1	NOUN
ap-1179	181	7	,	,	PUNCT
ap-1179	181	8	.	.	PUNCT
ap-1179	181	9	.	.	PUNCT
ap-1179	181	10	.	.	PUNCT
ap-1179	182	1	,	,	PUNCT
ap-1179	182	2	fn−1	fn−1	ADJ
ap-1179	182	3	,	,	PUNCT
ap-1179	182	4	g}h	g}h	PROPN
ap-1179	182	5	,	,	PUNCT
ap-1179	182	6	(	(	PUNCT
ap-1179	182	7	4.23	4.23	NUM
ap-1179	182	8	)	)	PUNCT
ap-1179	182	9	and	and	CCONJ
ap-1179	182	10	the	the	DET
ap-1179	182	11	characteristic	characteristic	ADJ
ap-1179	182	12	identity	identity	NOUN
ap-1179	182	13	of	of	ADP
ap-1179	182	14	the	the	DET
ap-1179	182	15	glas	gla	NOUN
ap-1179	182	16	,	,	PUNCT
ap-1179	182	17	the	the	DET
ap-1179	182	18	gji	gji	NOUN
ap-1179	182	19	(	(	PUNCT
ap-1179	182	20	1.3	1.3	NUM
ap-1179	182	21	)	)	PUNCT
ap-1179	182	22	,	,	PUNCT
ap-1179	182	23	∑	∑	PUNCT
ap-1179	182	24	σ∈s4s−1	σ∈s4s−1	ADJ
ap-1179	182	25	(	(	PUNCT
ap-1179	182	26	−1)π(σ){fσ(1	−1)π(σ){fσ(1	NOUN
ap-1179	182	27	)	)	PUNCT
ap-1179	182	28	,	,	PUNCT
ap-1179	182	29	.	.	PUNCT
ap-1179	182	30	.	.	PUNCT
ap-1179	182	31	.	.	PUNCT
ap-1179	183	1	,	,	PUNCT
ap-1179	183	2	fσ(2s−1	fσ(2s−1	NUM
ap-1179	183	3	)	)	PUNCT
ap-1179	183	4	,	,	PUNCT
ap-1179	183	5	{	{	PUNCT
ap-1179	183	6	fσ(2s	fσ(2s	NOUN
ap-1179	183	7	)	)	PUNCT
ap-1179	183	8	,	,	PUNCT
ap-1179	183	9	.	.	PUNCT
ap-1179	183	10	.	.	PUNCT
ap-1179	184	1	.	.	PUNCT
ap-1179	185	1	,	,	PUNCT
ap-1179	185	2	fσ(4s−1	fσ(4s−1	NUM
ap-1179	185	3	)	)	PUNCT
ap-1179	185	4	}	}	PUNCT
ap-1179	185	5	}	}	PUNCT
ap-1179	186	1	=	=	SYM
ap-1179	186	2	0	0	X
ap-1179	186	3	.	.	PUNCT
ap-1179	187	1	(	(	PUNCT
ap-1179	187	2	4.24	4.24	NUM
ap-1179	187	3	)	)	PUNCT
ap-1179	187	4	as	as	ADP
ap-1179	187	5	with	with	ADP
ap-1179	187	6	ordinary	ordinary	ADJ
ap-1179	187	7	poisson	poisson	NOUN
ap-1179	187	8	structures	structure	NOUN
ap-1179	187	9	,	,	PUNCT
ap-1179	187	10	there	there	PRON
ap-1179	187	11	are	be	VERB
ap-1179	187	12	linear	linear	ADJ
ap-1179	187	13	gps	gps	NOUN
ap-1179	187	14	given	give	VERB
ap-1179	187	15	in	in	ADP
ap-1179	187	16	terms	term	NOUN
ap-1179	187	17	of	of	ADP
ap-1179	187	18	coordinates	coordinate	NOUN
ap-1179	187	19	of	of	ADP
ap-1179	187	20	the	the	DET
ap-1179	187	21	odd	odd	ADJ
ap-1179	187	22	cocyles	cocyle	NOUN
ap-1179	187	23	of	of	ADP
ap-1179	187	24	the	the	DET
ap-1179	187	25	g	g	NOUN
ap-1179	187	26	in	in	ADP
ap-1179	187	27	the	the	DET
ap-1179	187	28	table	table	NOUN
ap-1179	187	29	of	of	ADP
ap-1179	187	30	sec	sec	PROPN
ap-1179	187	31	.	.	PROPN
ap-1179	187	32	3.1	3.1	NUM
ap-1179	187	33	.	.	PUNCT
ap-1179	188	1	they	they	PRON
ap-1179	188	2	are	be	AUX
ap-1179	188	3	given	give	VERB
ap-1179	188	4	by	by	ADP
ap-1179	188	5	the	the	DET
ap-1179	188	6	multivector	multivector	NOUN
ap-1179	188	7	λ	λ	NOUN
ap-1179	188	8	=	=	SYM
ap-1179	188	9	1	1	NUM
ap-1179	188	10	(	(	PUNCT
ap-1179	188	11	2m−	2m−	PROPN
ap-1179	188	12	2)!ωi1	2)!ωi1	NUM
ap-1179	188	13	...	...	PUNCT
ap-1179	189	1	i2m−2	i2m−2	PROPN
ap-1179	189	2	σ	σ	PROPN
ap-1179	189	3	·	·	PUNCT
ap-1179	189	4	xσ∂i1	xσ∂i1	PUNCT
ap-1179	190	1	∧	∧	PROPN
ap-1179	190	2	.	.	PUNCT
ap-1179	190	3	.	.	PUNCT
ap-1179	190	4	.	.	PUNCT
ap-1179	191	1	∧	∧	NOUN
ap-1179	191	2	∂i2m−2	∂i2m−2	PROPN
ap-1179	191	3	(	(	PUNCT
ap-1179	191	4	4.25	4.25	NUM
ap-1179	191	5	)	)	PUNCT
ap-1179	191	6	since	since	SCONJ
ap-1179	191	7	,	,	PUNCT
ap-1179	191	8	as	as	SCONJ
ap-1179	191	9	it	it	PRON
ap-1179	191	10	may	may	AUX
ap-1179	191	11	be	be	AUX
ap-1179	191	12	checked	check	VERB
ap-1179	191	13	[	[	PUNCT
ap-1179	191	14	2	2	NUM
ap-1179	191	15	]	]	PUNCT
ap-1179	191	16	,	,	PUNCT
ap-1179	191	17	λ	λ	PROPN
ap-1179	191	18	has	have	VERB
ap-1179	191	19	zero	zero	NUM
ap-1179	191	20	schoutennijenhuis	schoutennijenhuis	ADJ
ap-1179	191	21	bracket	bracket	NOUN
ap-1179	191	22	with	with	ADP
ap-1179	191	23	itself	itself	PRON
ap-1179	191	24	,	,	PUNCT
ap-1179	191	25	[	[	X
ap-1179	191	26	λ	λ	X
ap-1179	191	27	,	,	PUNCT
ap-1179	191	28	λ]sn	λ]sn	X
ap-1179	191	29	=	=	SYM
ap-1179	191	30	0	0	NUM
ap-1179	191	31	,	,	PUNCT
ap-1179	191	32	which	which	PRON
ap-1179	191	33	corresponds	correspond	VERB
ap-1179	191	34	to	to	ADP
ap-1179	191	35	the	the	DET
ap-1179	191	36	gji	gji	NOUN
ap-1179	191	37	.	.	PUNCT
ap-1179	192	1	all	all	DET
ap-1179	192	2	glas	gla	NOUN
ap-1179	192	3	associated	associate	VERB
ap-1179	192	4	with	with	ADP
ap-1179	192	5	a	a	DET
ap-1179	192	6	simple	simple	ADJ
ap-1179	192	7	algebra	algebra	NOUN
ap-1179	192	8	define	define	VERB
ap-1179	192	9	linear	linear	ADJ
ap-1179	192	10	gps	gps	PROPN
ap-1179	192	11	.	.	PUNCT
ap-1179	193	1	4.2	4.2	NUM
ap-1179	193	2	nambu	nambu	NOUN
ap-1179	193	3	-	-	PUNCT
ap-1179	193	4	poisson	poisson	NOUN
ap-1179	193	5	structures	structure	NOUN
ap-1179	193	6	(	(	PUNCT
ap-1179	193	7	n	n	CCONJ
ap-1179	193	8	-	-	PUNCT
ap-1179	193	9	p	p	X
ap-1179	193	10	)	)	PUNCT
ap-1179	193	11	these	these	PRON
ap-1179	193	12	are	be	AUX
ap-1179	193	13	defined	define	VERB
ap-1179	193	14	by	by	ADP
ap-1179	193	15	relations	relation	NOUN
ap-1179	193	16	(	(	PUNCT
ap-1179	193	17	4.22	4.22	NUM
ap-1179	193	18	)	)	PUNCT
ap-1179	193	19	and	and	CCONJ
ap-1179	193	20	(	(	PUNCT
ap-1179	193	21	4.23	4.23	NUM
ap-1179	193	22	)	)	PUNCT
ap-1179	193	23	,	,	PUNCT
ap-1179	193	24	but	but	CCONJ
ap-1179	193	25	now	now	ADV
ap-1179	193	26	the	the	DET
ap-1179	193	27	characteristic	characteristic	ADJ
ap-1179	193	28	identity	identity	NOUN
ap-1179	193	29	is	be	AUX
ap-1179	193	30	the	the	DET
ap-1179	193	31	fi	fi	NOUN
ap-1179	193	32	,	,	PUNCT
ap-1179	193	33	{	{	PUNCT
ap-1179	193	34	f1	f1	NOUN
ap-1179	193	35	,	,	PUNCT
ap-1179	193	36	.	.	PUNCT
ap-1179	193	37	.	.	PUNCT
ap-1179	193	38	.	.	PUNCT
ap-1179	194	1	,	,	PUNCT
ap-1179	194	2	fn−1	fn−1	PROPN
ap-1179	194	3	,	,	PUNCT
ap-1179	194	4	{	{	PUNCT
ap-1179	194	5	g1	g1	PROPN
ap-1179	194	6	,	,	PUNCT
ap-1179	194	7	.	.	PUNCT
ap-1179	194	8	.	.	PUNCT
ap-1179	195	1	.	.	PUNCT
ap-1179	196	1	,	,	PUNCT
ap-1179	196	2	gn	gn	PROPN
ap-1179	196	3	}	}	PUNCT
ap-1179	196	4	}	}	PUNCT
ap-1179	196	5	=	=	SYM
ap-1179	196	6	{	{	PUNCT
ap-1179	196	7	{	{	PUNCT
ap-1179	196	8	f1	f1	NOUN
ap-1179	196	9	,	,	PUNCT
ap-1179	196	10	.	.	PUNCT
ap-1179	196	11	.	.	PUNCT
ap-1179	197	1	.	.	PUNCT
ap-1179	198	1	,	,	PUNCT
ap-1179	198	2	fn−1	fn−1	ADJ
ap-1179	198	3	,	,	PUNCT
ap-1179	198	4	g1	g1	PROPN
ap-1179	198	5	}	}	PUNCT
ap-1179	198	6	,	,	PUNCT
ap-1179	198	7	g2	g2	PROPN
ap-1179	198	8	,	,	PUNCT
ap-1179	198	9	.	.	PUNCT
ap-1179	198	10	.	.	PUNCT
ap-1179	198	11	.	.	PUNCT
ap-1179	199	1	,	,	PUNCT
ap-1179	199	2	gn}+	gn}+	PROPN
ap-1179	199	3	{	{	PUNCT
ap-1179	199	4	g1	g1	PROPN
ap-1179	199	5	,	,	PUNCT
ap-1179	199	6	{	{	PUNCT
ap-1179	199	7	f1	f1	NOUN
ap-1179	199	8	,	,	PUNCT
ap-1179	199	9	.	.	PUNCT
ap-1179	199	10	.	.	PUNCT
ap-1179	200	1	.	.	PUNCT
ap-1179	201	1	,	,	PUNCT
ap-1179	201	2	fn−1	fn−1	PROPN
ap-1179	201	3	,	,	PUNCT
ap-1179	201	4	g2	g2	PROPN
ap-1179	201	5	}	}	PUNCT
ap-1179	201	6	,	,	PUNCT
ap-1179	201	7	g3	g3	PROPN
ap-1179	201	8	,	,	PUNCT
ap-1179	201	9	.	.	PUNCT
ap-1179	201	10	.	.	PUNCT
ap-1179	201	11	.	.	PUNCT
ap-1179	202	1	,	,	PUNCT
ap-1179	202	2	gn}+	gn}+	PROPN
ap-1179	202	3	.	.	PUNCT
ap-1179	202	4	.	.	PUNCT
ap-1179	203	1	.+	.+	NOUN
ap-1179	203	2	(	(	PUNCT
ap-1179	203	3	4.26	4.26	NUM
ap-1179	203	4	)	)	PUNCT
ap-1179	203	5	{	{	PUNCT
ap-1179	203	6	g1	g1	PROPN
ap-1179	203	7	.	.	PUNCT
ap-1179	203	8	.	.	PUNCT
ap-1179	204	1	.	.	PUNCT
ap-1179	205	1	,	,	PUNCT
ap-1179	205	2	gn−1	gn−1	PROPN
ap-1179	205	3	,	,	PUNCT
ap-1179	205	4	{	{	PUNCT
ap-1179	205	5	f1	f1	NOUN
ap-1179	205	6	,	,	PUNCT
ap-1179	205	7	.	.	PUNCT
ap-1179	205	8	.	.	PUNCT
ap-1179	206	1	.	.	PUNCT
ap-1179	207	1	,	,	PUNCT
ap-1179	207	2	fn−1	fn−1	PROPN
ap-1179	207	3	,	,	PUNCT
ap-1179	207	4	gn	gn	ADJ
ap-1179	207	5	}	}	PUNCT
ap-1179	207	6	}	}	PUNCT
ap-1179	207	7	.	.	PUNCT
ap-1179	208	1	the	the	DET
ap-1179	208	2	filippov	filippov	ADJ
ap-1179	208	3	identity	identity	NOUN
ap-1179	208	4	for	for	ADP
ap-1179	208	5	the	the	DET
ap-1179	208	6	(	(	PUNCT
ap-1179	208	7	nambu	nambu	PROPN
ap-1179	208	8	)	)	PUNCT
ap-1179	208	9	jacobians	jacobian	NOUN
ap-1179	208	10	of	of	ADP
ap-1179	208	11	n	n	PRON
ap-1179	208	12	functions	function	NOUN
ap-1179	208	13	was	be	AUX
ap-1179	208	14	first	first	ADV
ap-1179	208	15	written	write	VERB
ap-1179	208	16	by	by	ADP
ap-1179	208	17	filippov	filippov	NOUN
ap-1179	208	18	[	[	X
ap-1179	208	19	8	8	NUM
ap-1179	208	20	]	]	PUNCT
ap-1179	208	21	,	,	PUNCT
ap-1179	208	22	and	and	CCONJ
ap-1179	208	23	by	by	ADP
ap-1179	208	24	sahoo	sahoo	PROPN
ap-1179	208	25	and	and	CCONJ
ap-1179	208	26	valsakumar	valsakumar	NOUN
ap-1179	209	1	[	[	X
ap-1179	209	2	13	13	NUM
ap-1179	209	3	]	]	PUNCT
ap-1179	209	4	and	and	CCONJ
ap-1179	209	5	takhtajan	takhtajan	VERB
ap-1179	209	6	[	[	X
ap-1179	209	7	14	14	NUM
ap-1179	209	8	]	]	X
ap-1179	209	9	(	(	PUNCT
ap-1179	209	10	who	who	PRON
ap-1179	209	11	called	call	VERB
ap-1179	209	12	it	it	PRON
ap-1179	209	13	fundamental	fundamental	ADJ
ap-1179	209	14	identity	identity	NOUN
ap-1179	209	15	)	)	PUNCT
ap-1179	209	16	in	in	ADP
ap-1179	209	17	the	the	DET
ap-1179	209	18	context	context	NOUN
ap-1179	209	19	of	of	ADP
ap-1179	209	20	nambu	nambu	PROPN
ap-1179	209	21	mechanics	mechanic	NOUN
ap-1179	209	22	[	[	X
ap-1179	209	23	12	12	NUM
ap-1179	209	24	]	]	PUNCT
ap-1179	209	25	.	.	PUNCT
ap-1179	210	1	physically	physically	ADV
ap-1179	210	2	,	,	PUNCT
ap-1179	210	3	the	the	DET
ap-1179	210	4	fi	fi	NOUN
ap-1179	210	5	is	be	AUX
ap-1179	210	6	a	a	DET
ap-1179	210	7	consistency	consistency	NOUN
ap-1179	210	8	condition	condition	NOUN
ap-1179	210	9	for	for	ADP
ap-1179	210	10	the	the	DET
ap-1179	210	11	time	time	NOUN
ap-1179	210	12	evolution	evolution	NOUN
ap-1179	210	13	[	[	X
ap-1179	210	14	13	13	NUM
ap-1179	210	15	,	,	PUNCT
ap-1179	210	16	14	14	NUM
ap-1179	210	17	]	]	PUNCT
ap-1179	210	18	,	,	PUNCT
ap-1179	210	19	given	give	VERB
ap-1179	210	20	in	in	ADP
ap-1179	210	21	terms	term	NOUN
ap-1179	210	22	of	of	ADP
ap-1179	210	23	(	(	PUNCT
ap-1179	210	24	n	n	CCONJ
ap-1179	210	25	−	−	PROPN
ap-1179	210	26	1	1	NUM
ap-1179	210	27	)	)	PUNCT
ap-1179	210	28	‘	'	PUNCT
ap-1179	210	29	hamiltonian	hamiltonian	ADJ
ap-1179	210	30	’	'	PUNCT
ap-1179	210	31	functions	function	NOUN
ap-1179	210	32	that	that	PRON
ap-1179	210	33	correspond	correspond	VERB
ap-1179	210	34	to	to	ADP
ap-1179	210	35	the	the	DET
ap-1179	210	36	adx	adx	NOUN
ap-1179	210	37	derivations	derivation	NOUN
ap-1179	210	38	of	of	ADP
ap-1179	210	39	a	a	DET
ap-1179	210	40	fa	fa	NOUN
ap-1179	210	41	.	.	PUNCT
ap-1179	211	1	every	every	DET
ap-1179	211	2	even	even	ADJ
ap-1179	211	3	n	n	CCONJ
ap-1179	211	4	-	-	PUNCT
ap-1179	211	5	p	p	NOUN
ap-1179	211	6	structure	structure	NOUN
ap-1179	211	7	is	be	AUX
ap-1179	211	8	also	also	ADV
ap-1179	211	9	a	a	DET
ap-1179	211	10	gps	gps	NOUN
ap-1179	211	11	,	,	PUNCT
ap-1179	211	12	but	but	CCONJ
ap-1179	211	13	the	the	DET
ap-1179	211	14	converse	converse	NOUN
ap-1179	211	15	does	do	AUX
ap-1179	211	16	not	not	PART
ap-1179	211	17	hold	hold	VERB
ap-1179	211	18	.	.	PUNCT
ap-1179	212	1	the	the	DET
ap-1179	212	2	question	question	NOUN
ap-1179	212	3	of	of	ADP
ap-1179	212	4	the	the	DET
ap-1179	212	5	quantization	quantization	NOUN
ap-1179	212	6	of	of	ADP
ap-1179	212	7	nambu	nambu	NOUN
ap-1179	212	8	-	-	PUNCT
ap-1179	212	9	poisson	poisson	NOUN
ap-1179	212	10	mechanics	mechanic	NOUN
ap-1179	212	11	has	have	AUX
ap-1179	212	12	been	be	AUX
ap-1179	212	13	the	the	DET
ap-1179	212	14	subject	subject	NOUN
ap-1179	212	15	of	of	ADP
ap-1179	212	16	a	a	DET
ap-1179	212	17	vast	vast	ADJ
ap-1179	212	18	literature	literature	NOUN
ap-1179	212	19	;	;	PUNCT
ap-1179	212	20	it	it	PRON
ap-1179	212	21	is	be	AUX
ap-1179	212	22	probably	probably	ADV
ap-1179	212	23	fair	fair	ADJ
ap-1179	212	24	to	to	PART
ap-1179	212	25	say	say	VERB
ap-1179	212	26	that	that	SCONJ
ap-1179	212	27	it	it	PRON
ap-1179	212	28	remains	remain	VERB
ap-1179	212	29	a	a	DET
ap-1179	212	30	problem	problem	NOUN
ap-1179	212	31	(	(	PUNCT
ap-1179	212	32	for	for	ADP
ap-1179	212	33	n	n	X
ap-1179	212	34	>	>	X
ap-1179	212	35	2	2	NUM
ap-1179	212	36	!	!	PUNCT
ap-1179	212	37	)	)	PUNCT
ap-1179	212	38	aggravated	aggravate	VERB
ap-1179	212	39	by	by	ADP
ap-1179	212	40	the	the	DET
ap-1179	212	41	fact	fact	NOUN
ap-1179	212	42	that	that	SCONJ
ap-1179	212	43	there	there	PRON
ap-1179	212	44	are	be	VERB
ap-1179	212	45	not	not	PART
ap-1179	212	46	so	so	ADV
ap-1179	212	47	many	many	ADJ
ap-1179	212	48	physical	physical	ADJ
ap-1179	212	49	examples	example	NOUN
ap-1179	212	50	of	of	ADP
ap-1179	212	51	n	n	CCONJ
ap-1179	212	52	-	-	PUNCT
ap-1179	212	53	p	p	ADJ
ap-1179	212	54	mechanical	mechanical	ADJ
ap-1179	212	55	systems	system	NOUN
ap-1179	212	56	to	to	PART
ap-1179	212	57	be	be	AUX
ap-1179	212	58	quantized	quantize	VERB
ap-1179	212	59	.	.	PUNCT
ap-1179	213	1	we	we	PRON
ap-1179	213	2	shall	shall	AUX
ap-1179	213	3	just	just	ADV
ap-1179	213	4	refer	refer	VERB
ap-1179	213	5	here	here	ADV
ap-1179	213	6	to	to	ADP
ap-1179	213	7	[	[	X
ap-1179	213	8	15	15	NUM
ap-1179	213	9	,	,	PUNCT
ap-1179	213	10	16	16	NUM
ap-1179	213	11	,	,	PUNCT
ap-1179	213	12	17	17	NUM
ap-1179	213	13	]	]	PUNCT
ap-1179	213	14	,	,	PUNCT
ap-1179	213	15	from	from	ADP
ap-1179	213	16	which	which	PRON
ap-1179	213	17	the	the	DET
ap-1179	213	18	earlier	early	ADJ
ap-1179	213	19	literature	literature	NOUN
ap-1179	213	20	can	can	AUX
ap-1179	213	21	be	be	AUX
ap-1179	213	22	traced	trace	VERB
ap-1179	213	23	.	.	PUNCT
ap-1179	214	1	5	5	NUM
ap-1179	214	2	lie	lie	NOUN
ap-1179	214	3	algebra	algebra	NOUN
ap-1179	214	4	cohomology	cohomology	NOUN
ap-1179	214	5	,	,	PUNCT
ap-1179	214	6	extensions	extension	NOUN
ap-1179	214	7	and	and	CCONJ
ap-1179	214	8	deformations	deformation	NOUN
ap-1179	214	9	given	give	VERB
ap-1179	214	10	a	a	DET
ap-1179	214	11	lie	lie	NOUN
ap-1179	214	12	algebra	algebra	NOUN
ap-1179	214	13	g	g	PROPN
ap-1179	214	14	,	,	PUNCT
ap-1179	214	15	the	the	DET
ap-1179	214	16	p	p	NOUN
ap-1179	214	17	-	-	PUNCT
ap-1179	214	18	cochains	cochain	NOUN
ap-1179	214	19	of	of	ADP
ap-1179	214	20	the	the	DET
ap-1179	214	21	lie	lie	NOUN
ap-1179	214	22	algebra	algebra	NOUN
ap-1179	214	23	cohomology	cohomology	NOUN
ap-1179	214	24	are	be	AUX
ap-1179	214	25	p	p	NOUN
ap-1179	214	26	-	-	PUNCT
ap-1179	214	27	antisymmetric	antisymmetric	ADJ
ap-1179	214	28	,	,	PUNCT
ap-1179	214	29	v	v	ADP
ap-1179	214	30	-valued	-value	VERB
ap-1179	214	31	maps	map	NOUN
ap-1179	214	32	(	(	PUNCT
ap-1179	214	33	where	where	SCONJ
ap-1179	214	34	v	v	NOUN
ap-1179	214	35	is	be	AUX
ap-1179	214	36	a	a	DET
ap-1179	214	37	g	g	NOUN
ap-1179	214	38	-	-	PUNCT
ap-1179	214	39	module	module	NOUN
ap-1179	214	40	)	)	PUNCT
ap-1179	214	41	,	,	PUNCT
ap-1179	214	42	ωp	ωp	X
ap-1179	214	43	:	:	PUNCT
ap-1179	214	44	g×	g×	X
ap-1179	214	45	p	p	X
ap-1179	214	46	·	·	PUNCT
ap-1179	214	47	·	·	PUNCT
ap-1179	214	48	·	·	PUNCT
ap-1179	215	1	×g→	×g→	X
ap-1179	215	2	v	v	NOUN
ap-1179	215	3	,	,	PUNCT
ap-1179	215	4	ωa	ωa	PROPN
ap-1179	215	5	=	=	SYM
ap-1179	215	6	1	1	NUM
ap-1179	215	7	p	p	NOUN
ap-1179	215	8	!	!	PUNCT
ap-1179	216	1	ωa	ωa	PROPN
ap-1179	216	2	i1	i1	PROPN
ap-1179	216	3	...	...	PUNCT
ap-1179	216	4	ip	ip	NOUN
ap-1179	216	5	ωi1	ωi1	NOUN
ap-1179	216	6	∧	∧	NOUN
ap-1179	216	7	.	.	PUNCT
ap-1179	216	8	.	.	PUNCT
ap-1179	216	9	.	.	PUNCT
ap-1179	217	1	∧	∧	PROPN
ap-1179	217	2	ωip	ωip	NOUN
ap-1179	217	3	,	,	PUNCT
ap-1179	217	4	(	(	PUNCT
ap-1179	217	5	5.27	5.27	NUM
ap-1179	217	6	)	)	PUNCT
ap-1179	217	7	where	where	SCONJ
ap-1179	217	8	{	{	PUNCT
ap-1179	217	9	ωi	ωi	NOUN
ap-1179	217	10	}	}	PUNCT
ap-1179	217	11	is	be	AUX
ap-1179	217	12	a	a	DET
ap-1179	217	13	basis	basis	NOUN
ap-1179	217	14	of	of	ADP
ap-1179	217	15	the	the	DET
ap-1179	217	16	coalgebra	coalgebra	NOUN
ap-1179	217	17	g∗.	g∗.	VERB
ap-1179	217	18	the	the	DET
ap-1179	217	19	coboundary	coboundary	ADJ
ap-1179	217	20	operator	operator	NOUN
ap-1179	217	21	(	(	PUNCT
ap-1179	217	22	for	for	ADP
ap-1179	217	23	the	the	DET
ap-1179	217	24	left	left	ADJ
ap-1179	217	25	action	action	NOUN
ap-1179	217	26	)	)	PUNCT
ap-1179	218	1	s	s	VERB
ap-1179	218	2	:	:	PUNCT
ap-1179	218	3	ωp	ωp	PART
ap-1179	218	4	∈	∈	PROPN
ap-1179	218	5	cp(g	cp(g	X
ap-1179	218	6	,	,	PUNCT
ap-1179	218	7	v	v	NOUN
ap-1179	218	8	)	)	PUNCT
ap-1179	218	9	�	�	PROPN
ap-1179	218	10	→	→	SYM
ap-1179	218	11	(	(	PUNCT
ap-1179	218	12	sωp	sωp	NOUN
ap-1179	218	13	)	)	PUNCT
ap-1179	218	14	∈	∈	PROPN
ap-1179	218	15	cp+1(g	cp+1(g	PROPN
ap-1179	218	16	,	,	PUNCT
ap-1179	218	17	v	v	NOUN
ap-1179	218	18	)	)	PUNCT
ap-1179	218	19	,	,	PUNCT
ap-1179	218	20	s2	s2	X
ap-1179	218	21	=	=	SYM
ap-1179	218	22	0	0	NUM
ap-1179	218	23	,	,	PUNCT
ap-1179	218	24	is	be	AUX
ap-1179	218	25	given	give	VERB
ap-1179	218	26	by	by	ADP
ap-1179	218	27	9	9	NUM
ap-1179	218	28	acta	acta	PROPN
ap-1179	218	29	polytechnica	polytechnica	PROPN
ap-1179	218	30	vol	vol	NOUN
ap-1179	218	31	.	.	PROPN
ap-1179	219	1	50	50	NUM
ap-1179	219	2	no	no	NOUN
ap-1179	219	3	.	.	PUNCT
ap-1179	220	1	3/2010	3/2010	NUM
ap-1179	220	2	(	(	PUNCT
ap-1179	220	3	sωp)a	sωp)a	PROPN
ap-1179	220	4	(	(	PUNCT
ap-1179	220	5	x1	x1	PROPN
ap-1179	220	6	,	,	PUNCT
ap-1179	220	7	.	.	PUNCT
ap-1179	220	8	.	.	PUNCT
ap-1179	220	9	.	.	PUNCT
ap-1179	221	1	,	,	PUNCT
ap-1179	221	2	xp+1	xp+1	NUM
ap-1179	221	3	)	)	PUNCT
ap-1179	221	4	:	:	PUNCT
ap-1179	222	1	=	=	SYM
ap-1179	222	2	p+1∑	p+1∑	PROPN
ap-1179	222	3	i=1	i=1	X
ap-1179	222	4	(	(	PUNCT
ap-1179	222	5	−)i+1ρ(xi	−)i+1ρ(xi	PROPN
ap-1179	222	6	)	)	PUNCT
ap-1179	222	7	a	a	DET
ap-1179	222	8	.b	.b	PROPN
ap-1179	222	9	ω	ω	NUM
ap-1179	222	10	pb(x1	pb(x1	NOUN
ap-1179	222	11	,	,	PUNCT
ap-1179	222	12	.	.	PUNCT
ap-1179	222	13	.	.	PUNCT
ap-1179	222	14	.	.	PUNCT
ap-1179	223	1	,	,	PUNCT
ap-1179	223	2	x̂i	x̂i	PROPN
ap-1179	223	3	,	,	PUNCT
ap-1179	223	4	.	.	PUNCT
ap-1179	223	5	.	.	PUNCT
ap-1179	224	1	.	.	PUNCT
ap-1179	225	1	,	,	PUNCT
ap-1179	225	2	xp+1	xp+1	X
ap-1179	225	3	)	)	PUNCT
ap-1179	225	4	(	(	PUNCT
ap-1179	225	5	5.28	5.28	NUM
ap-1179	225	6	)	)	PUNCT
ap-1179	226	1	+	+	CCONJ
ap-1179	226	2	p+1∑	p+1∑	PROPN
ap-1179	226	3	j	j	NOUN
ap-1179	226	4	,	,	PUNCT
ap-1179	226	5	k=1	k=1	PROPN
ap-1179	226	6	j	j	PROPN
ap-1179	226	7	<	<	X
ap-1179	226	8	k	k	X
ap-1179	226	9	(	(	PUNCT
ap-1179	226	10	−)j+kωpa([xj	−)j+kωpa([xj	NOUN
ap-1179	226	11	,	,	PUNCT
ap-1179	226	12	xk	xk	PROPN
ap-1179	226	13	]	]	X
ap-1179	226	14	,	,	PUNCT
ap-1179	226	15	x1	x1	PROPN
ap-1179	226	16	,	,	PUNCT
ap-1179	226	17	.	.	PUNCT
ap-1179	226	18	.	.	PUNCT
ap-1179	226	19	.	.	PUNCT
ap-1179	227	1	,	,	PUNCT
ap-1179	227	2	x̂j	x̂j	PROPN
ap-1179	227	3	,	,	PUNCT
ap-1179	227	4	.	.	PUNCT
ap-1179	227	5	.	.	PUNCT
ap-1179	227	6	.	.	PUNCT
ap-1179	228	1	,	,	PUNCT
ap-1179	228	2	x̂k	x̂k	PROPN
ap-1179	228	3	,	,	PUNCT
ap-1179	228	4	.	.	PUNCT
ap-1179	228	5	.	.	PUNCT
ap-1179	228	6	.	.	PUNCT
ap-1179	229	1	,	,	PUNCT
ap-1179	229	2	xp+1	xp+1	NUM
ap-1179	229	3	)	)	PUNCT
ap-1179	229	4	.	.	PUNCT
ap-1179	230	1	for	for	ADP
ap-1179	230	2	the	the	DET
ap-1179	230	3	trivial	trivial	ADJ
ap-1179	230	4	action	action	NOUN
ap-1179	230	5	(	(	PUNCT
ap-1179	230	6	ρ	ρ	NOUN
ap-1179	230	7	=	=	NOUN
ap-1179	230	8	0	0	NUM
ap-1179	230	9	)	)	PUNCT
ap-1179	230	10	,	,	PUNCT
ap-1179	230	11	this	this	DET
ap-1179	230	12	simplifies	simplifie	NOUN
ap-1179	230	13	to	to	PART
ap-1179	230	14	(	(	PUNCT
ap-1179	230	15	sωp	sωp	NOUN
ap-1179	230	16	)	)	PUNCT
ap-1179	230	17	(	(	PUNCT
ap-1179	230	18	x1	x1	PROPN
ap-1179	230	19	,	,	PUNCT
ap-1179	230	20	.	.	PUNCT
ap-1179	230	21	.	.	PUNCT
ap-1179	230	22	.	.	PUNCT
ap-1179	231	1	,	,	PUNCT
ap-1179	231	2	xp+1	xp+1	X
ap-1179	231	3	)	)	PUNCT
ap-1179	231	4	=	=	SYM
ap-1179	231	5	p+1∑	p+1∑	PROPN
ap-1179	232	1	1≤j	1≤j	NOUN
ap-1179	232	2	<	<	X
ap-1179	232	3	k	k	X
ap-1179	232	4	(	(	PUNCT
ap-1179	232	5	−1)jωp(x1	−1)jωp(x1	PROPN
ap-1179	232	6	,	,	PUNCT
ap-1179	232	7	.	.	PUNCT
ap-1179	232	8	.	.	PUNCT
ap-1179	232	9	.	.	PUNCT
ap-1179	233	1	,	,	PUNCT
ap-1179	233	2	x̂j	x̂j	PROPN
ap-1179	233	3	,	,	PUNCT
ap-1179	233	4	.	.	PUNCT
ap-1179	233	5	.	.	PUNCT
ap-1179	234	1	.	.	PUNCT
ap-1179	235	1	,	,	PUNCT
ap-1179	235	2	adxj	adxj	PROPN
ap-1179	235	3	xk	xk	PROPN
ap-1179	235	4	,	,	PUNCT
ap-1179	235	5	.	.	PUNCT
ap-1179	235	6	.	.	PUNCT
ap-1179	236	1	.	.	PUNCT
ap-1179	237	1	,	,	PUNCT
ap-1179	237	2	xp+1	xp+1	NUM
ap-1179	237	3	)	)	PUNCT
ap-1179	237	4	.	.	PUNCT
ap-1179	238	1	(	(	PUNCT
ap-1179	238	2	5.29	5.29	NUM
ap-1179	238	3	)	)	PUNCT
ap-1179	238	4	the	the	DET
ap-1179	238	5	p	p	NOUN
ap-1179	238	6	-	-	PUNCT
ap-1179	238	7	cocycles	cocycle	NOUN
ap-1179	238	8	ωp	ωp	ADP
ap-1179	238	9	∈	∈	PROPN
ap-1179	238	10	zp	zp	PROPN
ap-1179	238	11	ρ(g	ρ(g	PROPN
ap-1179	238	12	,	,	PUNCT
ap-1179	238	13	v	v	NOUN
ap-1179	238	14	)	)	PUNCT
ap-1179	238	15	are	be	AUX
ap-1179	238	16	p	p	NOUN
ap-1179	238	17	-	-	PUNCT
ap-1179	238	18	cochains	cochain	NOUN
ap-1179	238	19	such	such	ADJ
ap-1179	238	20	that	that	DET
ap-1179	238	21	sωp	sωp	NOUN
ap-1179	238	22	=	=	SYM
ap-1179	238	23	0	0	NUM
ap-1179	238	24	;	;	PUNCT
ap-1179	238	25	the	the	DET
ap-1179	238	26	p	p	NOUN
ap-1179	238	27	-	-	PUNCT
ap-1179	238	28	coboundaries	coboundarie	NOUN
ap-1179	238	29	ωp	ωp	ADP
ap-1179	238	30	∈	∈	PROPN
ap-1179	238	31	bp	bp	PROPN
ap-1179	238	32	ρ(g	ρ(g	PROPN
ap-1179	238	33	,	,	PUNCT
ap-1179	238	34	v	v	NOUN
ap-1179	238	35	)	)	PUNCT
ap-1179	238	36	are	be	AUX
ap-1179	238	37	such	such	ADJ
ap-1179	238	38	that	that	SCONJ
ap-1179	238	39	ωp	ωp	NOUN
ap-1179	238	40	=	=	PUNCT
ap-1179	238	41	sωp−1	sωp−1	PROPN
ap-1179	238	42	for	for	ADP
ap-1179	238	43	some	some	PRON
ap-1179	238	44	(	(	PUNCT
ap-1179	238	45	p	p	NOUN
ap-1179	238	46	−	−	PROPN
ap-1179	238	47	1)-cochain	1)-cochain	NUM
ap-1179	238	48	.	.	PUNCT
ap-1179	239	1	the	the	DET
ap-1179	239	2	p	p	PROPN
ap-1179	239	3	-	-	PUNCT
ap-1179	239	4	th	th	X
ap-1179	239	5	cohomology	cohomology	NOUN
ap-1179	239	6	groups	group	NOUN
ap-1179	239	7	are	be	AUX
ap-1179	239	8	then	then	ADV
ap-1179	239	9	hp	hp	PROPN
ap-1179	239	10	ρ	ρ	PROPN
ap-1179	239	11	(	(	PUNCT
ap-1179	239	12	g	g	PROPN
ap-1179	239	13	,	,	PUNCT
ap-1179	239	14	v	v	NOUN
ap-1179	239	15	)	)	PUNCT
ap-1179	239	16	:	:	PUNCT
ap-1179	240	1	=	=	PUNCT
ap-1179	240	2	zp	zp	PROPN
ap-1179	240	3	ρ(g	ρ(g	PROPN
ap-1179	240	4	,	,	PUNCT
ap-1179	240	5	v	v	NOUN
ap-1179	240	6	)	)	PUNCT
ap-1179	240	7	/bp	/bp	PUNCT
ap-1179	240	8	ρ(g	ρ(g	ADJ
ap-1179	240	9	,	,	PUNCT
ap-1179	240	10	v	v	NOUN
ap-1179	240	11	)	)	PUNCT
ap-1179	240	12	.	.	PUNCT
ap-1179	241	1	for	for	ADP
ap-1179	241	2	semisimple	semisimple	ADJ
ap-1179	241	3	lie	lie	NOUN
ap-1179	241	4	algebras	algebra	NOUN
ap-1179	241	5	,	,	PUNCT
ap-1179	241	6	whitehead	whitehead	PROPN
ap-1179	241	7	’s	’s	PART
ap-1179	241	8	lemma	lemma	PROPN
ap-1179	241	9	states	state	VERB
ap-1179	241	10	that	that	SCONJ
ap-1179	241	11	h20	h20	PROPN
ap-1179	241	12	(	(	PUNCT
ap-1179	241	13	g	g	NOUN
ap-1179	241	14	)	)	PUNCT
ap-1179	241	15	=	=	SYM
ap-1179	241	16	0	0	NUM
ap-1179	241	17	,	,	PUNCT
ap-1179	241	18	h	h	NOUN
ap-1179	241	19	2	2	NUM
ap-1179	241	20	ad(g	ad(g	PUNCT
ap-1179	241	21	,	,	PUNCT
ap-1179	241	22	g	g	NOUN
ap-1179	241	23	)	)	PUNCT
ap-1179	241	24	=	=	SYM
ap-1179	241	25	0	0	X
ap-1179	241	26	.	.	PUNCT
ap-1179	242	1	hence	hence	ADV
ap-1179	242	2	,	,	PUNCT
ap-1179	242	3	semisimple	semisimple	NOUN
ap-1179	242	4	lie	lie	NOUN
ap-1179	242	5	algebras	algebra	NOUN
ap-1179	242	6	do	do	AUX
ap-1179	242	7	not	not	PART
ap-1179	242	8	admit	admit	VERB
ap-1179	242	9	non	non	ADJ
ap-1179	242	10	-	-	ADJ
ap-1179	242	11	trivial	trivial	ADJ
ap-1179	242	12	central	central	ADJ
ap-1179	242	13	extensions	extension	NOUN
ap-1179	242	14	and	and	CCONJ
ap-1179	242	15	are	be	AUX
ap-1179	242	16	moreover	moreover	ADV
ap-1179	242	17	rigid	rigid	ADJ
ap-1179	242	18	(	(	PUNCT
ap-1179	242	19	non	non	ADJ
ap-1179	242	20	-	-	ADJ
ap-1179	242	21	deformable	deformable	ADJ
ap-1179	242	22	)	)	PUNCT
ap-1179	242	23	since	since	SCONJ
ap-1179	242	24	central	central	ADJ
ap-1179	242	25	extensions	extension	NOUN
ap-1179	242	26	and	and	CCONJ
ap-1179	242	27	infinitesimal	infinitesimal	ADJ
ap-1179	242	28	deformations	deformation	NOUN
ap-1179	242	29	are	be	AUX
ap-1179	242	30	governed	govern	VERB
ap-1179	242	31	,	,	PUNCT
ap-1179	242	32	respectively	respectively	ADV
ap-1179	242	33	,	,	PUNCT
ap-1179	242	34	by	by	ADP
ap-1179	242	35	h20	h20	PROPN
ap-1179	242	36	(	(	PUNCT
ap-1179	242	37	g	g	NOUN
ap-1179	242	38	)	)	PUNCT
ap-1179	242	39	and	and	CCONJ
ap-1179	242	40	h2ad(g	h2ad(g	PROPN
ap-1179	242	41	,	,	PUNCT
ap-1179	242	42	g	g	NOUN
ap-1179	242	43	)	)	PUNCT
ap-1179	242	44	.	.	PUNCT
ap-1179	243	1	let	let	VERB
ap-1179	243	2	us	we	PRON
ap-1179	243	3	now	now	ADV
ap-1179	243	4	turn	turn	VERB
ap-1179	243	5	to	to	ADP
ap-1179	243	6	the	the	DET
ap-1179	243	7	fa	fa	PROPN
ap-1179	243	8	case	case	NOUN
ap-1179	243	9	.	.	PUNCT
ap-1179	244	1	6	6	NUM
ap-1179	244	2	central	central	ADJ
ap-1179	244	3	extensions	extension	NOUN
ap-1179	244	4	and	and	CCONJ
ap-1179	244	5	deformations	deformation	NOUN
ap-1179	244	6	of	of	ADP
ap-1179	244	7	fas	fas	PROPN
ap-1179	244	8	6.1	6.1	NUM
ap-1179	244	9	central	central	ADJ
ap-1179	244	10	extensions	extension	NOUN
ap-1179	244	11	of	of	ADP
ap-1179	244	12	a	a	DET
ap-1179	244	13	fa	fa	NOUN
ap-1179	244	14	given	give	VERB
ap-1179	244	15	a	a	DET
ap-1179	244	16	filippov	filippov	NOUN
ap-1179	244	17	algebrag	algebrag	NOUN
ap-1179	244	18	with	with	ADP
ap-1179	244	19	n	n	NOUN
ap-1179	244	20	-	-	PUNCT
ap-1179	244	21	bracket	bracket	NOUN
ap-1179	244	22	[	[	X
ap-1179	244	23	.	.	PUNCT
ap-1179	244	24	.	.	PUNCT
ap-1179	244	25	.	.	PUNCT
ap-1179	245	1	]	]	X
ap-1179	245	2	,	,	PUNCT
ap-1179	245	3	a	a	DET
ap-1179	245	4	central	central	ADJ
ap-1179	245	5	extension	extension	NOUN
ap-1179	245	6	g̃	g̃	PROPN
ap-1179	245	7	has	have	VERB
ap-1179	245	8	the	the	DET
ap-1179	245	9	form	form	NOUN
ap-1179	245	10	[	[	X
ap-1179	245	11	x̃a1	x̃a1	X
ap-1179	245	12	,	,	PUNCT
ap-1179	245	13	.	.	PUNCT
ap-1179	245	14	.	.	PUNCT
ap-1179	246	1	.	.	PUNCT
ap-1179	247	1	,	,	PUNCT
ap-1179	247	2	x̃an	x̃an	PROPN
ap-1179	247	3	]	]	X
ap-1179	248	1	:	:	PUNCT
ap-1179	248	2	=	=	SYM
ap-1179	248	3	f	f	PROPN
ap-1179	248	4	b	b	X
ap-1179	248	5	a1	a1	PROPN
ap-1179	248	6	...	...	PUNCT
ap-1179	248	7	an	an	PRON
ap-1179	248	8	x̃b	x̃b	PROPN
ap-1179	248	9	+	+	PROPN
ap-1179	248	10	α1(x1	α1(x1	NUM
ap-1179	248	11	,	,	PUNCT
ap-1179	248	12	.	.	PUNCT
ap-1179	248	13	.	.	PUNCT
ap-1179	249	1	.	.	PUNCT
ap-1179	250	1	,	,	PUNCT
ap-1179	250	2	xn)ξ	xn)ξ	PROPN
ap-1179	250	3	,	,	PUNCT
ap-1179	251	1	[	[	X
ap-1179	251	2	x̃1	x̃1	PROPN
ap-1179	251	3	,	,	PUNCT
ap-1179	251	4	.	.	PUNCT
ap-1179	251	5	.	.	PUNCT
ap-1179	252	1	.	.	PUNCT
ap-1179	253	1	,	,	PUNCT
ap-1179	253	2	x̃n−1,ξ	x̃n−1,ξ	X
ap-1179	253	3	]	]	X
ap-1179	253	4	=	=	SYM
ap-1179	253	5	0	0	NUM
ap-1179	253	6	,	,	PUNCT
ap-1179	253	7	(	(	PUNCT
ap-1179	253	8	6.30	6.30	NUM
ap-1179	253	9	)	)	PUNCT
ap-1179	254	1	x̃	x̃	PROPN
ap-1179	254	2	∈	∈	PROPN
ap-1179	254	3	g̃	g̃	PROPN
ap-1179	254	4	,	,	PUNCT
ap-1179	254	5	α1	α1	PROPN
ap-1179	254	6	∈	∈	PROPN
ap-1179	254	7	∧n−1g∗	∧n−1g∗	NOUN
ap-1179	254	8	∧g	∧g	ADJ
ap-1179	254	9	∗	∗	NOUN
ap-1179	254	10	.	.	PUNCT
ap-1179	255	1	if	if	SCONJ
ap-1179	255	2	α1	α1	PROPN
ap-1179	255	3	defines	define	VERB
ap-1179	255	4	a	a	DET
ap-1179	255	5	centrally	centrally	ADV
ap-1179	255	6	extended	extended	ADJ
ap-1179	255	7	fa	fa	NOUN
ap-1179	255	8	,	,	PUNCT
ap-1179	255	9	it	it	PRON
ap-1179	255	10	must	must	AUX
ap-1179	255	11	satisfy	satisfy	VERB
ap-1179	255	12	the	the	DET
ap-1179	255	13	condition	condition	NOUN
ap-1179	255	14	that	that	PRON
ap-1179	255	15	follows	follow	VERB
ap-1179	255	16	from	from	ADP
ap-1179	255	17	the	the	DET
ap-1179	255	18	fi	fi	NOUN
ap-1179	255	19	for	for	ADP
ap-1179	255	20	the	the	DET
ap-1179	255	21	above	above	ADJ
ap-1179	255	22	bracket	bracket	NOUN
ap-1179	255	23	.	.	PUNCT
ap-1179	256	1	if	if	SCONJ
ap-1179	256	2	we	we	PRON
ap-1179	256	3	now	now	ADV
ap-1179	256	4	introduce	introduce	VERB
ap-1179	256	5	p	p	NOUN
ap-1179	256	6	-	-	PUNCT
ap-1179	256	7	cochains	cochain	NOUN
ap-1179	256	8	as	as	ADP
ap-1179	256	9	maps	map	NOUN
ap-1179	256	10	αp	αp	VERB
ap-1179	256	11	∈	∈	PROPN
ap-1179	256	12	∧n−1g∗	∧n−1g∗	PROPN
ap-1179	256	13	⊗	⊗	PROPN
ap-1179	256	14	.	.	PUNCT
ap-1179	256	15	.	.	PUNCT
ap-1179	257	1	.⊗	.⊗	PRON
ap-1179	257	2	∧n−1g∗	∧n−1g∗	NOUN
ap-1179	257	3	∧g	∧g	NUM
ap-1179	257	4	∗	∗	NOUN
ap-1179	257	5	,	,	PUNCT
ap-1179	257	6	αp	αp	INTJ
ap-1179	257	7	:	:	PUNCT
ap-1179	257	8	(	(	PUNCT
ap-1179	257	9	x1	x1	ADJ
ap-1179	257	10	,	,	PUNCT
ap-1179	257	11	.	.	PUNCT
ap-1179	257	12	.	.	PUNCT
ap-1179	257	13	.	.	PUNCT
ap-1179	258	1	,	,	PUNCT
ap-1179	258	2	xp	xp	INTJ
ap-1179	258	3	,	,	PUNCT
ap-1179	258	4	z	z	NOUN
ap-1179	258	5	)	)	PUNCT
ap-1179	258	6	�	�	PROPN
ap-1179	258	7	→	→	SYM
ap-1179	258	8	αp(x1	αp(x1	NOUN
ap-1179	258	9	,	,	PUNCT
ap-1179	258	10	.	.	PUNCT
ap-1179	258	11	.	.	PUNCT
ap-1179	259	1	.	.	PUNCT
ap-1179	260	1	,	,	PUNCT
ap-1179	260	2	xp	xp	INTJ
ap-1179	260	3	,	,	PUNCT
ap-1179	260	4	z	z	NOUN
ap-1179	260	5	)	)	PUNCT
ap-1179	260	6	,	,	PUNCT
ap-1179	260	7	(	(	PUNCT
ap-1179	260	8	6.31	6.31	NUM
ap-1179	260	9	)	)	PUNCT
ap-1179	260	10	the	the	DET
ap-1179	260	11	condition	condition	NOUN
ap-1179	260	12	imposed	impose	VERB
ap-1179	260	13	by	by	ADP
ap-1179	260	14	the	the	DET
ap-1179	260	15	fi	fi	NOUN
ap-1179	260	16	on	on	ADP
ap-1179	260	17	the	the	DET
ap-1179	260	18	one	one	NUM
ap-1179	260	19	-	-	PUNCT
ap-1179	260	20	cochain	cochain	NOUN
ap-1179	260	21	in	in	ADP
ap-1179	260	22	(	(	PUNCT
ap-1179	260	23	6.30	6.30	NUM
ap-1179	260	24	)	)	PUNCT
ap-1179	260	25	,	,	PUNCT
ap-1179	260	26	written	write	VERB
ap-1179	260	27	in	in	ADP
ap-1179	260	28	terms	term	NOUN
ap-1179	260	29	of	of	ADP
ap-1179	260	30	the	the	DET
ap-1179	260	31	fundamental	fundamental	ADJ
ap-1179	260	32	objects	object	NOUN
ap-1179	260	33	with	with	ADP
ap-1179	260	34	yn	yn	PROPN
ap-1179	260	35	=	=	SYM
ap-1179	260	36	z	z	PROPN
ap-1179	260	37	,	,	PUNCT
ap-1179	260	38	reads	read	VERB
ap-1179	260	39	α1(x	α1(x	PROPN
ap-1179	260	40	,	,	PUNCT
ap-1179	260	41	y	y	PROPN
ap-1179	260	42	·	·	PUNCT
ap-1179	261	1	z)−	z)−	PROPN
ap-1179	261	2	α1(x	α1(x	NUM
ap-1179	261	3	·	·	PUNCT
ap-1179	261	4	y	y	PROPN
ap-1179	261	5	,	,	PUNCT
ap-1179	261	6	z)−	z)−	PROPN
ap-1179	261	7	α1(y	α1(y	PROPN
ap-1179	261	8	,	,	PUNCT
ap-1179	261	9	x	x	X
ap-1179	261	10	·	·	PUNCT
ap-1179	261	11	z	z	X
ap-1179	261	12	)	)	PUNCT
ap-1179	261	13	≡	≡	PROPN
ap-1179	261	14	(	(	PUNCT
ap-1179	261	15	δα1)(x	δα1)(x	PROPN
ap-1179	261	16	,	,	PUNCT
ap-1179	261	17	y	y	PROPN
ap-1179	261	18	,	,	PUNCT
ap-1179	261	19	z	z	NOUN
ap-1179	261	20	)	)	PUNCT
ap-1179	261	21	=	=	SYM
ap-1179	261	22	0	0	X
ap-1179	261	23	.	.	PUNCT
ap-1179	262	1	(	(	PUNCT
ap-1179	262	2	6.32	6.32	NUM
ap-1179	262	3	)	)	PUNCT
ap-1179	262	4	note	note	NOUN
ap-1179	262	5	that	that	SCONJ
ap-1179	262	6	α1	α1	PROPN
ap-1179	262	7	above	above	ADV
ap-1179	262	8	would	would	AUX
ap-1179	262	9	become	become	VERB
ap-1179	262	10	a	a	DET
ap-1179	262	11	two	two	NUM
ap-1179	262	12	-	-	PUNCT
ap-1179	262	13	cochain	cochain	NOUN
ap-1179	262	14	for	for	ADP
ap-1179	262	15	n	n	NOUN
ap-1179	262	16	=	=	SYM
ap-1179	262	17	2	2	NUM
ap-1179	262	18	;	;	PUNCT
ap-1179	262	19	we	we	PRON
ap-1179	262	20	define	define	VERB
ap-1179	262	21	the	the	DET
ap-1179	262	22	order	order	NOUN
ap-1179	262	23	of	of	ADP
ap-1179	262	24	the	the	DET
ap-1179	262	25	p	p	NOUN
ap-1179	262	26	-	-	PUNCT
ap-1179	262	27	cochains	cochain	NOUN
ap-1179	262	28	for	for	ADP
ap-1179	262	29	fas	fas	X
ap-1179	262	30	(	(	PUNCT
ap-1179	262	31	n	n	CCONJ
ap-1179	262	32	≥	≥	NOUN
ap-1179	262	33	3	3	NUM
ap-1179	262	34	)	)	PUNCT
ap-1179	262	35	as	as	ADP
ap-1179	262	36	the	the	DET
ap-1179	262	37	number	number	NOUN
ap-1179	262	38	p	p	NOUN
ap-1179	262	39	of	of	ADP
ap-1179	262	40	fundamental	fundamental	ADJ
ap-1179	262	41	objects	object	NOUN
ap-1179	262	42	among	among	ADP
ap-1179	262	43	the	the	DET
ap-1179	262	44	arguments	argument	NOUN
ap-1179	262	45	of	of	ADP
ap-1179	262	46	the	the	DET
ap-1179	262	47	cochain	cochain	NOUN
ap-1179	262	48	(	(	PUNCT
ap-1179	262	49	for	for	ADP
ap-1179	262	50	a	a	DET
ap-1179	262	51	lie	lie	NOUN
ap-1179	262	52	algebrax	algebrax	NOUN
ap-1179	262	53	=	=	PUNCT
ap-1179	263	1	x	x	X
ap-1179	263	2	and	and	CCONJ
ap-1179	263	3	p	p	NOUN
ap-1179	263	4	counts	count	VERB
ap-1179	263	5	the	the	DET
ap-1179	263	6	number	number	NOUN
ap-1179	263	7	of	of	ADP
ap-1179	263	8	algebra	algebra	NOUN
ap-1179	263	9	elements	element	NOUN
ap-1179	263	10	)	)	PUNCT
ap-1179	263	11	.	.	PUNCT
ap-1179	264	1	a	a	DET
ap-1179	264	2	central	central	ADJ
ap-1179	264	3	extension	extension	NOUN
ap-1179	264	4	is	be	AUX
ap-1179	264	5	actually	actually	ADV
ap-1179	264	6	trivial	trivial	ADJ
ap-1179	264	7	if	if	SCONJ
ap-1179	264	8	it	it	PRON
ap-1179	264	9	is	be	AUX
ap-1179	264	10	possible	possible	ADJ
ap-1179	264	11	to	to	PART
ap-1179	264	12	find	find	VERB
ap-1179	264	13	new	new	ADJ
ap-1179	264	14	generators	generator	NOUN
ap-1179	265	1	x̃	x̃	PROPN
ap-1179	265	2	′	′	NUM
ap-1179	266	1	=	=	PUNCT
ap-1179	267	1	x̃	x̃	PROPN
ap-1179	268	1	−	−	PROPN
ap-1179	268	2	β(x)ξ	β(x)ξ	PROPN
ap-1179	268	3	such	such	ADJ
ap-1179	268	4	that	that	SCONJ
ap-1179	268	5	[	[	X
ap-1179	268	6	x̃	x̃	PROPN
ap-1179	268	7	′	′	NOUN
ap-1179	268	8	a1	a1	NOUN
ap-1179	268	9	,	,	PUNCT
ap-1179	268	10	.	.	PUNCT
ap-1179	268	11	.	.	PUNCT
ap-1179	269	1	.	.	PUNCT
ap-1179	270	1	,	,	PUNCT
ap-1179	270	2	x̃	x̃	PROPN
ap-1179	270	3	′	′	NUM
ap-1179	271	1	an	an	DET
ap-1179	271	2	]	]	X
ap-1179	271	3	=	=	PUNCT
ap-1179	271	4	f	f	PROPN
ap-1179	271	5	b	b	X
ap-1179	271	6	a1	a1	PROPN
ap-1179	271	7	...	...	PUNCT
ap-1179	271	8	an	an	DET
ap-1179	271	9	x̃	x̃	PROPN
ap-1179	271	10	′	′	NUM
ap-1179	271	11	b	b	X
ap-1179	272	1	=	=	SYM
ap-1179	272	2	f	f	PROPN
ap-1179	272	3	b	b	PROPN
ap-1179	272	4	a1	a1	PROPN
ap-1179	272	5	...	...	PUNCT
ap-1179	272	6	an	an	DET
ap-1179	272	7	x̃b	x̃b	NOUN
ap-1179	272	8	−	−	NOUN
ap-1179	272	9	β([xa1	β([xa1	NOUN
ap-1179	272	10	,	,	PUNCT
ap-1179	272	11	.	.	PUNCT
ap-1179	272	12	.	.	PUNCT
ap-1179	272	13	.	.	PUNCT
ap-1179	273	1	,	,	PUNCT
ap-1179	273	2	xan	xan	PROPN
ap-1179	273	3	]	]	PUNCT
ap-1179	273	4	)	)	PUNCT
ap-1179	274	1	ξ	ξ	X
ap-1179	274	2	.	.	PUNCT
ap-1179	275	1	but	but	CCONJ
ap-1179	275	2	this	this	PRON
ap-1179	275	3	is	be	AUX
ap-1179	275	4	equivalent	equivalent	ADJ
ap-1179	275	5	to	to	ADP
ap-1179	275	6	saying	say	VERB
ap-1179	275	7	(	(	PUNCT
ap-1179	275	8	with	with	ADP
ap-1179	275	9	xan	xan	PROPN
ap-1179	275	10	=	=	SYM
ap-1179	275	11	z	z	PROPN
ap-1179	275	12	)	)	PUNCT
ap-1179	275	13	that	that	PRON
ap-1179	275	14	α1(x1	α1(x1	X
ap-1179	275	15	,	,	PUNCT
ap-1179	275	16	.	.	PUNCT
ap-1179	275	17	.	.	PUNCT
ap-1179	276	1	.	.	PUNCT
ap-1179	277	1	,	,	PUNCT
ap-1179	277	2	xn−1	xn−1	PROPN
ap-1179	277	3	,	,	PUNCT
ap-1179	277	4	z	z	NOUN
ap-1179	277	5	)	)	PUNCT
ap-1179	277	6	=	=	SYM
ap-1179	277	7	−β([x1	−β([x1	PROPN
ap-1179	277	8	,	,	PUNCT
ap-1179	277	9	.	.	PUNCT
ap-1179	277	10	.	.	PUNCT
ap-1179	278	1	.	.	PUNCT
ap-1179	279	1	,	,	PUNCT
ap-1179	279	2	xn−1	xn−1	PROPN
ap-1179	279	3	,	,	PUNCT
ap-1179	279	4	z	z	NOUN
ap-1179	279	5	]	]	X
ap-1179	279	6	)	)	PUNCT
ap-1179	279	7	,	,	PUNCT
ap-1179	279	8	(	(	PUNCT
ap-1179	279	9	6.33	6.33	NUM
ap-1179	279	10	)	)	PUNCT
ap-1179	279	11	which	which	PRON
ap-1179	279	12	may	may	AUX
ap-1179	279	13	be	be	AUX
ap-1179	279	14	rewritten	rewrite	VERB
ap-1179	279	15	in	in	ADP
ap-1179	279	16	the	the	DET
ap-1179	279	17	form	form	NOUN
ap-1179	279	18	α1(x	α1(x	PROPN
ap-1179	279	19	,	,	PUNCT
ap-1179	279	20	z	z	NOUN
ap-1179	279	21	)	)	PUNCT
ap-1179	279	22	=	=	SYM
ap-1179	279	23	−β([x1	−β([x1	PROPN
ap-1179	279	24	,	,	PUNCT
ap-1179	279	25	.	.	PUNCT
ap-1179	279	26	.	.	PUNCT
ap-1179	279	27	.	.	PUNCT
ap-1179	280	1	,	,	PUNCT
ap-1179	280	2	xn−1	xn−1	PROPN
ap-1179	280	3	,	,	PUNCT
ap-1179	280	4	z	z	NOUN
ap-1179	280	5	]	]	X
ap-1179	280	6	)	)	PUNCT
ap-1179	280	7	≡	≡	PROPN
ap-1179	280	8	(	(	PUNCT
ap-1179	280	9	δβ)(x1	δβ)(x1	NOUN
ap-1179	280	10	,	,	PUNCT
ap-1179	280	11	.	.	PUNCT
ap-1179	280	12	.	.	PUNCT
ap-1179	280	13	.	.	PUNCT
ap-1179	281	1	,	,	PUNCT
ap-1179	281	2	xn−1	xn−1	PROPN
ap-1179	281	3	,	,	PUNCT
ap-1179	281	4	z	z	NOUN
ap-1179	281	5	)	)	PUNCT
ap-1179	281	6	≡	≡	PROPN
ap-1179	281	7	(	(	PUNCT
ap-1179	281	8	δβ)(x	δβ)(x	PROPN
ap-1179	281	9	,	,	PUNCT
ap-1179	281	10	z	z	NOUN
ap-1179	281	11	)	)	PUNCT
ap-1179	281	12	,	,	PUNCT
ap-1179	281	13	(	(	PUNCT
ap-1179	281	14	6.34	6.34	NUM
ap-1179	281	15	)	)	PUNCT
ap-1179	281	16	where	where	SCONJ
ap-1179	281	17	β	β	PROPN
ap-1179	281	18	is	be	AUX
ap-1179	281	19	the	the	DET
ap-1179	281	20	zero	zero	NUM
ap-1179	281	21	-	-	PUNCT
ap-1179	281	22	cochain	cochain	NOUN
ap-1179	281	23	β	β	NOUN
ap-1179	281	24	∈	∈	PROPN
ap-1179	281	25	g	g	PROPN
ap-1179	281	26	∗	∗	NOUN
ap-1179	281	27	generating	generate	VERB
ap-1179	281	28	the	the	DET
ap-1179	281	29	onecocycle	onecocycle	NOUN
ap-1179	281	30	.	.	PUNCT
ap-1179	282	1	therefore	therefore	ADV
ap-1179	282	2	,	,	PUNCT
ap-1179	282	3	central	central	ADJ
ap-1179	282	4	extensions	extension	NOUN
ap-1179	282	5	of	of	ADP
ap-1179	282	6	fas	fas	NOUN
ap-1179	282	7	are	be	AUX
ap-1179	282	8	characterized	characterize	VERB
ap-1179	282	9	by	by	ADP
ap-1179	282	10	one	one	NUM
ap-1179	282	11	-	-	PUNCT
ap-1179	282	12	cocycles	cocycle	NOUN
ap-1179	282	13	modulo	modulo	VERB
ap-1179	282	14	one	one	NUM
ap-1179	282	15	-	-	PUNCT
ap-1179	282	16	coboundaries	coboundarie	NOUN
ap-1179	282	17	.	.	PUNCT
ap-1179	283	1	the	the	DET
ap-1179	283	2	above	above	ADJ
ap-1179	283	3	suffices	suffice	NOUN
ap-1179	283	4	to	to	PART
ap-1179	283	5	define	define	VERB
ap-1179	283	6	the	the	DET
ap-1179	283	7	full	full	ADJ
ap-1179	283	8	fa	fa	NOUN
ap-1179	283	9	cohomology	cohomology	NOUN
ap-1179	283	10	complex	complex	NOUN
ap-1179	283	11	suitable	suitable	ADJ
ap-1179	283	12	for	for	ADP
ap-1179	283	13	central	central	ADJ
ap-1179	283	14	extensions	extension	NOUN
ap-1179	283	15	.	.	PUNCT
ap-1179	284	1	let	let	VERB
ap-1179	284	2	αp	αp	PRON
ap-1179	284	3	∈	∈	PROPN
ap-1179	284	4	∧n−1g∗	∧n−1g∗	PROPN
ap-1179	284	5	⊗	⊗	PROPN
ap-1179	284	6	.	.	PUNCT
ap-1179	284	7	.	.	PUNCT
ap-1179	284	8	.	.	PUNCT
ap-1179	285	1	⊗	⊗	PROPN
ap-1179	285	2	∧n−1g∗	∧n−1g∗	PROPN
ap-1179	285	3	∧	∧	PROPN
ap-1179	285	4	g	g	PROPN
ap-1179	285	5	∗	∗	NOUN
ap-1179	285	6	be	be	VERB
ap-1179	285	7	a	a	DET
ap-1179	285	8	p	p	NOUN
ap-1179	285	9	-	-	PUNCT
ap-1179	285	10	cochain	cochain	NOUN
ap-1179	285	11	.	.	PUNCT
ap-1179	286	1	then	then	ADV
ap-1179	286	2	(	(	PUNCT
ap-1179	286	3	c•	c•	NOUN
ap-1179	286	4	0	0	NUM
ap-1179	286	5	(	(	PUNCT
ap-1179	286	6	g	g	NOUN
ap-1179	286	7	)	)	PUNCT
ap-1179	286	8	,	,	PUNCT
ap-1179	286	9	δ	δ	PROPN
ap-1179	286	10	)	)	PUNCT
ap-1179	286	11	is	be	AUX
ap-1179	286	12	defined	define	VERB
ap-1179	286	13	by	by	ADP
ap-1179	286	14	(	(	PUNCT
ap-1179	286	15	δα)(x1	δα)(x1	ADJ
ap-1179	286	16	,	,	PUNCT
ap-1179	286	17	.	.	PUNCT
ap-1179	286	18	.	.	PUNCT
ap-1179	286	19	.	.	PUNCT
ap-1179	287	1	,	,	PUNCT
ap-1179	287	2	xp+1	xp+1	NUM
ap-1179	287	3	,	,	PUNCT
ap-1179	287	4	z	z	NOUN
ap-1179	287	5	)	)	PUNCT
ap-1179	287	6	=	=	SYM
ap-1179	287	7	(	(	PUNCT
ap-1179	287	8	6.35	6.35	NUM
ap-1179	287	9	)	)	PUNCT
ap-1179	287	10	p+1∑	p+1∑	NOUN
ap-1179	288	1	1≤i	1≤i	NUM
ap-1179	288	2	<	<	X
ap-1179	288	3	j	j	PROPN
ap-1179	288	4	(	(	PUNCT
ap-1179	288	5	−1)iα(x1	−1)iα(x1	PROPN
ap-1179	288	6	,	,	PUNCT
ap-1179	288	7	.	.	PUNCT
ap-1179	288	8	.	.	PUNCT
ap-1179	289	1	.	.	PUNCT
ap-1179	290	1	,	,	PUNCT
ap-1179	290	2	x̂i	x̂i	PROPN
ap-1179	290	3	,	,	PUNCT
ap-1179	290	4	.	.	PUNCT
ap-1179	290	5	.	.	PUNCT
ap-1179	291	1	.	.	PUNCT
ap-1179	292	1	,	,	PUNCT
ap-1179	292	2	xi	xi	PROPN
ap-1179	292	3	·	·	PUNCT
ap-1179	292	4	xj	xj	PROPN
ap-1179	292	5	,	,	PUNCT
ap-1179	292	6	.	.	PUNCT
ap-1179	292	7	.	.	PUNCT
ap-1179	293	1	.	.	PUNCT
ap-1179	294	1	,	,	PUNCT
ap-1179	294	2	xp+1	xp+1	NUM
ap-1179	294	3	,	,	PUNCT
ap-1179	294	4	z	z	NOUN
ap-1179	294	5	)	)	PUNCT
ap-1179	295	1	+	+	CCONJ
ap-1179	295	2	p+1∑	p+1∑	PROPN
ap-1179	295	3	i=1	i=1	X
ap-1179	296	1	(	(	PUNCT
ap-1179	296	2	−1)iα(x1	−1)iα(x1	PROPN
ap-1179	296	3	,	,	PUNCT
ap-1179	296	4	.	.	PUNCT
ap-1179	296	5	.	.	PUNCT
ap-1179	297	1	.	.	PUNCT
ap-1179	298	1	,	,	PUNCT
ap-1179	298	2	x̂i	x̂i	PROPN
ap-1179	298	3	,	,	PUNCT
ap-1179	298	4	.	.	PUNCT
ap-1179	298	5	.	.	PUNCT
ap-1179	299	1	.	.	PUNCT
ap-1179	300	1	,	,	PUNCT
ap-1179	300	2	xp+1	xp+1	NUM
ap-1179	300	3	,	,	PUNCT
ap-1179	300	4	xi	xi	X
ap-1179	300	5	·	·	PUNCT
ap-1179	301	1	z	z	X
ap-1179	301	2	)	)	PUNCT
ap-1179	301	3	.	.	PUNCT
ap-1179	302	1	defining	define	VERB
ap-1179	302	2	p	p	NOUN
ap-1179	302	3	-	-	PUNCT
ap-1179	302	4	cocycles	cocycle	NOUN
ap-1179	302	5	and	and	CCONJ
ap-1179	302	6	p	p	NOUN
ap-1179	302	7	-	-	PUNCT
ap-1179	302	8	coboundaries	coboundarie	NOUN
ap-1179	302	9	as	as	ADP
ap-1179	302	10	usual	usual	ADJ
ap-1179	302	11	,	,	PUNCT
ap-1179	302	12	the	the	DET
ap-1179	302	13	p	p	NOUN
ap-1179	302	14	-	-	PUNCT
ap-1179	302	15	th	th	X
ap-1179	302	16	fa	fa	NOUN
ap-1179	302	17	cohomology	cohomology	NOUN
ap-1179	302	18	group	group	NOUN
ap-1179	302	19	(	(	PUNCT
ap-1179	302	20	for	for	ADP
ap-1179	302	21	the	the	DET
ap-1179	302	22	trivial	trivial	ADJ
ap-1179	302	23	action	action	NOUN
ap-1179	302	24	)	)	PUNCT
ap-1179	302	25	is	be	AUX
ap-1179	302	26	hp	hp	ADJ
ap-1179	302	27	0	0	PUNCT
ap-1179	302	28	(	(	PUNCT
ap-1179	302	29	g	g	NOUN
ap-1179	302	30	)	)	PUNCT
ap-1179	303	1	=	=	NOUN
ap-1179	303	2	zp	zp	NOUN
ap-1179	303	3	0	0	PUNCT
ap-1179	303	4	(	(	PUNCT
ap-1179	303	5	g)/bp	g)/bp	PROPN
ap-1179	303	6	0(g	0(g	NUM
ap-1179	303	7	)	)	PUNCT
ap-1179	303	8	.	.	PUNCT
ap-1179	304	1	therefore	therefore	ADV
ap-1179	304	2	,	,	PUNCT
ap-1179	304	3	a	a	DET
ap-1179	304	4	fa	fa	PROPN
ap-1179	304	5	admits	admit	VERB
ap-1179	304	6	nontrivial	nontrivial	ADJ
ap-1179	304	7	central	central	ADJ
ap-1179	304	8	extensions	extension	NOUN
ap-1179	304	9	when	when	SCONJ
ap-1179	304	10	h10	h10	PROPN
ap-1179	304	11	(	(	PUNCT
ap-1179	304	12	g	g	NOUN
ap-1179	304	13	)	)	PUNCT
ap-1179	304	14	�	�	PROPN
ap-1179	304	15	=	=	SYM
ap-1179	304	16	0	0	NUM
ap-1179	304	17	.	.	NOUN
ap-1179	304	18	6.2	6.2	NUM
ap-1179	304	19	infinitesimal	infinitesimal	ADJ
ap-1179	304	20	deformations	deformation	NOUN
ap-1179	304	21	of	of	ADP
ap-1179	304	22	fas	fas	NOUN
ap-1179	304	23	an	an	DET
ap-1179	304	24	infinitesimal	infinitesimal	ADJ
ap-1179	304	25	deformation	deformation	NOUN
ap-1179	304	26	of	of	ADP
ap-1179	304	27	a	a	DET
ap-1179	304	28	fa	fa	NOUN
ap-1179	304	29	in	in	ADP
ap-1179	304	30	gerstenhaber	gerstenhaber	PROPN
ap-1179	304	31	’s	’s	PART
ap-1179	304	32	[	[	X
ap-1179	304	33	18	18	NUM
ap-1179	304	34	]	]	PUNCT
ap-1179	304	35	sense	sense	NOUN
ap-1179	304	36	is	be	AUX
ap-1179	304	37	obtained	obtain	VERB
ap-1179	304	38	by	by	ADP
ap-1179	304	39	modifying	modify	VERB
ap-1179	304	40	the	the	DET
ap-1179	304	41	n	n	NOUN
ap-1179	304	42	-	-	PUNCT
ap-1179	304	43	bracket	bracket	NOUN
ap-1179	304	44	as	as	ADP
ap-1179	304	45	[	[	X
ap-1179	304	46	x1	x1	PROPN
ap-1179	304	47	,	,	PUNCT
ap-1179	304	48	.	.	PUNCT
ap-1179	304	49	.	.	PUNCT
ap-1179	305	1	.	.	PUNCT
ap-1179	306	1	,	,	PUNCT
ap-1179	307	1	xn]t	xn]t	PROPN
ap-1179	307	2	=	=	PUNCT
ap-1179	308	1	[	[	X
ap-1179	308	2	x1	x1	PROPN
ap-1179	308	3	,	,	PUNCT
ap-1179	308	4	.	.	PUNCT
ap-1179	308	5	.	.	PUNCT
ap-1179	309	1	.	.	PUNCT
ap-1179	310	1	,	,	PUNCT
ap-1179	311	1	xn	xn	X
ap-1179	311	2	]	]	X
ap-1179	312	1	+	+	CCONJ
ap-1179	312	2	tα1(x1	tα1(x1	NOUN
ap-1179	312	3	,	,	PUNCT
ap-1179	312	4	.	.	PUNCT
ap-1179	312	5	.	.	PUNCT
ap-1179	313	1	.	.	PUNCT
ap-1179	314	1	,	,	PUNCT
ap-1179	314	2	xn	xn	PROPN
ap-1179	314	3	)	)	PUNCT
ap-1179	314	4	,	,	PUNCT
ap-1179	314	5	(	(	PUNCT
ap-1179	314	6	6.36	6.36	NUM
ap-1179	314	7	)	)	PUNCT
ap-1179	314	8	where	where	SCONJ
ap-1179	314	9	α1	α1	PROPN
ap-1179	314	10	is	be	AUX
ap-1179	314	11	now	now	ADV
ap-1179	314	12	g	g	NOUN
ap-1179	314	13	-	-	PUNCT
ap-1179	314	14	valued	value	VERB
ap-1179	314	15	,	,	PUNCT
ap-1179	314	16	so	so	SCONJ
ap-1179	314	17	that	that	SCONJ
ap-1179	314	18	g	g	PROPN
ap-1179	314	19	will	will	AUX
ap-1179	314	20	now	now	ADV
ap-1179	314	21	act	act	VERB
ap-1179	314	22	on	on	ADP
ap-1179	314	23	it	it	PRON
ap-1179	314	24	.	.	PUNCT
ap-1179	315	1	again	again	ADV
ap-1179	315	2	,	,	PUNCT
ap-1179	315	3	the	the	DET
ap-1179	315	4	fi	fi	NOUN
ap-1179	315	5	constrains	constrain	VERB
ap-1179	315	6	α1	α1	NOUN
ap-1179	315	7	by	by	ADP
ap-1179	315	8	[	[	X
ap-1179	315	9	x1	x1	PROPN
ap-1179	315	10	,	,	PUNCT
ap-1179	315	11	.	.	PUNCT
ap-1179	315	12	.	.	PUNCT
ap-1179	316	1	.	.	PUNCT
ap-1179	317	1	,	,	PUNCT
ap-1179	317	2	xn−1	xn−1	PROPN
ap-1179	317	3	,	,	PUNCT
ap-1179	317	4	[	[	X
ap-1179	317	5	y1	y1	X
ap-1179	317	6	,	,	PUNCT
ap-1179	317	7	.	.	PUNCT
ap-1179	317	8	.	.	PUNCT
ap-1179	318	1	.	.	PUNCT
ap-1179	319	1	,	,	PUNCT
ap-1179	319	2	yn]t]t	yn]t]t	PROPN
ap-1179	319	3	=	=	SYM
ap-1179	319	4	(	(	PUNCT
ap-1179	319	5	6.37	6.37	NUM
ap-1179	319	6	)	)	PUNCT
ap-1179	319	7	n∑	n∑	NOUN
ap-1179	319	8	a=1	a=1	PUNCT
ap-1179	320	1	[	[	X
ap-1179	320	2	y1	y1	NOUN
ap-1179	320	3	,	,	PUNCT
ap-1179	320	4	.	.	PUNCT
ap-1179	320	5	.	.	PUNCT
ap-1179	321	1	.	.	PUNCT
ap-1179	322	1	,	,	PUNCT
ap-1179	322	2	ya−1	ya−1	NOUN
ap-1179	322	3	,	,	PUNCT
ap-1179	322	4	[	[	X
ap-1179	322	5	x1	x1	X
ap-1179	322	6	,	,	PUNCT
ap-1179	322	7	.	.	PUNCT
ap-1179	322	8	.	.	PUNCT
ap-1179	323	1	.	.	PUNCT
ap-1179	324	1	,	,	PUNCT
ap-1179	324	2	xn−1	xn−1	PROPN
ap-1179	324	3	,	,	PUNCT
ap-1179	324	4	ya]t	ya]t	PROPN
ap-1179	324	5	,	,	PUNCT
ap-1179	324	6	ya+1	ya+1	PROPN
ap-1179	324	7	,	,	PUNCT
ap-1179	324	8	.	.	PUNCT
ap-1179	324	9	.	.	PUNCT
ap-1179	324	10	.	.	PUNCT
ap-1179	325	1	,	,	PUNCT
ap-1179	325	2	yn]t	yn]t	PROPN
ap-1179	325	3	which	which	PRON
ap-1179	325	4	,	,	PUNCT
ap-1179	325	5	with	with	ADP
ap-1179	325	6	yn	yn	PROPN
ap-1179	325	7	=	=	SYM
ap-1179	325	8	z	z	PROPN
ap-1179	325	9	,	,	PUNCT
ap-1179	325	10	may	may	AUX
ap-1179	325	11	we	we	PRON
ap-1179	325	12	rewritten	rewrite	VERB
ap-1179	325	13	as	as	ADP
ap-1179	325	14	[	[	X
ap-1179	325	15	x	x	X
ap-1179	325	16	,	,	PUNCT
ap-1179	325	17	(	(	PUNCT
ap-1179	325	18	y	y	PROPN
ap-1179	325	19	·	·	PUNCT
ap-1179	325	20	z)t]t	z)t]t	X
ap-1179	326	1	=	=	PUNCT
ap-1179	327	1	[	[	X
ap-1179	327	2	(	(	PUNCT
ap-1179	327	3	x	x	X
ap-1179	327	4	·	·	PUNCT
ap-1179	327	5	y)t	y)t	ADJ
ap-1179	327	6	,	,	PUNCT
ap-1179	327	7	z]t	z]t	X
ap-1179	327	8	+	+	PUNCT
ap-1179	328	1	[	[	X
ap-1179	328	2	y	y	X
ap-1179	328	3	,	,	PUNCT
ap-1179	328	4	(	(	PUNCT
ap-1179	328	5	x	x	X
ap-1179	328	6	·	·	PUNCT
ap-1179	328	7	z)t]t	z)t]t	X
ap-1179	328	8	.	.	PUNCT
ap-1179	329	1	(	(	PUNCT
ap-1179	329	2	6.38	6.38	NUM
ap-1179	329	3	)	)	PUNCT
ap-1179	329	4	10	10	NUM
ap-1179	329	5	acta	acta	PROPN
ap-1179	329	6	polytechnica	polytechnica	PROPN
ap-1179	329	7	vol	vol	NOUN
ap-1179	329	8	.	.	PROPN
ap-1179	330	1	50	50	NUM
ap-1179	330	2	no	no	NOUN
ap-1179	330	3	.	.	PUNCT
ap-1179	331	1	3/2010	3/2010	NUM
ap-1179	331	2	at	at	ADP
ap-1179	331	3	first	first	ADJ
ap-1179	331	4	order	order	NOUN
ap-1179	331	5	in	in	ADP
ap-1179	331	6	t	t	PROPN
ap-1179	331	7	,	,	PUNCT
ap-1179	331	8	this	this	PRON
ap-1179	331	9	gives	give	VERB
ap-1179	331	10	the	the	DET
ap-1179	331	11	following	follow	VERB
ap-1179	331	12	condition	condition	NOUN
ap-1179	331	13	on	on	ADP
ap-1179	331	14	α1	α1	PROPN
ap-1179	331	15	:	:	PUNCT
ap-1179	332	1	[	[	X
ap-1179	332	2	x1	x1	X
ap-1179	332	3	,	,	PUNCT
ap-1179	332	4	.	.	PUNCT
ap-1179	332	5	.	.	PUNCT
ap-1179	333	1	.	.	PUNCT
ap-1179	334	1	,	,	PUNCT
ap-1179	334	2	xn−1	xn−1	PROPN
ap-1179	334	3	,	,	PUNCT
ap-1179	334	4	α	α	NOUN
ap-1179	334	5	1(y1	1(y1	NUM
ap-1179	334	6	,	,	PUNCT
ap-1179	334	7	.	.	PUNCT
ap-1179	334	8	.	.	PUNCT
ap-1179	334	9	.	.	PUNCT
ap-1179	335	1	,	,	PUNCT
ap-1179	335	2	yn	yn	PROPN
ap-1179	335	3	)	)	PUNCT
ap-1179	335	4	]	]	PUNCT
ap-1179	336	1	+	+	CCONJ
ap-1179	336	2	α1(x1	α1(x1	NUM
ap-1179	336	3	,	,	PUNCT
ap-1179	336	4	.	.	PUNCT
ap-1179	336	5	.	.	PUNCT
ap-1179	337	1	.	.	PUNCT
ap-1179	338	1	,	,	PUNCT
ap-1179	338	2	xn−1	xn−1	PROPN
ap-1179	338	3	,	,	PUNCT
ap-1179	338	4	[	[	X
ap-1179	338	5	y1	y1	X
ap-1179	338	6	,	,	PUNCT
ap-1179	338	7	.	.	PUNCT
ap-1179	338	8	.	.	PUNCT
ap-1179	338	9	.	.	PUNCT
ap-1179	339	1	,	,	PUNCT
ap-1179	339	2	yn	yn	PRON
ap-1179	339	3	]	]	X
ap-1179	339	4	)	)	PUNCT
ap-1179	339	5	=	=	SYM
ap-1179	339	6	(	(	PUNCT
ap-1179	339	7	6.39	6.39	NUM
ap-1179	339	8	)	)	PUNCT
ap-1179	339	9	n∑	n∑	NOUN
ap-1179	339	10	a=1	a=1	PUNCT
ap-1179	340	1	[	[	X
ap-1179	340	2	y1	y1	NOUN
ap-1179	340	3	,	,	PUNCT
ap-1179	340	4	.	.	PUNCT
ap-1179	340	5	.	.	PUNCT
ap-1179	341	1	.	.	PUNCT
ap-1179	342	1	,	,	PUNCT
ap-1179	342	2	ya−1	ya−1	PROPN
ap-1179	342	3	,	,	PUNCT
ap-1179	342	4	α	α	PROPN
ap-1179	342	5	1(x1	1(x1	PROPN
ap-1179	342	6	,	,	PUNCT
ap-1179	342	7	.	.	PUNCT
ap-1179	342	8	.	.	PUNCT
ap-1179	343	1	.	.	PUNCT
ap-1179	344	1	,	,	PUNCT
ap-1179	344	2	xn−1	xn−1	PROPN
ap-1179	344	3	,	,	PUNCT
ap-1179	344	4	ya	ya	PROPN
ap-1179	344	5	)	)	PUNCT
ap-1179	344	6	,	,	PUNCT
ap-1179	344	7	ya+1	ya+1	PROPN
ap-1179	344	8	,	,	PUNCT
ap-1179	344	9	.	.	PUNCT
ap-1179	344	10	.	.	PUNCT
ap-1179	344	11	.	.	PUNCT
ap-1179	345	1	,	,	PUNCT
ap-1179	345	2	yn	yn	X
ap-1179	345	3	]	]	X
ap-1179	346	1	+	+	NUM
ap-1179	346	2	n∑	n∑	ADJ
ap-1179	346	3	a=1	a=1	X
ap-1179	346	4	α1(y1	α1(y1	NOUN
ap-1179	346	5	,	,	PUNCT
ap-1179	346	6	.	.	PUNCT
ap-1179	346	7	.	.	PUNCT
ap-1179	347	1	.	.	PUNCT
ap-1179	348	1	,	,	PUNCT
ap-1179	348	2	ya−1	ya−1	NOUN
ap-1179	348	3	,	,	PUNCT
ap-1179	348	4	[	[	X
ap-1179	348	5	x1	x1	X
ap-1179	348	6	,	,	PUNCT
ap-1179	348	7	.	.	PUNCT
ap-1179	348	8	.	.	PUNCT
ap-1179	349	1	.	.	PUNCT
ap-1179	350	1	,	,	PUNCT
ap-1179	350	2	xn−1	xn−1	PROPN
ap-1179	350	3	,	,	PUNCT
ap-1179	350	4	ya	ya	PROPN
ap-1179	350	5	]	]	X
ap-1179	350	6	,	,	PUNCT
ap-1179	350	7	ya+1	ya+1	PROPN
ap-1179	350	8	,	,	PUNCT
ap-1179	350	9	.	.	PUNCT
ap-1179	350	10	.	.	PUNCT
ap-1179	350	11	.	.	PUNCT
ap-1179	351	1	,	,	PUNCT
ap-1179	351	2	yn	yn	PROPN
ap-1179	351	3	)	)	PUNCT
ap-1179	351	4	.	.	PUNCT
ap-1179	352	1	in	in	ADP
ap-1179	352	2	terms	term	NOUN
ap-1179	352	3	of	of	ADP
ap-1179	352	4	the	the	DET
ap-1179	352	5	fundamental	fundamental	ADJ
ap-1179	352	6	objects	object	NOUN
ap-1179	352	7	and	and	CCONJ
ap-1179	352	8	with	with	ADP
ap-1179	352	9	yn	yn	PROPN
ap-1179	352	10	=	=	SYM
ap-1179	352	11	z	z	PROPN
ap-1179	352	12	,	,	PUNCT
ap-1179	352	13	this	this	PRON
ap-1179	352	14	may	may	AUX
ap-1179	352	15	be	be	AUX
ap-1179	352	16	read	read	VERB
ap-1179	352	17	as	as	ADP
ap-1179	352	18	a	a	DET
ap-1179	352	19	one	one	NUM
ap-1179	352	20	-	-	PUNCT
ap-1179	352	21	cocycle	cocycle	NOUN
ap-1179	352	22	conditon	conditon	NOUN
ap-1179	352	23	for	for	ADP
ap-1179	352	24	α1	α1	PROPN
ap-1179	352	25	,	,	PUNCT
ap-1179	352	26	(	(	PUNCT
ap-1179	352	27	δα)(x	δα)(x	PROPN
ap-1179	352	28	,	,	PUNCT
ap-1179	352	29	y	y	PROPN
ap-1179	352	30	,	,	PUNCT
ap-1179	352	31	z	z	NOUN
ap-1179	352	32	)	)	PUNCT
ap-1179	352	33	=	=	SYM
ap-1179	352	34	adxα(y	adxα(y	PROPN
ap-1179	352	35	,	,	PUNCT
ap-1179	352	36	z)−	z)−	PROPN
ap-1179	352	37	adyα(x	adyα(x	PROPN
ap-1179	352	38	,	,	PUNCT
ap-1179	352	39	z)−	z)−	PROPN
ap-1179	352	40	(	(	PUNCT
ap-1179	352	41	α(x	α(x	PROPN
ap-1179	352	42	,	,	PUNCT
ap-1179	352	43	)	)	PUNCT
ap-1179	352	44	·	·	PUNCT
ap-1179	353	1	y	y	X
ap-1179	353	2	)	)	PUNCT
ap-1179	353	3	·	·	PUNCT
ap-1179	353	4	z−	z−	PROPN
ap-1179	353	5	α(x	α(x	PROPN
ap-1179	353	6	·	·	PUNCT
ap-1179	353	7	y	y	PROPN
ap-1179	353	8	,	,	PUNCT
ap-1179	353	9	z)−	z)−	PROPN
ap-1179	353	10	α(y	α(y	NOUN
ap-1179	353	11	,	,	PUNCT
ap-1179	353	12	x	x	X
ap-1179	353	13	·	·	PUNCT
ap-1179	353	14	z	z	X
ap-1179	353	15	)	)	PUNCT
ap-1179	353	16	+	+	CCONJ
ap-1179	353	17	α(x	α(x	PROPN
ap-1179	353	18	,	,	PUNCT
ap-1179	353	19	y	y	PROPN
ap-1179	353	20	·	·	PUNCT
ap-1179	353	21	z	z	X
ap-1179	353	22	)	)	PUNCT
ap-1179	353	23	=	=	SYM
ap-1179	353	24	0	0	NUM
ap-1179	353	25	,	,	PUNCT
ap-1179	353	26	(	(	PUNCT
ap-1179	353	27	6.40	6.40	NUM
ap-1179	353	28	)	)	PUNCT
ap-1179	354	1	where	where	SCONJ
ap-1179	354	2	,	,	PUNCT
ap-1179	354	3	for	for	ADP
ap-1179	354	4	instance	instance	NOUN
ap-1179	354	5	for	for	ADP
ap-1179	354	6	n	n	NOUN
ap-1179	354	7	=	=	SYM
ap-1179	354	8	3	3	NUM
ap-1179	354	9	,	,	PUNCT
ap-1179	354	10	α1(x	α1(x	PROPN
ap-1179	354	11	,	,	PUNCT
ap-1179	354	12	)	)	PUNCT
ap-1179	354	13	·	·	PUNCT
ap-1179	355	1	y	y	X
ap-1179	355	2	:	:	PUNCT
ap-1179	355	3	=	=	SYM
ap-1179	355	4	(	(	PUNCT
ap-1179	355	5	α1(x	α1(x	PROPN
ap-1179	355	6	,	,	PUNCT
ap-1179	355	7	)	)	PUNCT
ap-1179	355	8	·	·	PUNCT
ap-1179	356	1	y1	y1	INTJ
ap-1179	356	2	,	,	PUNCT
ap-1179	356	3	y2	y2	PROPN
ap-1179	356	4	)	)	PUNCT
ap-1179	357	1	+	+	CCONJ
ap-1179	357	2	(	(	PUNCT
ap-1179	357	3	y1	y1	INTJ
ap-1179	357	4	,	,	PUNCT
ap-1179	357	5	α1(x	α1(x	PROPN
ap-1179	357	6	,	,	PUNCT
ap-1179	357	7	)	)	PUNCT
ap-1179	357	8	·	·	PUNCT
ap-1179	358	1	y2	y2	X
ap-1179	358	2	)	)	PUNCT
ap-1179	358	3	=	=	PUNCT
ap-1179	358	4	(	(	PUNCT
ap-1179	358	5	6.41	6.41	NUM
ap-1179	358	6	)	)	PUNCT
ap-1179	358	7	(	(	PUNCT
ap-1179	358	8	α1(x	α1(x	PROPN
ap-1179	358	9	,	,	PUNCT
ap-1179	358	10	y1	y1	PROPN
ap-1179	358	11	)	)	PUNCT
ap-1179	358	12	,	,	PUNCT
ap-1179	358	13	y2	y2	PROPN
ap-1179	358	14	)	)	PUNCT
ap-1179	359	1	+	+	CCONJ
ap-1179	359	2	(	(	PUNCT
ap-1179	359	3	y1	y1	INTJ
ap-1179	359	4	,	,	PUNCT
ap-1179	359	5	α1(x	α1(x	PROPN
ap-1179	359	6	,	,	PUNCT
ap-1179	359	7	y2	y2	PROPN
ap-1179	359	8	)	)	PUNCT
ap-1179	359	9	)	)	PUNCT
ap-1179	359	10	.	.	PUNCT
ap-1179	360	1	to	to	PART
ap-1179	360	2	see	see	VERB
ap-1179	360	3	whether	whether	SCONJ
ap-1179	360	4	the	the	DET
ap-1179	360	5	g	g	NOUN
ap-1179	360	6	-	-	PUNCT
ap-1179	360	7	valued	value	VERB
ap-1179	360	8	cocycle	cocycle	NOUN
ap-1179	360	9	α1	α1	PROPN
ap-1179	360	10	is	be	AUX
ap-1179	360	11	a	a	DET
ap-1179	360	12	coboundary	coboundary	NOUN
ap-1179	360	13	,	,	PUNCT
ap-1179	360	14	we	we	PRON
ap-1179	360	15	look	look	VERB
ap-1179	360	16	for	for	ADP
ap-1179	360	17	the	the	DET
ap-1179	360	18	possible	possible	ADJ
ap-1179	360	19	triviality	triviality	NOUN
ap-1179	360	20	of	of	ADP
ap-1179	360	21	the	the	DET
ap-1179	360	22	infinitesimal	infinitesimal	ADJ
ap-1179	360	23	deformation	deformation	NOUN
ap-1179	360	24	.	.	PUNCT
ap-1179	361	1	it	it	PRON
ap-1179	361	2	will	will	AUX
ap-1179	361	3	be	be	AUX
ap-1179	361	4	trivial	trivial	ADJ
ap-1179	361	5	if	if	SCONJ
ap-1179	361	6	new	new	ADJ
ap-1179	361	7	generators	generator	NOUN
ap-1179	361	8	can	can	AUX
ap-1179	361	9	been	be	AUX
ap-1179	361	10	found	find	VERB
ap-1179	361	11	in	in	ADP
ap-1179	361	12	terms	term	NOUN
ap-1179	361	13	of	of	ADP
ap-1179	361	14	β	β	X
ap-1179	361	15	,	,	PUNCT
ap-1179	361	16	β	β	X
ap-1179	361	17	:	:	PUNCT
ap-1179	361	18	g	g	PROPN
ap-1179	361	19	→	→	SYM
ap-1179	361	20	g	g	PROPN
ap-1179	361	21	,	,	PUNCT
ap-1179	361	22	x	x	NOUN
ap-1179	361	23	′	′	NUM
ap-1179	362	1	i	i	PRON
ap-1179	362	2	=	=	PUNCT
ap-1179	362	3	xi	xi	PROPN
ap-1179	362	4	−	−	PROPN
ap-1179	362	5	tβ(xi	tβ(xi	PROPN
ap-1179	362	6	)	)	PUNCT
ap-1179	362	7	,	,	PUNCT
ap-1179	362	8	such	such	ADJ
ap-1179	362	9	that	that	SCONJ
ap-1179	363	1	[	[	X
ap-1179	363	2	x	x	SYM
ap-1179	363	3	′	′	NUM
ap-1179	363	4	1	1	NUM
ap-1179	363	5	,	,	PUNCT
ap-1179	363	6	.	.	PUNCT
ap-1179	363	7	.	.	PUNCT
ap-1179	363	8	.	.	PUNCT
ap-1179	364	1	,	,	PUNCT
ap-1179	364	2	x	x	X
ap-1179	364	3	′	′	NUM
ap-1179	364	4	n]t	n]t	NOUN
ap-1179	365	1	=	=	X
ap-1179	366	1	[	[	X
ap-1179	366	2	x1	x1	X
ap-1179	366	3	,	,	PUNCT
ap-1179	366	4	.	.	PUNCT
ap-1179	366	5	.	.	PUNCT
ap-1179	367	1	.	.	PUNCT
ap-1179	368	1	,	,	PUNCT
ap-1179	369	1	xn	xn	X
ap-1179	369	2	]	]	PUNCT
ap-1179	369	3	′	′	NUM
ap-1179	369	4	≡	≡	PROPN
ap-1179	370	1	[	[	X
ap-1179	370	2	x1	x1	PROPN
ap-1179	370	3	,	,	PUNCT
ap-1179	370	4	.	.	PUNCT
ap-1179	370	5	.	.	PUNCT
ap-1179	370	6	.	.	PUNCT
ap-1179	371	1	,	,	PUNCT
ap-1179	371	2	xn]−	xn]−	PROPN
ap-1179	371	3	tβ([x1	tβ([x1	PROPN
ap-1179	371	4	,	,	PUNCT
ap-1179	371	5	.	.	PUNCT
ap-1179	371	6	.	.	PUNCT
ap-1179	371	7	.	.	PUNCT
ap-1179	372	1	,	,	PUNCT
ap-1179	372	2	xn	xn	PROPN
ap-1179	372	3	]	]	X
ap-1179	372	4	)	)	PUNCT
ap-1179	372	5	.	.	PUNCT
ap-1179	373	1	(	(	PUNCT
ap-1179	373	2	6.42	6.42	NUM
ap-1179	373	3	)	)	PUNCT
ap-1179	373	4	at	at	ADP
ap-1179	373	5	first	first	ADJ
ap-1179	373	6	order	order	NOUN
ap-1179	373	7	in	in	ADP
ap-1179	373	8	t	t	PROPN
ap-1179	373	9	this	this	PRON
ap-1179	373	10	implies	imply	VERB
ap-1179	373	11	[	[	X
ap-1179	373	12	x	x	X
ap-1179	373	13	′	′	NUM
ap-1179	373	14	1	1	NUM
ap-1179	373	15	,	,	PUNCT
ap-1179	373	16	.	.	PUNCT
ap-1179	373	17	.	.	PUNCT
ap-1179	374	1	.	.	PUNCT
ap-1179	375	1	,	,	PUNCT
ap-1179	375	2	x	x	X
ap-1179	375	3	′	′	NUM
ap-1179	375	4	n]t	n]t	NOUN
ap-1179	376	1	=	=	X
ap-1179	377	1	[	[	X
ap-1179	377	2	x1	x1	X
ap-1179	377	3	,	,	PUNCT
ap-1179	377	4	.	.	PUNCT
ap-1179	377	5	.	.	PUNCT
ap-1179	378	1	.	.	PUNCT
ap-1179	379	1	,	,	PUNCT
ap-1179	379	2	xn]t	xn]t	PROPN
ap-1179	379	3	−	−	PROPN
ap-1179	379	4	t	t	PROPN
ap-1179	379	5	n∑	n∑	PROPN
ap-1179	379	6	a=1	a=1	PUNCT
ap-1179	380	1	[	[	X
ap-1179	380	2	x1	x1	NUM
ap-1179	380	3	,	,	PUNCT
ap-1179	380	4	.	.	PUNCT
ap-1179	380	5	.	.	PUNCT
ap-1179	381	1	.	.	PUNCT
ap-1179	382	1	,	,	PUNCT
ap-1179	382	2	xa−1	xa−1	PROPN
ap-1179	382	3	,	,	PUNCT
ap-1179	382	4	β(xa	β(xa	NUM
ap-1179	382	5	)	)	PUNCT
ap-1179	382	6	,	,	PUNCT
ap-1179	382	7	xa+1	xa+1	PROPN
ap-1179	382	8	,	,	PUNCT
ap-1179	382	9	.	.	PUNCT
ap-1179	382	10	.	.	PUNCT
ap-1179	382	11	.	.	PUNCT
ap-1179	383	1	,	,	PUNCT
ap-1179	384	1	xn]t	xn]t	PROPN
ap-1179	384	2	=	=	PUNCT
ap-1179	385	1	[	[	X
ap-1179	385	2	x1	x1	PROPN
ap-1179	385	3	,	,	PUNCT
ap-1179	385	4	.	.	PUNCT
ap-1179	385	5	.	.	PUNCT
ap-1179	386	1	.	.	PUNCT
ap-1179	387	1	,	,	PUNCT
ap-1179	388	1	xn	xn	X
ap-1179	388	2	]	]	X
ap-1179	389	1	+	+	CCONJ
ap-1179	389	2	tα1(x1	tα1(x1	NOUN
ap-1179	389	3	,	,	PUNCT
ap-1179	389	4	.	.	PUNCT
ap-1179	389	5	.	.	PUNCT
ap-1179	389	6	.	.	PUNCT
ap-1179	390	1	,	,	PUNCT
ap-1179	391	1	xn)−	xn)−	X
ap-1179	391	2	(	(	PUNCT
ap-1179	391	3	6.43	6.43	NUM
ap-1179	391	4	)	)	PUNCT
ap-1179	391	5	t	t	NOUN
ap-1179	391	6	n∑	n∑	PUNCT
ap-1179	391	7	a=1	a=1	PUNCT
ap-1179	392	1	[	[	X
ap-1179	392	2	x1	x1	NUM
ap-1179	392	3	,	,	PUNCT
ap-1179	392	4	.	.	PUNCT
ap-1179	392	5	.	.	PUNCT
ap-1179	393	1	.	.	PUNCT
ap-1179	394	1	,	,	PUNCT
ap-1179	394	2	xa−1	xa−1	PROPN
ap-1179	394	3	,	,	PUNCT
ap-1179	394	4	β(xa	β(xa	NUM
ap-1179	394	5	)	)	PUNCT
ap-1179	394	6	,	,	PUNCT
ap-1179	394	7	xa+1	xa+1	PROPN
ap-1179	394	8	,	,	PUNCT
ap-1179	394	9	.	.	PUNCT
ap-1179	394	10	.	.	PUNCT
ap-1179	394	11	.	.	PUNCT
ap-1179	395	1	,	,	PUNCT
ap-1179	395	2	xn	xn	PROPN
ap-1179	395	3	]	]	PUNCT
ap-1179	395	4	.	.	PUNCT
ap-1179	396	1	therefore	therefore	ADV
ap-1179	396	2	,	,	PUNCT
ap-1179	396	3	the	the	DET
ap-1179	396	4	deformation	deformation	NOUN
ap-1179	396	5	is	be	AUX
ap-1179	396	6	trivial	trivial	ADJ
ap-1179	396	7	if	if	SCONJ
ap-1179	396	8	(	(	PUNCT
ap-1179	396	9	α1)(x1	α1)(x1	NOUN
ap-1179	396	10	,	,	PUNCT
ap-1179	396	11	.	.	PUNCT
ap-1179	396	12	.	.	PUNCT
ap-1179	396	13	.	.	PUNCT
ap-1179	397	1	,	,	PUNCT
ap-1179	397	2	xn	xn	X
ap-1179	397	3	)	)	PUNCT
ap-1179	397	4	:	:	PUNCT
ap-1179	397	5	=	=	SYM
ap-1179	397	6	−β([x1	−β([x1	PROPN
ap-1179	397	7	,	,	PUNCT
ap-1179	397	8	.	.	PUNCT
ap-1179	397	9	.	.	PUNCT
ap-1179	397	10	.	.	PUNCT
ap-1179	398	1	,	,	PUNCT
ap-1179	398	2	xn	xn	PROPN
ap-1179	398	3	]	]	PUNCT
ap-1179	398	4	)	)	PUNCT
ap-1179	399	1	+	+	NUM
ap-1179	399	2	n∑	n∑	ADJ
ap-1179	399	3	a=1	a=1	X
ap-1179	400	1	[	[	X
ap-1179	400	2	x1	x1	NUM
ap-1179	400	3	,	,	PUNCT
ap-1179	400	4	.	.	PUNCT
ap-1179	400	5	.	.	PUNCT
ap-1179	401	1	.	.	PUNCT
ap-1179	402	1	,	,	PUNCT
ap-1179	402	2	xa−1	xa−1	PROPN
ap-1179	402	3	,	,	PUNCT
ap-1179	402	4	β(xa	β(xa	NUM
ap-1179	402	5	)	)	PUNCT
ap-1179	402	6	,	,	PUNCT
ap-1179	402	7	xa+1	xa+1	PROPN
ap-1179	402	8	,	,	PUNCT
ap-1179	402	9	.	.	PUNCT
ap-1179	402	10	.	.	PUNCT
ap-1179	402	11	.	.	PUNCT
ap-1179	403	1	,	,	PUNCT
ap-1179	403	2	xn	xn	X
ap-1179	403	3	]	]	X
ap-1179	403	4	≡	≡	PROPN
ap-1179	403	5	(	(	PUNCT
ap-1179	403	6	δβ)(x	δβ)(x	PROPN
ap-1179	403	7	,	,	PUNCT
ap-1179	403	8	xn	xn	PROPN
ap-1179	403	9	)	)	PUNCT
ap-1179	403	10	(	(	PUNCT
ap-1179	403	11	6.44	6.44	NUM
ap-1179	403	12	)	)	PUNCT
ap-1179	403	13	i.e.	i.e.	X
ap-1179	403	14	,	,	PUNCT
ap-1179	403	15	when	when	SCONJ
ap-1179	403	16	α1(x	α1(x	PROPN
ap-1179	403	17	,	,	PUNCT
ap-1179	403	18	z	z	NOUN
ap-1179	403	19	)	)	PUNCT
ap-1179	403	20	=	=	SYM
ap-1179	403	21	(	(	PUNCT
ap-1179	403	22	δβ)(x	δβ)(x	PROPN
ap-1179	403	23	,	,	PUNCT
ap-1179	403	24	z	z	NOUN
ap-1179	403	25	)	)	PUNCT
ap-1179	403	26	=	=	SYM
ap-1179	403	27	−β(x	−β(x	NOUN
ap-1179	403	28	·	·	PUNCT
ap-1179	404	1	z	z	X
ap-1179	404	2	)	)	PUNCT
ap-1179	404	3	+	+	CCONJ
ap-1179	404	4	(	(	PUNCT
ap-1179	404	5	β	β	X
ap-1179	404	6	(	(	PUNCT
ap-1179	404	7	)	)	PUNCT
ap-1179	404	8	·	·	PUNCT
ap-1179	404	9	x	x	X
ap-1179	404	10	)	)	PUNCT
ap-1179	404	11	·	·	PUNCT
ap-1179	404	12	z	z	PUNCT
ap-1179	405	1	+	+	NOUN
ap-1179	405	2	x	x	X
ap-1179	405	3	·	·	PUNCT
ap-1179	405	4	β(z	β(z	PROPN
ap-1179	405	5	)	)	PUNCT
ap-1179	405	6	.	.	PUNCT
ap-1179	406	1	(	(	PUNCT
ap-1179	406	2	6.45	6.45	NUM
ap-1179	406	3	)	)	PUNCT
ap-1179	406	4	if	if	SCONJ
ap-1179	406	5	all	all	DET
ap-1179	406	6	one	one	NUM
ap-1179	406	7	-	-	PUNCT
ap-1179	406	8	cocycles	cocycle	NOUN
ap-1179	406	9	are	be	AUX
ap-1179	406	10	trivial	trivial	ADJ
ap-1179	406	11	,	,	PUNCT
ap-1179	406	12	the	the	DET
ap-1179	406	13	fa	fa	PROPN
ap-1179	406	14	is	be	AUX
ap-1179	406	15	stable	stable	ADJ
ap-1179	406	16	or	or	CCONJ
ap-1179	406	17	rigid	rigid	ADJ
ap-1179	406	18	.	.	PUNCT
ap-1179	407	1	the	the	DET
ap-1179	407	2	above	above	ADJ
ap-1179	407	3	allows	allow	VERB
ap-1179	407	4	us	we	PRON
ap-1179	407	5	to	to	PART
ap-1179	407	6	write	write	VERB
ap-1179	407	7	the	the	DET
ap-1179	407	8	full	full	ADJ
ap-1179	407	9	complex	complex	ADJ
ap-1179	407	10	(	(	PUNCT
ap-1179	407	11	c•	c•	NOUN
ap-1179	407	12	ad(g	ad(g	ADP
ap-1179	407	13	,	,	PUNCT
ap-1179	407	14	g	g	NOUN
ap-1179	407	15	)	)	PUNCT
ap-1179	407	16	,	,	PUNCT
ap-1179	407	17	δ	δ	PROPN
ap-1179	407	18	)	)	PUNCT
ap-1179	407	19	adapted	adapt	VERB
ap-1179	407	20	to	to	ADP
ap-1179	407	21	the	the	DET
ap-1179	407	22	deformations	deformation	NOUN
ap-1179	407	23	of	of	ADP
ap-1179	407	24	fa	fa	NOUN
ap-1179	407	25	problem	problem	NOUN
ap-1179	407	26	(	(	PUNCT
ap-1179	407	27	see	see	VERB
ap-1179	407	28	[	[	X
ap-1179	407	29	21	21	NUM
ap-1179	407	30	]	]	PUNCT
ap-1179	407	31	for	for	ADP
ap-1179	407	32	details	detail	NOUN
ap-1179	407	33	)	)	PUNCT
ap-1179	407	34	.	.	PUNCT
ap-1179	408	1	the	the	DET
ap-1179	408	2	p	p	PROPN
ap-1179	408	3	-	-	PUNCT
ap-1179	408	4	cochains	cochain	NOUN
ap-1179	408	5	are	be	AUX
ap-1179	408	6	maps	map	NOUN
ap-1179	408	7	αp	αp	NOUN
ap-1179	408	8	:	:	PUNCT
ap-1179	408	9	∧(n−1)g⊗	∧(n−1)g⊗	ADV
ap-1179	408	10	p	p	X
ap-1179	408	11	·	·	PUNCT
ap-1179	408	12	·	·	PUNCT
ap-1179	408	13	·	·	PUNCT
ap-1179	409	1	⊗∧(n−1)g∧g→	⊗∧(n−1)g∧g→	ADV
ap-1179	409	2	g	g	NOUN
ap-1179	409	3	and	and	CCONJ
ap-1179	409	4	the	the	DET
ap-1179	409	5	action	action	NOUN
ap-1179	409	6	of	of	ADP
ap-1179	409	7	the	the	DET
ap-1179	409	8	coboundary	coboundary	ADJ
ap-1179	409	9	operator	operator	NOUN
ap-1179	409	10	δ	δ	PROPN
ap-1179	409	11	is	be	AUX
ap-1179	409	12	now	now	ADV
ap-1179	409	13	defined	define	VERB
ap-1179	409	14	by	by	ADP
ap-1179	409	15	(	(	PUNCT
ap-1179	409	16	δαp)(x1	δαp)(x1	PROPN
ap-1179	409	17	,	,	PUNCT
ap-1179	409	18	.	.	PUNCT
ap-1179	409	19	.	.	PUNCT
ap-1179	410	1	.	.	PUNCT
ap-1179	411	1	,	,	PUNCT
ap-1179	411	2	xp	xp	INTJ
ap-1179	411	3	,	,	PUNCT
ap-1179	411	4	xp+1	xp+1	NUM
ap-1179	411	5	,	,	PUNCT
ap-1179	411	6	z	z	NOUN
ap-1179	411	7	)	)	PUNCT
ap-1179	411	8	=	=	SYM
ap-1179	411	9	p+1∑	p+1∑	PROPN
ap-1179	411	10	1≤j	1≤j	NOUN
ap-1179	411	11	<	<	X
ap-1179	411	12	k	k	X
ap-1179	411	13	(	(	PUNCT
ap-1179	411	14	−1)jαp(x1	−1)jαp(x1	PROPN
ap-1179	411	15	,	,	PUNCT
ap-1179	411	16	.	.	PUNCT
ap-1179	411	17	.	.	PUNCT
ap-1179	411	18	.	.	PUNCT
ap-1179	412	1	,	,	PUNCT
ap-1179	412	2	x̂j	x̂j	PROPN
ap-1179	412	3	,	,	PUNCT
ap-1179	412	4	.	.	PUNCT
ap-1179	412	5	.	.	PUNCT
ap-1179	412	6	.	.	PUNCT
ap-1179	413	1	,	,	PUNCT
ap-1179	413	2	xk−1	xk−1	PROPN
ap-1179	413	3	,	,	PUNCT
ap-1179	413	4	xj	xj	PROPN
ap-1179	413	5	·	·	PUNCT
ap-1179	413	6	xk	xk	PROPN
ap-1179	413	7	,	,	PUNCT
ap-1179	413	8	xk+1	xk+1	PROPN
ap-1179	413	9	,	,	PUNCT
ap-1179	413	10	.	.	PUNCT
ap-1179	413	11	.	.	PUNCT
ap-1179	413	12	.	.	PUNCT
ap-1179	414	1	,	,	PUNCT
ap-1179	414	2	xp+1	xp+1	NUM
ap-1179	414	3	,	,	PUNCT
ap-1179	414	4	z	z	NOUN
ap-1179	414	5	)	)	PUNCT
ap-1179	415	1	+	+	CCONJ
ap-1179	415	2	(	(	PUNCT
ap-1179	415	3	6.46	6.46	NUM
ap-1179	415	4	)	)	PUNCT
ap-1179	415	5	p+1∑	p+1∑	NOUN
ap-1179	415	6	j=1	j=1	NOUN
ap-1179	415	7	(	(	PUNCT
ap-1179	415	8	−1)jαp(x1	−1)jαp(x1	PROPN
ap-1179	415	9	,	,	PUNCT
ap-1179	415	10	.	.	PUNCT
ap-1179	415	11	.	.	PUNCT
ap-1179	415	12	.	.	PUNCT
ap-1179	416	1	,	,	PUNCT
ap-1179	416	2	x̂j	x̂j	PROPN
ap-1179	416	3	,	,	PUNCT
ap-1179	416	4	.	.	PUNCT
ap-1179	416	5	.	.	PUNCT
ap-1179	416	6	.	.	PUNCT
ap-1179	417	1	,	,	PUNCT
ap-1179	417	2	xp+1	xp+1	PROPN
ap-1179	417	3	,	,	PUNCT
ap-1179	417	4	xj	xj	PROPN
ap-1179	417	5	·	·	PUNCT
ap-1179	417	6	z	z	X
ap-1179	417	7	)	)	PUNCT
ap-1179	418	1	+	+	NUM
ap-1179	418	2	p+1∑	p+1∑	PROPN
ap-1179	418	3	j=1	j=1	NOUN
ap-1179	418	4	(	(	PUNCT
ap-1179	418	5	−1)j+1xj	−1)j+1xj	NOUN
ap-1179	418	6	·	·	PUNCT
ap-1179	418	7	αp(x1	αp(x1	NUM
ap-1179	418	8	,	,	PUNCT
ap-1179	418	9	.	.	PUNCT
ap-1179	418	10	.	.	PUNCT
ap-1179	418	11	.	.	PUNCT
ap-1179	419	1	,	,	PUNCT
ap-1179	419	2	x̂j	x̂j	PROPN
ap-1179	419	3	.	.	PUNCT
ap-1179	419	4	.	.	PUNCT
ap-1179	419	5	.	.	PUNCT
ap-1179	420	1	,	,	PUNCT
ap-1179	420	2	xp+1	xp+1	NUM
ap-1179	420	3	,	,	PUNCT
ap-1179	420	4	z	z	NOUN
ap-1179	420	5	)	)	PUNCT
ap-1179	421	1	+	+	CCONJ
ap-1179	421	2	(	(	PUNCT
ap-1179	421	3	−1)p(αp(x1	−1)p(αp(x1	PROPN
ap-1179	421	4	,	,	PUNCT
ap-1179	421	5	.	.	PUNCT
ap-1179	421	6	.	.	PUNCT
ap-1179	421	7	.	.	PUNCT
ap-1179	422	1	,	,	PUNCT
ap-1179	422	2	xp	xp	INTJ
ap-1179	422	3	,	,	PUNCT
ap-1179	422	4	)	)	PUNCT
ap-1179	422	5	·	·	PUNCT
ap-1179	422	6	xp+1	xp+1	NUM
ap-1179	422	7	)	)	PUNCT
ap-1179	422	8	·	·	PUNCT
ap-1179	423	1	z	z	NOUN
ap-1179	423	2	,	,	PUNCT
ap-1179	423	3	where	where	SCONJ
ap-1179	423	4	in	in	ADP
ap-1179	423	5	the	the	DET
ap-1179	423	6	last	last	ADJ
ap-1179	423	7	term	term	NOUN
ap-1179	423	8	αp(x1	αp(x1	NOUN
ap-1179	423	9	,	,	PUNCT
ap-1179	423	10	.	.	PUNCT
ap-1179	423	11	.	.	PUNCT
ap-1179	423	12	.	.	PUNCT
ap-1179	424	1	,	,	PUNCT
ap-1179	424	2	xp	xp	INTJ
ap-1179	424	3	,	,	PUNCT
ap-1179	424	4	)	)	PUNCT
ap-1179	424	5	·	·	PUNCT
ap-1179	425	1	y	y	X
ap-1179	425	2	=	=	PUNCT
ap-1179	425	3	n−1∑	n−1∑	PROPN
ap-1179	425	4	i=1	i=1	PROPN
ap-1179	425	5	(	(	PUNCT
ap-1179	425	6	y1	y1	INTJ
ap-1179	425	7	,	,	PUNCT
ap-1179	425	8	.	.	PUNCT
ap-1179	425	9	.	.	PUNCT
ap-1179	425	10	.	.	PUNCT
ap-1179	426	1	,	,	PUNCT
ap-1179	426	2	αp(x1	αp(x1	NOUN
ap-1179	426	3	,	,	PUNCT
ap-1179	426	4	.	.	PUNCT
ap-1179	426	5	.	.	PUNCT
ap-1179	427	1	.	.	PUNCT
ap-1179	428	1	,	,	PUNCT
ap-1179	428	2	xp	xp	INTJ
ap-1179	428	3	,	,	PUNCT
ap-1179	428	4	yi	yi	PROPN
ap-1179	428	5	)	)	PUNCT
ap-1179	428	6	,	,	PUNCT
ap-1179	428	7	.	.	PUNCT
ap-1179	428	8	.	.	PUNCT
ap-1179	429	1	.	.	PUNCT
ap-1179	430	1	,	,	PUNCT
ap-1179	430	2	yn−1	yn−1	PROPN
ap-1179	430	3	)	)	PUNCT
ap-1179	430	4	.	.	PUNCT
ap-1179	431	1	(	(	PUNCT
ap-1179	431	2	6.47	6.47	NUM
ap-1179	431	3	)	)	PUNCT
ap-1179	431	4	the	the	DET
ap-1179	431	5	above	above	ADJ
ap-1179	431	6	cohomology	cohomology	NOUN
ap-1179	431	7	complex	complex	NOUN
ap-1179	432	1	[	[	X
ap-1179	432	2	21	21	NUM
ap-1179	432	3	]	]	X
ap-1179	432	4	is	be	AUX
ap-1179	432	5	essentially	essentially	ADV
ap-1179	432	6	equivalent	equivalent	ADJ
ap-1179	432	7	to	to	ADP
ap-1179	432	8	that	that	PRON
ap-1179	432	9	given	give	VERB
ap-1179	432	10	by	by	ADP
ap-1179	432	11	gautheron	gautheron	NOUN
ap-1179	432	12	[	[	X
ap-1179	432	13	19	19	NUM
ap-1179	432	14	]	]	PUNCT
ap-1179	432	15	and	and	CCONJ
ap-1179	432	16	rotkiewicz	rotkiewicz	NOUN
ap-1179	432	17	[	[	X
ap-1179	432	18	20	20	NUM
ap-1179	432	19	]	]	PUNCT
ap-1179	432	20	.	.	PUNCT
ap-1179	433	1	7	7	NUM
ap-1179	433	2	whitehead	whitehead	PROPN
ap-1179	433	3	lemma	lemma	PROPN
ap-1179	433	4	for	for	ADP
ap-1179	433	5	fas	fas	PROPN
ap-1179	433	6	it	it	PRON
ap-1179	433	7	follows	follow	VERB
ap-1179	433	8	from	from	ADP
ap-1179	433	9	the	the	DET
ap-1179	433	10	above	above	ADJ
ap-1179	433	11	discussion	discussion	NOUN
ap-1179	433	12	that	that	SCONJ
ap-1179	433	13	an	an	DET
ap-1179	433	14	analogue	analogue	NOUN
ap-1179	433	15	of	of	ADP
ap-1179	433	16	the	the	DET
ap-1179	433	17	whitehead	whitehead	PROPN
ap-1179	433	18	lemma	lemma	PROPN
ap-1179	433	19	for	for	ADP
ap-1179	433	20	fas	fas	PROPN
ap-1179	433	21	would	would	AUX
ap-1179	433	22	require	require	VERB
ap-1179	433	23	h10	h10	NOUN
ap-1179	433	24	(	(	PUNCT
ap-1179	433	25	g	g	NOUN
ap-1179	433	26	)	)	PUNCT
ap-1179	433	27	=	=	SYM
ap-1179	433	28	0	0	NUM
ap-1179	433	29	and	and	CCONJ
ap-1179	433	30	h1ad(g	h1ad(g	PROPN
ap-1179	433	31	,	,	PUNCT
ap-1179	433	32	g	g	NOUN
ap-1179	433	33	)	)	PUNCT
ap-1179	433	34	=	=	SYM
ap-1179	433	35	0	0	NUM
ap-1179	434	1	for	for	ADP
ap-1179	434	2	g	g	PROPN
ap-1179	434	3	semisimple	semisimple	NOUN
ap-1179	434	4	.	.	PUNCT
ap-1179	435	1	this	this	PRON
ap-1179	435	2	may	may	AUX
ap-1179	435	3	be	be	AUX
ap-1179	435	4	proven	prove	VERB
ap-1179	435	5	taking	take	VERB
ap-1179	435	6	advantage	advantage	NOUN
ap-1179	435	7	of	of	ADP
ap-1179	435	8	the	the	DET
ap-1179	435	9	fact	fact	NOUN
ap-1179	435	10	that	that	SCONJ
ap-1179	435	11	all	all	DET
ap-1179	435	12	simple	simple	ADJ
ap-1179	435	13	fas	fas	NOUN
ap-1179	435	14	have	have	AUX
ap-1179	435	15	the	the	DET
ap-1179	435	16	same	same	ADJ
ap-1179	435	17	general	general	ADJ
ap-1179	435	18	structure	structure	NOUN
ap-1179	435	19	[	[	X
ap-1179	435	20	11	11	NUM
ap-1179	435	21	,	,	PUNCT
ap-1179	435	22	8	8	NUM
ap-1179	435	23	]	]	PUNCT
ap-1179	435	24	.	.	PUNCT
ap-1179	436	1	specifically	specifically	ADV
ap-1179	436	2	,	,	PUNCT
ap-1179	436	3	in	in	ADP
ap-1179	436	4	filippov	filippov	NOUN
ap-1179	436	5	’s	’s	PART
ap-1179	436	6	notation	notation	NOUN
ap-1179	436	7	,	,	PUNCT
ap-1179	436	8	they	they	PRON
ap-1179	436	9	have	have	VERB
ap-1179	436	10	the	the	DET
ap-1179	436	11	form	form	NOUN
ap-1179	436	12	[	[	X
ap-1179	436	13	e1	e1	NOUN
ap-1179	436	14	.	.	PUNCT
ap-1179	436	15	.	.	PUNCT
ap-1179	436	16	.	.	PUNCT
ap-1179	437	1	êi	êi	PROPN
ap-1179	437	2	.	.	PUNCT
ap-1179	437	3	.	.	PUNCT
ap-1179	437	4	.	.	PUNCT
ap-1179	438	1	en+1	en+1	PUNCT
ap-1179	438	2	]	]	X
ap-1179	439	1	=	=	SYM
ap-1179	440	1	(	(	PUNCT
ap-1179	440	2	−1)n+1εiei	−1)n+1εiei	PROPN
ap-1179	440	3	or	or	CCONJ
ap-1179	440	4	[	[	X
ap-1179	440	5	ei1	ei1	X
ap-1179	440	6	.	.	PUNCT
ap-1179	440	7	.	.	PUNCT
ap-1179	440	8	.	.	PUNCT
ap-1179	441	1	ein	ein	NOUN
ap-1179	441	2	]	]	PUNCT
ap-1179	441	3	=	=	PUNCT
ap-1179	441	4	(	(	PUNCT
ap-1179	441	5	−1)n	−1)n	PUNCT
ap-1179	441	6	n+1∑	n+1∑	PROPN
ap-1179	441	7	i=1	i=1	PROPN
ap-1179	441	8	εiεi1	εiεi1	PROPN
ap-1179	441	9	...	...	PUNCT
ap-1179	441	10	in	in	ADP
ap-1179	441	11	iei	iei	PROPN
ap-1179	441	12	,	,	PUNCT
ap-1179	441	13	(	(	PUNCT
ap-1179	441	14	7.48	7.48	NUM
ap-1179	441	15	)	)	PUNCT
ap-1179	441	16	where	where	SCONJ
ap-1179	441	17	εi	εi	VERB
ap-1179	441	18	=	=	SYM
ap-1179	441	19	±1	±1	ADJ
ap-1179	441	20	.	.	PUNCT
ap-1179	442	1	in	in	ADP
ap-1179	442	2	other	other	ADJ
ap-1179	442	3	words	word	NOUN
ap-1179	442	4	,	,	PUNCT
ap-1179	442	5	the	the	DET
ap-1179	442	6	simple	simple	ADJ
ap-1179	442	7	fas	fas	NOUN
ap-1179	442	8	are	be	AUX
ap-1179	442	9	the	the	DET
ap-1179	442	10	euclidean	euclidean	ADJ
ap-1179	442	11	an+1	an+1	NOUN
ap-1179	442	12	and	and	CCONJ
ap-1179	442	13	the	the	DET
ap-1179	442	14	lorentzian	lorentzian	NOUN
ap-1179	442	15	as	as	ADP
ap-1179	442	16	,	,	PUNCT
ap-1179	442	17	t	t	PROPN
ap-1179	442	18	,	,	PUNCT
ap-1179	442	19	(	(	PUNCT
ap-1179	442	20	s+t	s+t	PROPN
ap-1179	442	21	=	=	SYM
ap-1179	442	22	n+1	n+1	PROPN
ap-1179	442	23	)	)	PUNCT
ap-1179	442	24	generalizations	generalization	NOUN
ap-1179	442	25	of	of	ADP
ap-1179	442	26	the	the	DET
ap-1179	442	27	n	n	NOUN
ap-1179	442	28	=	=	SYM
ap-1179	442	29	2	2	NUM
ap-1179	442	30	so(3	so(3	NOUN
ap-1179	442	31	)	)	PUNCT
ap-1179	442	32	and	and	CCONJ
ap-1179	442	33	so(1	so(1	PROPN
ap-1179	442	34	,	,	PUNCT
ap-1179	442	35	2	2	NUM
ap-1179	442	36	)	)	PUNCT
ap-1179	442	37	lie	lie	NOUN
ap-1179	442	38	algebras	algebra	NOUN
ap-1179	442	39	,	,	PUNCT
ap-1179	442	40	[	[	X
ap-1179	442	41	ei	ei	X
ap-1179	442	42	,	,	PUNCT
ap-1179	442	43	ej	ej	X
ap-1179	442	44	]	]	PUNCT
ap-1179	443	1	=	=	PUNCT
ap-1179	443	2	∑	∑	PUNCT
ap-1179	443	3	k	k	PROPN
ap-1179	443	4	εkεijkek	εkεijkek	PROPN
ap-1179	443	5	,	,	PUNCT
ap-1179	443	6	for	for	ADP
ap-1179	443	7	which	which	PRON
ap-1179	443	8	whitehead	whitehead	PROPN
ap-1179	443	9	’s	’s	PART
ap-1179	443	10	lemma	lemma	PROPN
ap-1179	443	11	does	do	AUX
ap-1179	443	12	apply	apply	VERB
ap-1179	443	13	.	.	PUNCT
ap-1179	444	1	define	define	VERB
ap-1179	444	2	the	the	DET
ap-1179	444	3	z10	z10	NOUN
ap-1179	444	4	(	(	PUNCT
ap-1179	444	5	g	g	NOUN
ap-1179	444	6	)	)	PUNCT
ap-1179	444	7	and	and	CCONJ
ap-1179	444	8	z1ad(g	z1ad(g	NUM
ap-1179	444	9	,	,	PUNCT
ap-1179	444	10	g	g	NOUN
ap-1179	444	11	)	)	PUNCT
ap-1179	444	12	cocycles	cocycle	NOUN
ap-1179	444	13	by	by	ADP
ap-1179	444	14	its	its	PRON
ap-1179	444	15	coordinates	coordinate	NOUN
ap-1179	444	16	,	,	PUNCT
ap-1179	444	17	α1i1	α1i1	ADP
ap-1179	444	18	...	...	PUNCT
ap-1179	444	19	in	in	ADP
ap-1179	444	20	=	=	PUNCT
ap-1179	444	21	α1(ei1	α1(ei1	NOUN
ap-1179	444	22	,	,	PUNCT
ap-1179	444	23	.	.	PUNCT
ap-1179	444	24	.	.	PUNCT
ap-1179	445	1	.	.	PUNCT
ap-1179	446	1	,	,	PUNCT
ap-1179	446	2	ein	ein	PROPN
ap-1179	446	3	)	)	PUNCT
ap-1179	446	4	,	,	PUNCT
ap-1179	446	5	(	(	PUNCT
ap-1179	446	6	7.49	7.49	NUM
ap-1179	446	7	)	)	PUNCT
ap-1179	446	8	α1i1	α1i1	AUX
ap-1179	446	9	...	...	PUNCT
ap-1179	446	10	in	in	ADP
ap-1179	446	11	j	j	PROPN
ap-1179	446	12	=	=	SYM
ap-1179	446	13	α1(ei1	α1(ei1	PROPN
ap-1179	446	14	,	,	PUNCT
ap-1179	446	15	.	.	PUNCT
ap-1179	446	16	.	.	PUNCT
ap-1179	447	1	.	.	PUNCT
ap-1179	448	1	,	,	PUNCT
ap-1179	448	2	ein	ein	PROPN
ap-1179	448	3	)	)	PUNCT
ap-1179	449	1	j	j	PROPN
ap-1179	449	2	,	,	PUNCT
ap-1179	449	3	i	i	PRON
ap-1179	449	4	,	,	PUNCT
ap-1179	449	5	j	j	PROPN
ap-1179	449	6	=	=	SYM
ap-1179	449	7	1	1	NUM
ap-1179	449	8	,	,	PUNCT
ap-1179	449	9	.	.	PUNCT
ap-1179	449	10	.	.	PUNCT
ap-1179	449	11	.	.	PUNCT
ap-1179	450	1	,	,	PUNCT
ap-1179	450	2	(	(	PUNCT
ap-1179	450	3	n+	n+	NOUN
ap-1179	450	4	1	1	NUM
ap-1179	450	5	)	)	PUNCT
ap-1179	450	6	.	.	PUNCT
ap-1179	451	1	using	use	VERB
ap-1179	451	2	the	the	DET
ap-1179	451	3	explicit	explicit	ADJ
ap-1179	451	4	form	form	NOUN
ap-1179	451	5	of	of	ADP
ap-1179	451	6	the	the	DET
ap-1179	451	7	simple	simple	ADJ
ap-1179	451	8	fas	fas	NOUN
ap-1179	451	9	,	,	PUNCT
ap-1179	451	10	it	it	PRON
ap-1179	451	11	is	be	AUX
ap-1179	451	12	possible	possible	ADJ
ap-1179	451	13	to	to	PART
ap-1179	451	14	show	show	VERB
ap-1179	451	15	[	[	X
ap-1179	451	16	21	21	NUM
ap-1179	451	17	]	]	PUNCT
ap-1179	451	18	that	that	SCONJ
ap-1179	451	19	the	the	DET
ap-1179	451	20	above	above	ADJ
ap-1179	451	21	cocycles	cocycle	NOUN
ap-1179	451	22	are	be	AUX
ap-1179	451	23	necessarily	necessarily	ADV
ap-1179	451	24	11	11	NUM
ap-1179	451	25	acta	acta	PROPN
ap-1179	451	26	polytechnica	polytechnica	PROPN
ap-1179	451	27	vol	vol	NOUN
ap-1179	451	28	.	.	PROPN
ap-1179	452	1	50	50	NUM
ap-1179	452	2	no	no	NOUN
ap-1179	452	3	.	.	PUNCT
ap-1179	453	1	3/2010	3/2010	NUM
ap-1179	453	2	one	one	NUM
ap-1179	453	3	-	-	PUNCT
ap-1179	453	4	coboundaries	coboundarie	NOUN
ap-1179	453	5	respectively	respectively	ADV
ap-1179	453	6	generated	generate	VERB
ap-1179	453	7	by	by	ADP
ap-1179	453	8	the	the	DET
ap-1179	453	9	zerocochains	zerocochain	NOUN
ap-1179	453	10	βk	βk	ADV
ap-1179	453	11	,	,	PUNCT
ap-1179	453	12	βr	βr	ADP
ap-1179	453	13	k	k	X
ap-1179	453	14	i.e.	i.e.	X
ap-1179	453	15	,	,	PUNCT
ap-1179	453	16	that	that	PRON
ap-1179	453	17	α1i1	α1i1	ADP
ap-1179	453	18	...	...	PUNCT
ap-1179	453	19	in	in	ADP
ap-1179	453	20	=	=	X
ap-1179	453	21	β([ei1	β([ei1	NOUN
ap-1179	453	22	.	.	PUNCT
ap-1179	453	23	.	.	PUNCT
ap-1179	453	24	.	.	PUNCT
ap-1179	454	1	ein	ein	PROPN
ap-1179	454	2	]	]	PUNCT
ap-1179	454	3	)	)	PUNCT
ap-1179	454	4	=	=	SYM
ap-1179	454	5	εkεi1	εkεi1	NOUN
ap-1179	454	6	...	...	PUNCT
ap-1179	454	7	in	in	ADP
ap-1179	454	8	kβk	kβk	ADJ
ap-1179	454	9	⇒	⇒	NOUN
ap-1179	454	10	βk	βk	ADP
ap-1179	454	11	=	=	PUNCT
ap-1179	454	12	εk	εk	NOUN
ap-1179	454	13	n	n	CCONJ
ap-1179	454	14	!	!	PUNCT
ap-1179	455	1	n+1∑	n+1∑	PROPN
ap-1179	455	2	i1,	i1,	PRON
ap-1179	455	3	...	...	PUNCT
ap-1179	455	4	,in=1	,in=1	PUNCT
ap-1179	455	5	εi1	εi1	PROPN
ap-1179	455	6	...	...	PUNCT
ap-1179	455	7	in	in	ADP
ap-1179	455	8	k	k	PROPN
ap-1179	456	1	α1i1	α1i1	PUNCT
ap-1179	456	2	...	...	PUNCT
ap-1179	456	3	in	in	ADV
ap-1179	456	4	;	;	PUNCT
ap-1179	456	5	α1i1	α1i1	X
ap-1179	456	6	...	...	PUNCT
ap-1179	456	7	in	in	ADP
ap-1179	456	8	r	r	NOUN
ap-1179	456	9	=	=	NOUN
ap-1179	456	10	−(−1)n	−(−1)n	X
ap-1179	456	11	n+1∑	n+1∑	ADJ
ap-1179	456	12	s=1	s=1	X
ap-1179	456	13	εsεi1	εsεi1	NOUN
ap-1179	456	14	...	...	PUNCT
ap-1179	456	15	in	in	ADP
ap-1179	456	16	sβr	sβr	PROPN
ap-1179	456	17	s	s	PART
ap-1179	456	18	+	+	CCONJ
ap-1179	456	19	(	(	PUNCT
ap-1179	456	20	7.50	7.50	NUM
ap-1179	456	21	)	)	PUNCT
ap-1179	456	22	(	(	PUNCT
ap-1179	456	23	−1)n	−1)n	PROPN
ap-1179	456	24	n∑	n∑	X
ap-1179	456	25	a=1	a=1	X
ap-1179	456	26	n+1∑	n+1∑	PROPN
ap-1179	456	27	r=1	r=1	NOUN
ap-1179	456	28	εsεi1	εsεi1	NOUN
ap-1179	456	29	...	...	PUNCT
ap-1179	456	30	ia−1aia+1	ia−1aia+1	INTJ
ap-1179	456	31	...	...	PUNCT
ap-1179	456	32	in	in	ADP
ap-1179	456	33	sβr	sβr	PROPN
ap-1179	456	34	ia	ia	PROPN
ap-1179	456	35	⇒	⇒	PROPN
ap-1179	456	36	βrs	βrs	VERB
ap-1179	456	37	=	=	SYM
ap-1179	456	38	−	−	PROPN
ap-1179	456	39	(	(	PUNCT
ap-1179	456	40	−1	−1	NOUN
ap-1179	456	41	)	)	PUNCT
ap-1179	456	42	n	n	PRON
ap-1179	456	43	2	2	NUM
ap-1179	456	44	[	[	PUNCT
ap-1179	456	45	εs(α1)rs	εs(α1)rs	ADP
ap-1179	456	46	−	−	PROPN
ap-1179	456	47	1	1	NUM
ap-1179	456	48	n−	n−	NOUN
ap-1179	456	49	1	1	NUM
ap-1179	456	50	n+1∑	n+1∑	ADP
ap-1179	456	51	t=1	t=1	PROPN
ap-1179	456	52	εt(α1)ttδ	εt(α1)ttδ	PROPN
ap-1179	456	53	rs	rs	NOUN
ap-1179	456	54	]	]	PUNCT
ap-1179	456	55	.	.	PUNCT
ap-1179	457	1	the	the	DET
ap-1179	457	2	(	(	PUNCT
ap-1179	457	3	α1)rs	α1)rs	PROPN
ap-1179	457	4	above	above	ADV
ap-1179	457	5	is	be	AUX
ap-1179	457	6	the	the	DET
ap-1179	457	7	poincaré	poincaré	ADJ
ap-1179	457	8	dual	dual	NOUN
ap-1179	457	9	(	(	PUNCT
ap-1179	457	10	with	with	ADP
ap-1179	457	11	ε11	ε11	NOUN
ap-1179	457	12	...	...	PUNCT
ap-1179	457	13	inr	inr	NOUN
ap-1179	457	14	)	)	PUNCT
ap-1179	457	15	of	of	ADP
ap-1179	457	16	α1i1	α1i1	ADP
ap-1179	457	17	...	...	PUNCT
ap-1179	457	18	in	in	ADP
ap-1179	457	19	s	s	PROPN
ap-1179	457	20	;	;	PUNCT
ap-1179	457	21	it	it	PRON
ap-1179	457	22	may	may	AUX
ap-1179	457	23	be	be	AUX
ap-1179	457	24	seen	see	VERB
ap-1179	457	25	to	to	PART
ap-1179	457	26	be	be	AUX
ap-1179	457	27	(	(	PUNCT
ap-1179	457	28	rs)-symmetric	rs)-symmetric	ADJ
ap-1179	457	29	because	because	SCONJ
ap-1179	457	30	of	of	ADP
ap-1179	457	31	the	the	DET
ap-1179	457	32	cocycle	cocycle	NOUN
ap-1179	457	33	condition	condition	NOUN
ap-1179	457	34	.	.	PUNCT
ap-1179	458	1	therefore	therefore	ADV
ap-1179	458	2	,	,	PUNCT
ap-1179	458	3	h10	h10	PROPN
ap-1179	458	4	(	(	PUNCT
ap-1179	458	5	g	g	NOUN
ap-1179	458	6	)	)	PUNCT
ap-1179	458	7	=	=	SYM
ap-1179	458	8	0	0	NUM
ap-1179	458	9	,	,	PUNCT
ap-1179	458	10	h1ad(g	h1ad(g	PROPN
ap-1179	458	11	,	,	PUNCT
ap-1179	458	12	g	g	NOUN
ap-1179	458	13	)	)	PUNCT
ap-1179	458	14	=	=	SYM
ap-1179	458	15	0	0	NUM
ap-1179	458	16	for	for	ADP
ap-1179	458	17	a	a	DET
ap-1179	458	18	simple	simple	ADJ
ap-1179	458	19	fa	fa	NOUN
ap-1179	458	20	.	.	PUNCT
ap-1179	458	21	using	use	VERB
ap-1179	458	22	now	now	ADV
ap-1179	458	23	that	that	SCONJ
ap-1179	458	24	a	a	DET
ap-1179	458	25	semisimple	semisimple	NOUN
ap-1179	458	26	fa	fa	PROPN
ap-1179	458	27	is	be	AUX
ap-1179	458	28	the	the	DET
ap-1179	458	29	sum	sum	NOUN
ap-1179	458	30	(	(	PUNCT
ap-1179	458	31	2.13	2.13	NUM
ap-1179	458	32	)	)	PUNCT
ap-1179	458	33	of	of	ADP
ap-1179	458	34	simple	simple	ADJ
ap-1179	458	35	ideals	ideal	NOUN
ap-1179	458	36	the	the	DET
ap-1179	458	37	following	following	ADJ
ap-1179	458	38	result	result	NOUN
ap-1179	458	39	is	be	AUX
ap-1179	458	40	obtained	obtain	VERB
ap-1179	458	41	[	[	PUNCT
ap-1179	458	42	21	21	NUM
ap-1179	458	43	]	]	X
ap-1179	458	44	:	:	PUNCT
ap-1179	458	45	lemma	lemma	PROPN
ap-1179	458	46	(	(	PUNCT
ap-1179	458	47	whitehead	whitehead	PROPN
ap-1179	458	48	lemma	lemma	PROPN
ap-1179	458	49	for	for	ADP
ap-1179	458	50	n	n	PRON
ap-1179	458	51	≥	≥	NUM
ap-1179	458	52	2	2	NUM
ap-1179	458	53	)	)	PUNCT
ap-1179	458	54	semisimple	semisimple	NOUN
ap-1179	458	55	filippov	filippov	NOUN
ap-1179	458	56	(	(	PUNCT
ap-1179	458	57	n	n	CCONJ
ap-1179	458	58	-	-	PUNCT
ap-1179	458	59	lie	lie	NOUN
ap-1179	458	60	)	)	PUNCT
ap-1179	458	61	algebras	algebra	NOUN
ap-1179	458	62	,	,	PUNCT
ap-1179	458	63	n	n	PRON
ap-1179	458	64	≥	≥	NOUN
ap-1179	458	65	2	2	NUM
ap-1179	458	66	,	,	PUNCT
ap-1179	458	67	do	do	AUX
ap-1179	458	68	not	not	PART
ap-1179	458	69	admit	admit	VERB
ap-1179	458	70	non	non	ADJ
ap-1179	458	71	-	-	ADJ
ap-1179	458	72	trivial	trivial	ADJ
ap-1179	458	73	central	central	ADJ
ap-1179	458	74	extensions	extension	NOUN
ap-1179	458	75	and	and	CCONJ
ap-1179	458	76	are	be	AUX
ap-1179	458	77	,	,	PUNCT
ap-1179	458	78	moreover	moreover	ADV
ap-1179	458	79	,	,	PUNCT
ap-1179	458	80	rigid	rigid	ADJ
ap-1179	458	81	.	.	PUNCT
ap-1179	459	1	8	8	NUM
ap-1179	460	1	a	a	DET
ap-1179	460	2	comment	comment	NOUN
ap-1179	460	3	on	on	ADP
ap-1179	460	4	fa	fa	PROPN
ap-1179	460	5	and	and	CCONJ
ap-1179	460	6	leibniz	leibniz	PROPN
ap-1179	460	7	algebra	algebra	PROPN
ap-1179	460	8	cohomology	cohomology	PROPN
ap-1179	460	9	leibniz	leibniz	PROPN
ap-1179	460	10	algebras	algebras	PROPN
ap-1179	460	11	[	[	X
ap-1179	460	12	22	22	NUM
ap-1179	460	13	]	]	X
ap-1179	460	14	l	l	NOUN
ap-1179	460	15	are	be	AUX
ap-1179	460	16	a	a	DET
ap-1179	460	17	non	non	ADJ
ap-1179	460	18	-	-	ADJ
ap-1179	460	19	commutative	commutative	ADJ
ap-1179	460	20	version	version	NOUN
ap-1179	460	21	of	of	ADP
ap-1179	460	22	lie	lie	NOUN
ap-1179	460	23	algebras	algebra	VERB
ap-1179	460	24	:	:	PUNCT
ap-1179	460	25	their	their	PRON
ap-1179	460	26	bracket	bracket	NOUN
ap-1179	460	27	does	do	AUX
ap-1179	460	28	not	not	PART
ap-1179	460	29	need	need	VERB
ap-1179	460	30	being	be	AUX
ap-1179	460	31	anticommutative	anticommutative	ADJ
ap-1179	460	32	(	(	PUNCT
ap-1179	460	33	[	[	X
ap-1179	460	34	x	x	X
ap-1179	460	35	,	,	PUNCT
ap-1179	460	36	y	y	PROPN
ap-1179	460	37	]	]	PUNCT
ap-1179	460	38	�	�	PROPN
ap-1179	460	39	=	=	SYM
ap-1179	460	40	−[y	−[y	PROPN
ap-1179	460	41	,	,	PUNCT
ap-1179	460	42	x	x	X
ap-1179	460	43	]	]	PUNCT
ap-1179	460	44	)	)	PUNCT
ap-1179	460	45	but	but	CCONJ
ap-1179	460	46	still	still	ADV
ap-1179	460	47	satisfies	satisfy	VERB
ap-1179	460	48	the	the	DET
ap-1179	460	49	(	(	PUNCT
ap-1179	460	50	left	left	ADJ
ap-1179	460	51	,	,	PUNCT
ap-1179	460	52	say	say	INTJ
ap-1179	460	53	)	)	PUNCT
ap-1179	460	54	‘	'	PUNCT
ap-1179	460	55	leibniz	leibniz	NOUN
ap-1179	460	56	’	'	PUNCT
ap-1179	460	57	identity	identity	NOUN
ap-1179	460	58	[	[	X
ap-1179	460	59	x	x	X
ap-1179	460	60	,	,	PUNCT
ap-1179	460	61	[	[	X
ap-1179	460	62	y	y	X
ap-1179	460	63	,	,	PUNCT
ap-1179	460	64	z	z	X
ap-1179	460	65	]	]	X
ap-1179	460	66	]	]	X
ap-1179	461	1	=	=	PUNCT
ap-1179	462	1	[	[	X
ap-1179	462	2	[	[	X
ap-1179	462	3	x	x	X
ap-1179	462	4	,	,	PUNCT
ap-1179	462	5	y	y	PROPN
ap-1179	462	6	]	]	X
ap-1179	462	7	,	,	PUNCT
ap-1179	462	8	z	z	X
ap-1179	462	9	]	]	X
ap-1179	462	10	+	+	CCONJ
ap-1179	463	1	[	[	X
ap-1179	463	2	y	y	X
ap-1179	463	3	,	,	PUNCT
ap-1179	463	4	[	[	X
ap-1179	463	5	[	[	X
ap-1179	463	6	x	x	X
ap-1179	463	7	,	,	PUNCT
ap-1179	463	8	z	z	X
ap-1179	463	9	]	]	X
ap-1179	463	10	]	]	PUNCT
ap-1179	463	11	.	.	PUNCT
ap-1179	464	1	(	(	PUNCT
ap-1179	464	2	8.51	8.51	NUM
ap-1179	464	3	)	)	PUNCT
ap-1179	464	4	lie	lie	NOUN
ap-1179	464	5	algebras	algebra	NOUN
ap-1179	464	6	are	be	AUX
ap-1179	464	7	leibniz	leibniz	PROPN
ap-1179	464	8	algebras	algebras	PROPN
ap-1179	464	9	the	the	DET
ap-1179	464	10	bracket	bracket	NOUN
ap-1179	464	11	of	of	ADP
ap-1179	464	12	which	which	PRON
ap-1179	464	13	is	be	AUX
ap-1179	464	14	anticommutative	anticommutative	ADJ
ap-1179	464	15	.	.	PUNCT
ap-1179	465	1	similarly	similarly	ADV
ap-1179	465	2	,	,	PUNCT
ap-1179	465	3	one	one	PRON
ap-1179	465	4	may	may	AUX
ap-1179	465	5	define	define	VERB
ap-1179	465	6	n	n	CCONJ
ap-1179	465	7	-	-	PUNCT
ap-1179	465	8	leibniz	leibniz	NOUN
ap-1179	465	9	algebras	algebras	PROPN
ap-1179	465	10	l	l	PROPN
ap-1179	466	1	[	[	X
ap-1179	466	2	23	23	NUM
ap-1179	466	3	,	,	PUNCT
ap-1179	466	4	24	24	NUM
ap-1179	466	5	]	]	PUNCT
ap-1179	466	6	by	by	ADP
ap-1179	466	7	dropping	drop	VERB
ap-1179	466	8	the	the	DET
ap-1179	466	9	anticommutatitivity	anticommutatitivity	NOUN
ap-1179	466	10	of	of	ADP
ap-1179	466	11	the	the	DET
ap-1179	466	12	fa	fa	PROPN
ap-1179	466	13	n	n	CCONJ
ap-1179	466	14	-	-	PUNCT
ap-1179	466	15	bracket	bracket	NOUN
ap-1179	466	16	while	while	SCONJ
ap-1179	466	17	keeping	keep	VERB
ap-1179	466	18	the	the	PRON
ap-1179	466	19	(	(	PUNCT
ap-1179	466	20	left	left	ADJ
ap-1179	466	21	,	,	PUNCT
ap-1179	466	22	say	say	INTJ
ap-1179	466	23	)	)	PUNCT
ap-1179	466	24	fi	fi	NOUN
ap-1179	466	25	.	.	PUNCT
ap-1179	466	26	introducing	introduce	VERB
ap-1179	466	27	also	also	ADV
ap-1179	466	28	here	here	ADV
ap-1179	466	29	fundamental	fundamental	ADJ
ap-1179	466	30	objects	object	NOUN
ap-1179	466	31	for	for	ADP
ap-1179	466	32	l	l	NOUN
ap-1179	466	33	,	,	PUNCT
ap-1179	466	34	the	the	DET
ap-1179	466	35	identity	identity	NOUN
ap-1179	466	36	reads	read	VERB
ap-1179	466	37	x	x	X
ap-1179	466	38	·	·	PUNCT
ap-1179	466	39	(	(	PUNCT
ap-1179	466	40	y	y	PROPN
ap-1179	466	41	·	·	PUNCT
ap-1179	466	42	z	z	X
ap-1179	466	43	)	)	PUNCT
ap-1179	466	44	=	=	SYM
ap-1179	467	1	(	(	PUNCT
ap-1179	467	2	x	x	X
ap-1179	467	3	·	·	PUNCT
ap-1179	467	4	y	y	X
ap-1179	467	5	)	)	PUNCT
ap-1179	467	6	·	·	PUNCT
ap-1179	467	7	z+	z+	X
ap-1179	467	8	y	y	X
ap-1179	467	9	·	·	PUNCT
ap-1179	467	10	(	(	PUNCT
ap-1179	467	11	x	x	X
ap-1179	467	12	·	·	SYM
ap-1179	467	13	z	z	NOUN
ap-1179	467	14	)	)	PUNCT
ap-1179	467	15	∀x	∀x	NUM
ap-1179	467	16	,	,	PUNCT
ap-1179	467	17	y	y	PROPN
ap-1179	467	18	,	,	PUNCT
ap-1179	467	19	z	z	PROPN
ap-1179	467	20	∈	∈	PROPN
ap-1179	467	21	⊗n−1l	⊗n−1l	X
ap-1179	467	22	.	.	PUNCT
ap-1179	468	1	(	(	PUNCT
ap-1179	468	2	8.52	8.52	NUM
ap-1179	468	3	)	)	PUNCT
ap-1179	468	4	note	note	NOUN
ap-1179	468	5	that	that	SCONJ
ap-1179	468	6	nowx	nowx	PROPN
ap-1179	468	7	∈	∈	PROPN
ap-1179	468	8	⊗n−1l	⊗n−1l	PUNCT
ap-1179	468	9	since	since	SCONJ
ap-1179	468	10	,	,	PUNCT
ap-1179	468	11	in	in	ADP
ap-1179	468	12	contrast	contrast	NOUN
ap-1179	468	13	with	with	ADP
ap-1179	468	14	fas	fas	NOUN
ap-1179	468	15	,	,	PUNCT
ap-1179	468	16	the	the	DET
ap-1179	468	17	anticommutativity	anticommutativity	NOUN
ap-1179	468	18	of	of	ADP
ap-1179	468	19	the	the	DET
ap-1179	468	20	(	(	PUNCT
ap-1179	468	21	n−	n−	NOUN
ap-1179	468	22	1	1	NUM
ap-1179	468	23	)	)	PUNCT
ap-1179	468	24	arguments	argument	NOUN
ap-1179	468	25	of	of	ADP
ap-1179	468	26	x	x	SYM
ap-1179	468	27	is	be	AUX
ap-1179	468	28	not	not	PART
ap-1179	468	29	assumed	assume	VERB
ap-1179	468	30	.	.	PUNCT
ap-1179	469	1	the	the	DET
ap-1179	469	2	above	above	ADJ
ap-1179	469	3	is	be	AUX
ap-1179	469	4	still	still	ADV
ap-1179	469	5	the	the	DET
ap-1179	469	6	(	(	PUNCT
ap-1179	469	7	left	left	ADJ
ap-1179	469	8	)	)	PUNCT
ap-1179	469	9	fi	fi	NOUN
ap-1179	469	10	(	(	PUNCT
ap-1179	469	11	1.4	1.4	NUM
ap-1179	469	12	)	)	PUNCT
ap-1179	469	13	previously	previously	ADV
ap-1179	469	14	defining	define	VERB
ap-1179	469	15	fas	fas	NOUN
ap-1179	469	16	;	;	PUNCT
ap-1179	469	17	n	n	CCONJ
ap-1179	469	18	-	-	PUNCT
ap-1179	469	19	lie	lie	NOUN
ap-1179	469	20	algebras	algebra	NOUN
ap-1179	469	21	are	be	AUX
ap-1179	469	22	n	n	PRON
ap-1179	469	23	-	-	PUNCT
ap-1179	469	24	leibniz	leibniz	NOUN
ap-1179	469	25	algebras	algebra	VERB
ap-1179	469	26	the	the	DET
ap-1179	469	27	bracket	bracket	NOUN
ap-1179	469	28	of	of	ADP
ap-1179	469	29	which	which	PRON
ap-1179	469	30	is	be	AUX
ap-1179	469	31	fully	fully	ADV
ap-1179	469	32	anticommutative	anticommutative	ADJ
ap-1179	469	33	.	.	PUNCT
ap-1179	470	1	as	as	ADP
ap-1179	470	2	a	a	DET
ap-1179	470	3	result	result	NOUN
ap-1179	470	4	,	,	PUNCT
ap-1179	470	5	the	the	DET
ap-1179	470	6	characteristic	characteristic	ADJ
ap-1179	470	7	fi	fi	NOUN
ap-1179	470	8	x	x	X
ap-1179	470	9	·	·	PUNCT
ap-1179	470	10	(	(	PUNCT
ap-1179	470	11	y	y	PROPN
ap-1179	470	12	·	·	PUNCT
ap-1179	470	13	z)−	z)−	PROPN
ap-1179	470	14	y	y	PROPN
ap-1179	470	15	·	·	PUNCT
ap-1179	470	16	(	(	PUNCT
ap-1179	470	17	x	x	X
ap-1179	470	18	·	·	SYM
ap-1179	470	19	z	z	NOUN
ap-1179	470	20	)	)	PUNCT
ap-1179	470	21	=	=	SYM
ap-1179	470	22	(	(	PUNCT
ap-1179	470	23	x	x	X
ap-1179	470	24	·	·	PUNCT
ap-1179	470	25	y	y	X
ap-1179	470	26	)	)	PUNCT
ap-1179	470	27	·	·	PUNCT
ap-1179	470	28	z	z	X
ap-1179	470	29	∀x	∀x	X
ap-1179	470	30	,	,	PUNCT
ap-1179	470	31	y	y	PROPN
ap-1179	470	32	,	,	PUNCT
ap-1179	470	33	z	z	PROPN
ap-1179	470	34	∈	∈	PROPN
ap-1179	471	1	⊗n−1l	⊗n−1l	PUNCT
ap-1179	471	2	,	,	PUNCT
ap-1179	471	3	(	(	PUNCT
ap-1179	471	4	8.53	8.53	NUM
ap-1179	471	5	)	)	PUNCT
ap-1179	471	6	which	which	PRON
ap-1179	471	7	determined	determine	VERB
ap-1179	471	8	the	the	DET
ap-1179	471	9	nilpotency	nilpotency	NOUN
ap-1179	471	10	of	of	ADP
ap-1179	471	11	the	the	DET
ap-1179	471	12	coboundary	coboundary	ADJ
ap-1179	471	13	operator	operator	NOUN
ap-1179	471	14	δ	δ	PROPN
ap-1179	471	15	and	and	CCONJ
ap-1179	471	16	the	the	DET
ap-1179	471	17	different	different	ADJ
ap-1179	471	18	fa	fa	NOUN
ap-1179	471	19	cohomology	cohomology	NOUN
ap-1179	471	20	complexes	complex	NOUN
ap-1179	471	21	(	(	PUNCT
ap-1179	471	22	as	as	ADP
ap-1179	471	23	the	the	DET
ap-1179	471	24	ji	ji	PROPN
ap-1179	471	25	for	for	ADP
ap-1179	471	26	lie	lie	NOUN
ap-1179	471	27	algebras	algebra	NOUN
ap-1179	471	28	)	)	PUNCT
ap-1179	471	29	,	,	PUNCT
ap-1179	471	30	still	still	ADV
ap-1179	471	31	holds	hold	VERB
ap-1179	471	32	here	here	ADV
ap-1179	471	33	.	.	PUNCT
ap-1179	472	1	therefore	therefore	ADV
ap-1179	472	2	,	,	PUNCT
ap-1179	472	3	with	with	ADP
ap-1179	472	4	a	a	DET
ap-1179	472	5	suitable	suitable	ADJ
ap-1179	472	6	definition	definition	NOUN
ap-1179	472	7	of	of	ADP
ap-1179	472	8	p	p	PROPN
ap-1179	472	9	-	-	PUNCT
ap-1179	472	10	cochains	cochain	NOUN
ap-1179	472	11	,	,	PUNCT
ap-1179	472	12	the	the	DET
ap-1179	472	13	n	n	CCONJ
ap-1179	472	14	-	-	PUNCT
ap-1179	472	15	leibniz	leibniz	NOUN
ap-1179	472	16	and	and	CCONJ
ap-1179	472	17	the	the	DET
ap-1179	472	18	above	above	ADJ
ap-1179	472	19	fa	fa	INTJ
ap-1179	472	20	cohomological	cohomological	ADJ
ap-1179	472	21	complexes	complex	NOUN
ap-1179	472	22	have	have	VERB
ap-1179	472	23	the	the	DET
ap-1179	472	24	same	same	ADJ
ap-1179	472	25	structure	structure	NOUN
ap-1179	472	26	.	.	PUNCT
ap-1179	473	1	in	in	ADP
ap-1179	473	2	fact	fact	NOUN
ap-1179	473	3	,	,	PUNCT
ap-1179	473	4	n	n	CCONJ
ap-1179	473	5	-	-	PUNCT
ap-1179	473	6	leibniz	leibniz	NOUN
ap-1179	473	7	cohomology	cohomology	NOUN
ap-1179	473	8	underlies	underlie	VERB
ap-1179	473	9	n	n	CCONJ
ap-1179	473	10	-	-	PUNCT
ap-1179	473	11	lie	lie	NOUN
ap-1179	473	12	cohomology	cohomology	NOUN
ap-1179	473	13	.	.	PUNCT
ap-1179	474	1	this	this	PRON
ap-1179	474	2	is	be	AUX
ap-1179	474	3	why	why	SCONJ
ap-1179	474	4	the	the	DET
ap-1179	474	5	n	n	CCONJ
ap-1179	474	6	-	-	PUNCT
ap-1179	474	7	p	p	NOUN
ap-1179	474	8	cohomology	cohomology	NOUN
ap-1179	474	9	may	may	AUX
ap-1179	474	10	be	be	AUX
ap-1179	474	11	studied	study	VERB
ap-1179	474	12	from	from	ADP
ap-1179	474	13	the	the	DET
ap-1179	474	14	point	point	NOUN
ap-1179	474	15	of	of	ADP
ap-1179	474	16	view	view	NOUN
ap-1179	474	17	of	of	ADP
ap-1179	474	18	n	n	CCONJ
ap-1179	474	19	-	-	PUNCT
ap-1179	474	20	leibniz	leibniz	NOUN
ap-1179	474	21	cohomology	cohomology	NOUN
ap-1179	475	1	[	[	X
ap-1179	475	2	23	23	NUM
ap-1179	475	3	]	]	PUNCT
ap-1179	475	4	.	.	PUNCT
ap-1179	476	1	for	for	ADP
ap-1179	476	2	instance	instance	NOUN
ap-1179	476	3	,	,	PUNCT
ap-1179	476	4	for	for	ADP
ap-1179	476	5	n	n	NOUN
ap-1179	476	6	=	=	SYM
ap-1179	476	7	2	2	NUM
ap-1179	476	8	and	and	CCONJ
ap-1179	476	9	reverting	revert	VERB
ap-1179	476	10	to	to	ADP
ap-1179	476	11	the	the	DET
ap-1179	476	12	notation	notation	NOUN
ap-1179	476	13	that	that	PRON
ap-1179	476	14	labels	label	VERB
ap-1179	476	15	the	the	DET
ap-1179	476	16	cochains	cochain	NOUN
ap-1179	476	17	by	by	ADP
ap-1179	476	18	the	the	DET
ap-1179	476	19	number	number	NOUN
ap-1179	476	20	of	of	ADP
ap-1179	476	21	elements	element	NOUN
ap-1179	476	22	of	of	ADP
ap-1179	476	23	the	the	DET
ap-1179	476	24	algebra	algebra	NOUN
ap-1179	476	25	it	it	PRON
ap-1179	476	26	contains	contain	VERB
ap-1179	476	27	,	,	PUNCT
ap-1179	476	28	αp	αp	NOUN
ap-1179	476	29	∈	∈	PROPN
ap-1179	476	30	cp(l	cp(l	NOUN
ap-1179	476	31	,	,	PUNCT
ap-1179	476	32	l	l	NOUN
ap-1179	476	33	)	)	PUNCT
ap-1179	476	34	=	=	SYM
ap-1179	476	35	hom(⊗pl	hom(⊗pl	PROPN
ap-1179	476	36	,	,	PUNCT
ap-1179	476	37	l	l	NOUN
ap-1179	476	38	)	)	PUNCT
ap-1179	476	39	,	,	PUNCT
ap-1179	476	40	eq	eq	NOUN
ap-1179	476	41	.	.	PUNCT
ap-1179	477	1	(	(	PUNCT
ap-1179	477	2	6.46	6.46	NUM
ap-1179	477	3	)	)	PUNCT
ap-1179	477	4	for	for	ADP
ap-1179	477	5	the	the	DET
ap-1179	477	6	n	n	CCONJ
ap-1179	477	7	-	-	PUNCT
ap-1179	477	8	lie	lie	NOUN
ap-1179	477	9	case	case	NOUN
ap-1179	477	10	reduces	reduce	VERB
ap-1179	477	11	to	to	ADP
ap-1179	477	12	(	(	PUNCT
ap-1179	477	13	δαp)(x1	δαp)(x1	PROPN
ap-1179	477	14	,	,	PUNCT
ap-1179	477	15	.	.	PUNCT
ap-1179	477	16	.	.	PUNCT
ap-1179	478	1	.	.	PUNCT
ap-1179	479	1	,	,	PUNCT
ap-1179	479	2	xp	xp	INTJ
ap-1179	479	3	,	,	PUNCT
ap-1179	479	4	xp+1	xp+1	NUM
ap-1179	479	5	)	)	PUNCT
ap-1179	479	6	=	=	SYM
ap-1179	479	7	p+1∑	p+1∑	PROPN
ap-1179	480	1	1≤j	1≤j	NOUN
ap-1179	480	2	<	<	X
ap-1179	480	3	k	k	X
ap-1179	480	4	(	(	PUNCT
ap-1179	480	5	−1)jαp(x1	−1)jαp(x1	PROPN
ap-1179	480	6	,	,	PUNCT
ap-1179	480	7	.	.	PUNCT
ap-1179	480	8	.	.	PUNCT
ap-1179	480	9	.	.	PUNCT
ap-1179	481	1	,	,	PUNCT
ap-1179	481	2	x̂j	x̂j	PROPN
ap-1179	481	3	,	,	PUNCT
ap-1179	481	4	.	.	PUNCT
ap-1179	481	5	.	.	PUNCT
ap-1179	481	6	.	.	PUNCT
ap-1179	482	1	,	,	PUNCT
ap-1179	482	2	xk−1	xk−1	PROPN
ap-1179	482	3	,	,	PUNCT
ap-1179	482	4	[	[	X
ap-1179	482	5	xj	xj	X
ap-1179	482	6	,	,	PUNCT
ap-1179	482	7	xk	xk	PROPN
ap-1179	482	8	]	]	X
ap-1179	482	9	,	,	PUNCT
ap-1179	482	10	xk+1	xk+1	PROPN
ap-1179	482	11	,	,	PUNCT
ap-1179	482	12	.	.	PUNCT
ap-1179	482	13	.	.	PUNCT
ap-1179	482	14	.	.	PUNCT
ap-1179	483	1	,	,	PUNCT
ap-1179	483	2	xp+1	xp+1	X
ap-1179	483	3	)	)	PUNCT
ap-1179	484	1	+	+	CCONJ
ap-1179	484	2	(	(	PUNCT
ap-1179	484	3	8.54	8.54	NUM
ap-1179	484	4	)	)	PUNCT
ap-1179	484	5	p∑	p∑	NOUN
ap-1179	485	1	j=1	j=1	NOUN
ap-1179	485	2	(	(	PUNCT
ap-1179	485	3	−1)j+1xj	−1)j+1xj	NOUN
ap-1179	485	4	·	·	PUNCT
ap-1179	485	5	αp(x1	αp(x1	NUM
ap-1179	485	6	,	,	PUNCT
ap-1179	485	7	.	.	PUNCT
ap-1179	485	8	.	.	PUNCT
ap-1179	485	9	.	.	PUNCT
ap-1179	486	1	,	,	PUNCT
ap-1179	486	2	x̂j	x̂j	PROPN
ap-1179	486	3	.	.	PUNCT
ap-1179	486	4	.	.	PUNCT
ap-1179	486	5	.	.	PUNCT
ap-1179	487	1	,	,	PUNCT
ap-1179	487	2	xp+1	xp+1	X
ap-1179	487	3	)	)	PUNCT
ap-1179	488	1	+	+	CCONJ
ap-1179	488	2	(	(	PUNCT
ap-1179	488	3	−1)p+1(αp(x1	−1)p+1(αp(x1	NOUN
ap-1179	488	4	,	,	PUNCT
ap-1179	488	5	.	.	PUNCT
ap-1179	488	6	.	.	PUNCT
ap-1179	488	7	.	.	PUNCT
ap-1179	489	1	,	,	PUNCT
ap-1179	489	2	xp	xp	X
ap-1179	489	3	)	)	PUNCT
ap-1179	489	4	·	·	SYM
ap-1179	489	5	xp+1	xp+1	NUM
ap-1179	489	6	,	,	PUNCT
ap-1179	489	7	which	which	PRON
ap-1179	489	8	coincides	coincide	VERB
ap-1179	489	9	with	with	ADP
ap-1179	489	10	the	the	DET
ap-1179	489	11	cohomology	cohomology	NOUN
ap-1179	489	12	complex	complex	NOUN
ap-1179	489	13	(	(	PUNCT
ap-1179	489	14	c•(l	c•(l	PROPN
ap-1179	489	15	,	,	PUNCT
ap-1179	489	16	l	l	NOUN
ap-1179	489	17	)	)	PUNCT
ap-1179	489	18	,	,	PUNCT
ap-1179	489	19	δ	δ	PROPN
ap-1179	489	20	)	)	PUNCT
ap-1179	489	21	for	for	ADP
ap-1179	489	22	leibniz	leibniz	PROPN
ap-1179	489	23	algebras	algebras	PROPN
ap-1179	489	24	l	l	PROPN
ap-1179	490	1	[	[	X
ap-1179	490	2	25	25	NUM
ap-1179	490	3	,	,	PUNCT
ap-1179	490	4	24	24	NUM
ap-1179	490	5	]	]	PUNCT
ap-1179	490	6	.	.	PUNCT
ap-1179	491	1	our	our	PRON
ap-1179	491	2	proof	proof	NOUN
ap-1179	491	3	for	for	ADP
ap-1179	491	4	the	the	DET
ap-1179	491	5	whitehead	whitehead	PROPN
ap-1179	491	6	lemma	lemma	PROPN
ap-1179	491	7	for	for	ADP
ap-1179	491	8	fas	fas	PROPN
ap-1179	491	9	,	,	PUNCT
ap-1179	491	10	however	however	ADV
ap-1179	491	11	,	,	PUNCT
ap-1179	491	12	relied	rely	VERB
ap-1179	491	13	on	on	ADP
ap-1179	491	14	the	the	DET
ap-1179	491	15	antisymmetry	antisymmetry	NOUN
ap-1179	491	16	of	of	ADP
ap-1179	491	17	the	the	DET
ap-1179	491	18	n	n	CCONJ
ap-1179	491	19	-	-	PUNCT
ap-1179	491	20	commutator	commutator	NOUN
ap-1179	491	21	,	,	PUNCT
ap-1179	491	22	and	and	CCONJ
ap-1179	491	23	thus	thus	ADV
ap-1179	491	24	it	it	PRON
ap-1179	491	25	will	will	AUX
ap-1179	491	26	not	not	PART
ap-1179	491	27	hold	hold	VERB
ap-1179	491	28	when	when	SCONJ
ap-1179	491	29	the	the	DET
ap-1179	491	30	anticommutativity	anticommutativity	NOUN
ap-1179	491	31	is	be	AUX
ap-1179	491	32	relaxed	relax	VERB
ap-1179	491	33	.	.	PUNCT
ap-1179	492	1	thus	thus	ADV
ap-1179	492	2	,	,	PUNCT
ap-1179	492	3	one	one	PRON
ap-1179	492	4	might	might	AUX
ap-1179	492	5	expect	expect	VERB
ap-1179	492	6	having	have	VERB
ap-1179	492	7	a	a	DET
ap-1179	492	8	richer	rich	ADJ
ap-1179	492	9	deformation	deformation	NOUN
ap-1179	492	10	structure	structure	NOUN
ap-1179	492	11	for	for	ADP
ap-1179	492	12	leibniz	leibniz	NOUN
ap-1179	492	13	deformations	deformation	NOUN
ap-1179	492	14	.	.	PUNCT
ap-1179	493	1	this	this	PRON
ap-1179	493	2	has	have	AUX
ap-1179	493	3	been	be	AUX
ap-1179	493	4	observed	observe	VERB
ap-1179	493	5	already	already	ADV
ap-1179	493	6	for	for	ADP
ap-1179	493	7	the	the	DET
ap-1179	493	8	n	n	NOUN
ap-1179	493	9	=	=	SYM
ap-1179	493	10	2	2	NUM
ap-1179	493	11	case	case	NOUN
ap-1179	493	12	[	[	X
ap-1179	493	13	26	26	NUM
ap-1179	493	14	]	]	PUNCT
ap-1179	493	15	by	by	ADP
ap-1179	493	16	looking	look	VERB
ap-1179	493	17	at	at	ADP
ap-1179	493	18	leibniz	leibniz	NOUN
ap-1179	493	19	deformations	deformation	NOUN
ap-1179	493	20	of	of	ADP
ap-1179	493	21	a	a	DET
ap-1179	493	22	lie	lie	NOUN
ap-1179	493	23	algebra	algebra	NOUN
ap-1179	493	24	,	,	PUNCT
ap-1179	493	25	and	and	CCONJ
ap-1179	493	26	a	a	DET
ap-1179	493	27	specific	specific	ADJ
ap-1179	493	28	leibniz	leibniz	NOUN
ap-1179	493	29	deformation	deformation	NOUN
ap-1179	493	30	of	of	ADP
ap-1179	493	31	the	the	DET
ap-1179	493	32	euclidean	euclidean	ADJ
ap-1179	493	33	3	3	NUM
ap-1179	493	34	-	-	PUNCT
ap-1179	493	35	lie	lie	NOUN
ap-1179	493	36	algebra	algebra	NOUN
ap-1179	493	37	has	have	AUX
ap-1179	493	38	been	be	AUX
ap-1179	493	39	found	find	VERB
ap-1179	493	40	[	[	X
ap-1179	493	41	27	27	NUM
ap-1179	493	42	]	]	PUNCT
ap-1179	493	43	.	.	PUNCT
ap-1179	494	1	thus	thus	ADV
ap-1179	494	2	,	,	PUNCT
ap-1179	494	3	a	a	DET
ap-1179	494	4	natural	natural	ADJ
ap-1179	494	5	extension	extension	NOUN
ap-1179	494	6	of	of	ADP
ap-1179	494	7	our	our	PRON
ap-1179	494	8	work	work	NOUN
ap-1179	494	9	is	be	AUX
ap-1179	494	10	to	to	PART
ap-1179	494	11	look	look	VERB
ap-1179	494	12	e.g.	e.g.	ADV
ap-1179	494	13	at	at	ADP
ap-1179	494	14	n	n	CCONJ
ap-1179	494	15	-	-	PUNCT
ap-1179	494	16	leibniz	leibniz	NOUN
ap-1179	494	17	deformations	deformation	NOUN
ap-1179	494	18	of	of	ADP
ap-1179	494	19	simple	simple	ADJ
ap-1179	494	20	n	n	CCONJ
ap-1179	494	21	-	-	PUNCT
ap-1179	494	22	lie	lie	NOUN
ap-1179	494	23	algebras	algebra	NOUN
ap-1179	494	24	to	to	PART
ap-1179	494	25	see	see	VERB
ap-1179	494	26	whether	whether	SCONJ
ap-1179	494	27	this	this	PRON
ap-1179	494	28	opens	open	VERB
ap-1179	494	29	more	more	ADJ
ap-1179	494	30	possibilities	possibility	NOUN
ap-1179	494	31	.	.	PUNCT
ap-1179	495	1	our	our	PRON
ap-1179	495	2	results	result	NOUN
ap-1179	495	3	[	[	X
ap-1179	495	4	28	28	NUM
ap-1179	495	5	]	]	PUNCT
ap-1179	495	6	for	for	ADP
ap-1179	495	7	n	n	CCONJ
ap-1179	495	8	-	-	PUNCT
ap-1179	495	9	leibniz	leibniz	NOUN
ap-1179	495	10	deformations	deformation	NOUN
ap-1179	495	11	with	with	ADP
ap-1179	495	12	brackets	bracket	NOUN
ap-1179	495	13	that	that	PRON
ap-1179	495	14	keep	keep	VERB
ap-1179	495	15	the	the	DET
ap-1179	495	16	antisymmetry	antisymmetry	NOUN
ap-1179	495	17	in	in	ADP
ap-1179	495	18	their	their	PRON
ap-1179	495	19	first	first	ADJ
ap-1179	495	20	n	n	CCONJ
ap-1179	495	21	−	−	NUM
ap-1179	495	22	1	1	NUM
ap-1179	495	23	arguments	argument	NOUN
ap-1179	495	24	show	show	VERB
ap-1179	495	25	that	that	SCONJ
ap-1179	495	26	rigidity	rigidity	NOUN
ap-1179	495	27	still	still	ADV
ap-1179	495	28	holds	hold	VERB
ap-1179	495	29	for	for	ADP
ap-1179	495	30	n	n	X
ap-1179	495	31	>	>	X
ap-1179	495	32	3	3	X
ap-1179	495	33	.	.	PUNCT
ap-1179	495	34	acknowledgement	acknowledgement	NOUN
ap-1179	495	35	this	this	DET
ap-1179	495	36	work	work	NOUN
ap-1179	495	37	has	have	AUX
ap-1179	495	38	been	be	AUX
ap-1179	495	39	partially	partially	ADV
ap-1179	495	40	supported	support	VERB
ap-1179	495	41	by	by	ADP
ap-1179	495	42	the	the	DET
ap-1179	495	43	research	research	NOUN
ap-1179	495	44	grants	grant	NOUN
ap-1179	495	45	fis2008	fis2008	NOUN
ap-1179	495	46	-	-	PUNCT
ap-1179	495	47	01980	01980	NUM
ap-1179	495	48	and	and	CCONJ
ap-1179	495	49	fis2009	fis2009	NOUN
ap-1179	495	50	-	-	PUNCT
ap-1179	495	51	09002	09002	NUM
ap-1179	495	52	from	from	ADP
ap-1179	495	53	the	the	DET
ap-1179	495	54	spanish	spanish	ADJ
ap-1179	495	55	micinn	micinn	NOUN
ap-1179	495	56	,	,	PUNCT
ap-1179	495	57	and	and	CCONJ
ap-1179	495	58	va013c05	va013c05	NOUN
ap-1179	495	59	from	from	ADP
ap-1179	495	60	the	the	DET
ap-1179	495	61	junta	junta	PROPN
ap-1179	495	62	de	de	PROPN
ap-1179	495	63	castilla	castilla	PROPN
ap-1179	495	64	y	y	PROPN
ap-1179	495	65	león	león	PROPN
ap-1179	495	66	(	(	PUNCT
ap-1179	495	67	spain	spain	PROPN
ap-1179	495	68	)	)	PUNCT
ap-1179	495	69	.	.	PUNCT
ap-1179	496	1	references	reference	NOUN
ap-1179	496	2	[	[	X
ap-1179	496	3	1	1	NUM
ap-1179	496	4	]	]	X
ap-1179	496	5	de	de	X
ap-1179	496	6	azcárraga	azcárraga	PROPN
ap-1179	496	7	,	,	PUNCT
ap-1179	496	8	j.	j.	PROPN
ap-1179	496	9	a.	a.	PROPN
ap-1179	496	10	,	,	PUNCT
ap-1179	496	11	perelomov	perelomov	NOUN
ap-1179	496	12	,	,	PUNCT
ap-1179	496	13	a.	a.	NOUN
ap-1179	496	14	,	,	PUNCT
ap-1179	496	15	pérez	pérez	PROPN
ap-1179	496	16	bueno	bueno	PROPN
ap-1179	496	17	,	,	PUNCT
ap-1179	496	18	j.	j.	PROPN
ap-1179	496	19	c.	c.	PROPN
ap-1179	496	20	:	:	PUNCT
ap-1179	496	21	new	new	ADJ
ap-1179	496	22	generalized	generalized	ADJ
ap-1179	496	23	poisson	poisson	NOUN
ap-1179	496	24	structures	structure	NOUN
ap-1179	496	25	,	,	PUNCT
ap-1179	496	26	j.	j.	PROPN
ap-1179	496	27	phys	phys	PROPN
ap-1179	496	28	.	.	PUNCT
ap-1179	497	1	a29	a29	PROPN
ap-1179	497	2	,	,	PUNCT
ap-1179	497	3	l151	l151	PROPN
ap-1179	497	4	–	–	PUNCT
ap-1179	497	5	l157	l157	PROPN
ap-1179	497	6	(	(	PUNCT
ap-1179	497	7	1996	1996	NUM
ap-1179	497	8	)	)	PUNCT
ap-1179	497	9	,	,	PUNCT
ap-1179	497	10	arxiv	arxiv	NOUN
ap-1179	497	11	:	:	PUNCT
ap-1179	497	12	q	q	NOUN
ap-1179	497	13	-	-	PUNCT
ap-1179	497	14	alg/9601007	alg/9601007	ADJ
ap-1179	497	15	.	.	PUNCT
ap-1179	498	1	[	[	X
ap-1179	498	2	2	2	NUM
ap-1179	498	3	]	]	X
ap-1179	498	4	de	de	X
ap-1179	498	5	azcárraga	azcárraga	PROPN
ap-1179	498	6	,	,	PUNCT
ap-1179	498	7	j.	j.	PROPN
ap-1179	498	8	a.	a.	PROPN
ap-1179	498	9	,	,	PUNCT
ap-1179	498	10	perelomov	perelomov	NOUN
ap-1179	498	11	,	,	PUNCT
ap-1179	498	12	a.	a.	NOUN
ap-1179	498	13	m.	m.	NOUN
ap-1179	498	14	,	,	PUNCT
ap-1179	498	15	pérez	pérez	PROPN
ap-1179	498	16	bueno	bueno	PROPN
ap-1179	498	17	,	,	PUNCT
ap-1179	498	18	j.	j.	PROPN
ap-1179	498	19	c.	c.	PROPN
ap-1179	498	20	:	:	PUNCT
ap-1179	498	21	the	the	DET
ap-1179	498	22	schouten	schouten	VERB
ap-1179	498	23	-	-	PUNCT
ap-1179	498	24	nijenhuis	nijenhuis	NOUN
ap-1179	498	25	bracket	bracket	NOUN
ap-1179	498	26	,	,	PUNCT
ap-1179	498	27	cohomology	cohomology	NOUN
ap-1179	498	28	and	and	CCONJ
ap-1179	498	29	generalized	generalized	ADJ
ap-1179	498	30	poisson	poisson	NOUN
ap-1179	498	31	structures	structure	NOUN
ap-1179	498	32	,	,	PUNCT
ap-1179	498	33	j.	j.	PROPN
ap-1179	498	34	phys	phys	PROPN
ap-1179	498	35	.	.	PUNCT
ap-1179	498	36	a29	a29	PROPN
ap-1179	498	37	,	,	PUNCT
ap-1179	498	38	7	7	NUM
ap-1179	498	39	993–8010	993–8010	NUM
ap-1179	498	40	(	(	PUNCT
ap-1179	498	41	1996	1996	NUM
ap-1179	498	42	)	)	PUNCT
ap-1179	498	43	,	,	PUNCT
ap-1179	498	44	arxiv	arxiv	NOUN
ap-1179	498	45	:	:	PUNCT
ap-1179	498	46	hep	hep	NOUN
ap-1179	498	47	-	-	PUNCT
ap-1179	498	48	th/9605067	th/9605067	NOUN
ap-1179	498	49	.	.	NOUN
ap-1179	498	50	12	12	NUM
ap-1179	498	51	acta	acta	PROPN
ap-1179	498	52	polytechnica	polytechnica	PROPN
ap-1179	498	53	vol	vol	NOUN
ap-1179	498	54	.	.	PROPN
ap-1179	499	1	50	50	NUM
ap-1179	499	2	no	no	NOUN
ap-1179	499	3	.	.	PUNCT
ap-1179	500	1	3/2010	3/2010	NUM
ap-1179	500	2	[	[	X
ap-1179	500	3	3	3	NUM
ap-1179	500	4	]	]	X
ap-1179	500	5	de	de	X
ap-1179	500	6	azcárraga	azcárraga	PROPN
ap-1179	500	7	,	,	PUNCT
ap-1179	500	8	j.	j.	PROPN
ap-1179	500	9	a.	a.	PROPN
ap-1179	500	10	,	,	PUNCT
ap-1179	500	11	pérez	pérez	NOUN
ap-1179	500	12	-	-	PUNCT
ap-1179	500	13	bueno	bueno	NOUN
ap-1179	500	14	,	,	PUNCT
ap-1179	500	15	j.	j.	PROPN
ap-1179	500	16	c.	c.	PROPN
ap-1179	500	17	:	:	PUNCT
ap-1179	500	18	higherorder	higherorder	VERB
ap-1179	500	19	simple	simple	ADJ
ap-1179	500	20	lie	lie	NOUN
ap-1179	500	21	algebras	algebra	NOUN
ap-1179	500	22	,	,	PUNCT
ap-1179	500	23	commun	commun	PROPN
ap-1179	500	24	.	.	PUNCT
ap-1179	500	25	math	math	NOUN
ap-1179	500	26	.	.	PUNCT
ap-1179	501	1	phys	phy	NOUN
ap-1179	501	2	.	.	PUNCT
ap-1179	502	1	184	184	NUM
ap-1179	502	2	,	,	PUNCT
ap-1179	502	3	669–681	669–681	NUM
ap-1179	502	4	(	(	PUNCT
ap-1179	502	5	1997	1997	NUM
ap-1179	502	6	)	)	PUNCT
ap-1179	502	7	,	,	PUNCT
ap-1179	502	8	arxiv	arxiv	NOUN
ap-1179	502	9	:	:	PUNCT
ap-1179	502	10	hep	hep	PROPN
ap-1179	502	11	-	-	NOUN
ap-1179	502	12	th/9605213	th/9605213	NOUN
ap-1179	502	13	.	.	PUNCT
ap-1179	503	1	[	[	X
ap-1179	503	2	4	4	NUM
ap-1179	503	3	]	]	X
ap-1179	503	4	hanlon	hanlon	NOUN
ap-1179	503	5	,	,	PUNCT
ap-1179	503	6	p.	p.	NOUN
ap-1179	503	7	,	,	PUNCT
ap-1179	503	8	wachs	wach	NOUN
ap-1179	503	9	,	,	PUNCT
ap-1179	503	10	h.	h.	NOUN
ap-1179	503	11	:	:	PUNCT
ap-1179	503	12	on	on	ADP
ap-1179	503	13	lie	lie	NOUN
ap-1179	503	14	k	k	X
ap-1179	503	15	-	-	PUNCT
ap-1179	503	16	algebras	algebras	PROPN
ap-1179	503	17	,	,	PUNCT
ap-1179	503	18	adv	adv	PROPN
ap-1179	503	19	.	.	PUNCT
ap-1179	504	1	in	in	ADP
ap-1179	504	2	math	math	NOUN
ap-1179	504	3	.	.	PUNCT
ap-1179	505	1	113	113	NUM
ap-1179	505	2	,	,	PUNCT
ap-1179	505	3	206–236	206–236	NUM
ap-1179	505	4	(	(	PUNCT
ap-1179	505	5	1995	1995	NUM
ap-1179	505	6	)	)	PUNCT
ap-1179	505	7	.	.	PUNCT
ap-1179	506	1	[	[	X
ap-1179	506	2	5	5	NUM
ap-1179	506	3	]	]	PUNCT
ap-1179	506	4	gnedbaye	gnedbaye	NOUN
ap-1179	506	5	,	,	PUNCT
ap-1179	506	6	v.	v.	ADV
ap-1179	506	7	:	:	PUNCT
ap-1179	506	8	les	les	X
ap-1179	506	9	algèbres	algèbre	NOUN
ap-1179	506	10	k	k	PROPN
ap-1179	506	11	-	-	PUNCT
ap-1179	506	12	aires	aires	PROPN
ap-1179	506	13	el	el	PROPN
ap-1179	506	14	leurs	leurs	PROPN
ap-1179	506	15	opérads	opérads	PROPN
ap-1179	506	16	,	,	PUNCT
ap-1179	506	17	c.	c.	PROPN
ap-1179	506	18	r.	r.	PROPN
ap-1179	506	19	acad	acad	PROPN
ap-1179	506	20	.	.	PUNCT
ap-1179	507	1	sci	sci	PROPN
ap-1179	507	2	.	.	PROPN
ap-1179	507	3	paris	paris	PROPN
ap-1179	507	4	,	,	PUNCT
ap-1179	507	5	série	série	PROPN
ap-1179	507	6	i	i	PROPN
ap-1179	507	7	,	,	PUNCT
ap-1179	507	8	321	321	NUM
ap-1179	507	9	,	,	PUNCT
ap-1179	507	10	147–152	147–152	NUM
ap-1179	507	11	(	(	PUNCT
ap-1179	507	12	1995	1995	NUM
ap-1179	507	13	)	)	PUNCT
ap-1179	507	14	.	.	PUNCT
ap-1179	508	1	[	[	X
ap-1179	508	2	6	6	NUM
ap-1179	508	3	]	]	PUNCT
ap-1179	508	4	loday	loday	ADV
ap-1179	508	5	,	,	PUNCT
ap-1179	508	6	j.-l	j.-l	PROPN
ap-1179	508	7	.	.	PUNCT
ap-1179	508	8	:	:	PUNCT
ap-1179	509	1	la	la	PROPN
ap-1179	509	2	renaissance	renaissance	PROPN
ap-1179	509	3	des	des	PROPN
ap-1179	509	4	opérades	opérades	PROPN
ap-1179	509	5	,	,	PUNCT
ap-1179	509	6	sem	sem	PROPN
ap-1179	509	7	.	.	PROPN
ap-1179	509	8	bourbaki	bourbaki	PROPN
ap-1179	509	9	792	792	NUM
ap-1179	509	10	,	,	PUNCT
ap-1179	509	11	47–54	47–54	NUM
ap-1179	509	12	(	(	PUNCT
ap-1179	509	13	1994–1995	1994–1995	NUM
ap-1179	509	14	)	)	PUNCT
ap-1179	509	15	.	.	PUNCT
ap-1179	510	1	[	[	X
ap-1179	510	2	7	7	NUM
ap-1179	510	3	]	]	X
ap-1179	510	4	michor	michor	NOUN
ap-1179	510	5	,	,	PUNCT
ap-1179	510	6	p.	p.	PROPN
ap-1179	510	7	w.	w.	PROPN
ap-1179	510	8	,	,	PUNCT
ap-1179	510	9	vinogradov	vinogradov	PROPN
ap-1179	510	10	,	,	PUNCT
ap-1179	510	11	a.	a.	NOUN
ap-1179	510	12	m.	m.	NOUN
ap-1179	510	13	:	:	PUNCT
ap-1179	510	14	n	n	CCONJ
ap-1179	510	15	-	-	PUNCT
ap-1179	510	16	ary	ary	PROPN
ap-1179	510	17	lie	lie	NOUN
ap-1179	510	18	and	and	CCONJ
ap-1179	510	19	associative	associative	ADJ
ap-1179	510	20	algebras	algebra	NOUN
ap-1179	510	21	,	,	PUNCT
ap-1179	510	22	rend	rend	VERB
ap-1179	510	23	.	.	PUNCT
ap-1179	511	1	sem	sem	PROPN
ap-1179	511	2	.	.	PUNCT
ap-1179	511	3	mat	mat	PROPN
ap-1179	511	4	.	.	PROPN
ap-1179	511	5	univ	univ	PROPN
ap-1179	511	6	.	.	PUNCT
ap-1179	511	7	pol	pol	PROPN
ap-1179	511	8	.	.	PUNCT
ap-1179	512	1	torino	torino	PROPN
ap-1179	512	2	53	53	NUM
ap-1179	512	3	,	,	PUNCT
ap-1179	512	4	373–392	373–392	NUM
ap-1179	512	5	(	(	PUNCT
ap-1179	512	6	1996	1996	NUM
ap-1179	512	7	)	)	PUNCT
ap-1179	512	8	.	.	PUNCT
ap-1179	513	1	[	[	X
ap-1179	513	2	8	8	NUM
ap-1179	513	3	]	]	X
ap-1179	513	4	filippov	filippov	NOUN
ap-1179	513	5	,	,	PUNCT
ap-1179	513	6	v.	v.	CCONJ
ap-1179	513	7	:	:	PUNCT
ap-1179	513	8	n	n	CCONJ
ap-1179	513	9	-	-	PUNCT
ap-1179	513	10	lie	lie	NOUN
ap-1179	513	11	algebras	algebra	NOUN
ap-1179	513	12	,	,	PUNCT
ap-1179	513	13	sibirsk	sibirsk	PROPN
ap-1179	513	14	.	.	PUNCT
ap-1179	514	1	mat	mat	NOUN
ap-1179	514	2	.	.	PUNCT
ap-1179	515	1	zh	zh	PROPN
ap-1179	515	2	.	.	PROPN
ap-1179	515	3	26	26	NUM
ap-1179	515	4	(	(	PUNCT
ap-1179	515	5	1985	1985	NUM
ap-1179	515	6	)	)	PUNCT
ap-1179	515	7	,	,	PUNCT
ap-1179	515	8	126–140	126–140	NUM
ap-1179	515	9	,	,	PUNCT
ap-1179	515	10	191	191	NUM
ap-1179	515	11	(	(	PUNCT
ap-1179	515	12	english	english	ADJ
ap-1179	515	13	translation	translation	NOUN
ap-1179	515	14	:	:	PUNCT
ap-1179	515	15	siberian	siberian	ADJ
ap-1179	515	16	math	math	NOUN
ap-1179	515	17	.	.	PUNCT
ap-1179	516	1	j.	j.	PROPN
ap-1179	516	2	26	26	NUM
ap-1179	516	3	,	,	PUNCT
ap-1179	516	4	879–891	879–891	NUM
ap-1179	516	5	(	(	PUNCT
ap-1179	516	6	1985	1985	NUM
ap-1179	516	7	)	)	PUNCT
ap-1179	516	8	)	)	PUNCT
ap-1179	516	9	.	.	PUNCT
ap-1179	517	1	[	[	X
ap-1179	517	2	9	9	NUM
ap-1179	517	3	]	]	X
ap-1179	517	4	kasymov	kasymov	NOUN
ap-1179	517	5	,	,	PUNCT
ap-1179	517	6	s.	s.	PROPN
ap-1179	517	7	m.	m.	PROPN
ap-1179	517	8	:	:	PUNCT
ap-1179	517	9	theory	theory	NOUN
ap-1179	517	10	of	of	ADP
ap-1179	517	11	n	n	CCONJ
ap-1179	517	12	-	-	PUNCT
ap-1179	517	13	lie	lie	NOUN
ap-1179	517	14	algebras	algebra	NOUN
ap-1179	517	15	,	,	PUNCT
ap-1179	517	16	algebra	algebra	NOUN
ap-1179	517	17	i	i	PRON
ap-1179	517	18	logika	logika	PROPN
ap-1179	517	19	26	26	NUM
ap-1179	517	20	(	(	PUNCT
ap-1179	517	21	1987	1987	NUM
ap-1179	517	22	)	)	PUNCT
ap-1179	517	23	,	,	PUNCT
ap-1179	517	24	no	no	INTJ
ap-1179	517	25	.	.	NOUN
ap-1179	517	26	3	3	NUM
ap-1179	517	27	,	,	PUNCT
ap-1179	517	28	277–297	277–297	NUM
ap-1179	517	29	(	(	PUNCT
ap-1179	517	30	english	english	ADJ
ap-1179	517	31	translation	translation	NOUN
ap-1179	517	32	:	:	PUNCT
ap-1179	517	33	algebra	algebra	NOUN
ap-1179	517	34	and	and	CCONJ
ap-1179	517	35	logic	logic	NOUN
ap-1179	517	36	26	26	NUM
ap-1179	517	37	,	,	PUNCT
ap-1179	517	38	155–166	155–166	NUM
ap-1179	517	39	(	(	PUNCT
ap-1179	517	40	1988	1988	NUM
ap-1179	517	41	)	)	PUNCT
ap-1179	517	42	)	)	PUNCT
ap-1179	517	43	.	.	PUNCT
ap-1179	518	1	[	[	X
ap-1179	518	2	10	10	NUM
ap-1179	518	3	]	]	X
ap-1179	518	4	kasymov	kasymov	NOUN
ap-1179	518	5	,	,	PUNCT
ap-1179	518	6	s.	s.	PROPN
ap-1179	518	7	m.	m.	PROPN
ap-1179	518	8	:	:	PUNCT
ap-1179	518	9	on	on	ADP
ap-1179	518	10	analogues	analogue	NOUN
ap-1179	518	11	of	of	ADP
ap-1179	518	12	cartan	cartan	ADJ
ap-1179	518	13	criteria	criterion	NOUN
ap-1179	518	14	for	for	ADP
ap-1179	518	15	n	n	CCONJ
ap-1179	518	16	-	-	PUNCT
ap-1179	518	17	lie	lie	NOUN
ap-1179	518	18	algebras	algebra	NOUN
ap-1179	518	19	,	,	PUNCT
ap-1179	518	20	algebra	algebra	NOUN
ap-1179	518	21	i	i	PRON
ap-1179	518	22	logika	logika	PROPN
ap-1179	518	23	34	34	NUM
ap-1179	518	24	(	(	PUNCT
ap-1179	518	25	1995	1995	NUM
ap-1179	518	26	)	)	PUNCT
ap-1179	518	27	,	,	PUNCT
ap-1179	518	28	no	no	INTJ
ap-1179	518	29	.	.	NOUN
ap-1179	518	30	3	3	NUM
ap-1179	518	31	,	,	PUNCT
ap-1179	518	32	274–287	274–287	NUM
ap-1179	518	33	,	,	PUNCT
ap-1179	518	34	363	363	NUM
ap-1179	518	35	.	.	PUNCT
ap-1179	519	1	[	[	X
ap-1179	519	2	11	11	NUM
ap-1179	519	3	]	]	X
ap-1179	519	4	ling	ling	PROPN
ap-1179	519	5	,	,	PUNCT
ap-1179	519	6	w.	w.	PROPN
ap-1179	519	7	x.	x.	PROPN
ap-1179	519	8	:	:	PUNCT
ap-1179	519	9	on	on	ADP
ap-1179	519	10	the	the	DET
ap-1179	519	11	structure	structure	NOUN
ap-1179	519	12	of	of	ADP
ap-1179	519	13	n	n	CCONJ
ap-1179	519	14	-	-	PUNCT
ap-1179	519	15	lie	lie	NOUN
ap-1179	519	16	algebras	algebra	NOUN
ap-1179	519	17	.	.	PUNCT
ap-1179	520	1	phd	phd	NOUN
ap-1179	520	2	thesis	thesis	PROPN
ap-1179	520	3	,	,	PUNCT
ap-1179	520	4	siegen	siegen	PROPN
ap-1179	520	5	,	,	PUNCT
ap-1179	520	6	1993	1993	NUM
ap-1179	520	7	.	.	PUNCT
ap-1179	521	1	[	[	X
ap-1179	521	2	12	12	NUM
ap-1179	521	3	]	]	PUNCT
ap-1179	521	4	nambu	nambu	NOUN
ap-1179	521	5	,	,	PUNCT
ap-1179	521	6	y.	y.	NOUN
ap-1179	521	7	:	:	PUNCT
ap-1179	521	8	generalized	generalized	ADJ
ap-1179	521	9	hamiltonian	hamiltonian	ADJ
ap-1179	521	10	dynamics	dynamic	NOUN
ap-1179	521	11	,	,	PUNCT
ap-1179	521	12	phys	phy	NOUN
ap-1179	521	13	.	.	PUNCT
ap-1179	522	1	rev	rev	PROPN
ap-1179	522	2	.	.	PUNCT
ap-1179	523	1	d7	d7	PROPN
ap-1179	523	2	,	,	PUNCT
ap-1179	523	3	2	2	NUM
ap-1179	523	4	405–2	405–2	NUM
ap-1179	523	5	414	414	NUM
ap-1179	523	6	(	(	PUNCT
ap-1179	523	7	1973	1973	NUM
ap-1179	523	8	)	)	PUNCT
ap-1179	523	9	.	.	PUNCT
ap-1179	524	1	[	[	X
ap-1179	524	2	13	13	NUM
ap-1179	524	3	]	]	SYM
ap-1179	524	4	sahoo	sahoo	PROPN
ap-1179	524	5	,	,	PUNCT
ap-1179	524	6	d.	d.	PROPN
ap-1179	524	7	,	,	PUNCT
ap-1179	524	8	valsakumar	valsakumar	PROPN
ap-1179	524	9	,	,	PUNCT
ap-1179	524	10	m.	m.	PROPN
ap-1179	524	11	c.	c.	PROPN
ap-1179	524	12	:	:	PUNCT
ap-1179	524	13	nambu	nambu	VERB
ap-1179	524	14	mechanics	mechanic	NOUN
ap-1179	524	15	and	and	CCONJ
ap-1179	524	16	its	its	PRON
ap-1179	524	17	quantization	quantization	NOUN
ap-1179	524	18	,	,	PUNCT
ap-1179	524	19	phys	phy	NOUN
ap-1179	524	20	.	.	PUNCT
ap-1179	525	1	rev.a46	rev.a46	PROPN
ap-1179	525	2	,	,	PUNCT
ap-1179	525	3	4	4	NUM
ap-1179	525	4	410–4	410–4	NUM
ap-1179	525	5	412	412	NUM
ap-1179	525	6	(	(	PUNCT
ap-1179	525	7	1992	1992	NUM
ap-1179	525	8	)	)	PUNCT
ap-1179	525	9	.	.	PUNCT
ap-1179	526	1	[	[	X
ap-1179	526	2	14	14	NUM
ap-1179	526	3	]	]	PUNCT
ap-1179	526	4	takhtajan	takhtajan	PROPN
ap-1179	526	5	,	,	PUNCT
ap-1179	526	6	l.	l.	PROPN
ap-1179	526	7	:	:	PUNCT
ap-1179	526	8	a	a	DET
ap-1179	526	9	higher	high	ADJ
ap-1179	526	10	order	order	NOUN
ap-1179	526	11	analog	analog	NOUN
ap-1179	526	12	of	of	ADP
ap-1179	526	13	the	the	DET
ap-1179	526	14	chevalley	chevalley	NOUN
ap-1179	526	15	-	-	PUNCT
ap-1179	526	16	eilenberg	eilenberg	NOUN
ap-1179	526	17	complex	complex	NOUN
ap-1179	526	18	and	and	CCONJ
ap-1179	526	19	the	the	DET
ap-1179	526	20	deformation	deformation	NOUN
ap-1179	526	21	theory	theory	NOUN
ap-1179	526	22	of	of	ADP
ap-1179	526	23	lie	lie	NOUN
ap-1179	526	24	algebras	algebra	NOUN
ap-1179	526	25	,	,	PUNCT
ap-1179	526	26	st	st	PROPN
ap-1179	526	27	.	.	PROPN
ap-1179	526	28	petersburg	petersburg	PROPN
ap-1179	526	29	math	math	PROPN
ap-1179	526	30	.	.	PUNCT
ap-1179	527	1	j.	j.	PROPN
ap-1179	527	2	6	6	NUM
ap-1179	527	3	,	,	PUNCT
ap-1179	527	4	429–437	429–437	NUM
ap-1179	527	5	(	(	PUNCT
ap-1179	527	6	1995	1995	NUM
ap-1179	527	7	)	)	PUNCT
ap-1179	527	8	.	.	PUNCT
ap-1179	528	1	[	[	X
ap-1179	528	2	15	15	NUM
ap-1179	528	3	]	]	X
ap-1179	528	4	de	de	X
ap-1179	528	5	azcárraga	azcárraga	PROPN
ap-1179	528	6	,	,	PUNCT
ap-1179	528	7	j.	j.	PROPN
ap-1179	528	8	a.	a.	PROPN
ap-1179	528	9	,	,	PUNCT
ap-1179	528	10	izquierdo	izquierdo	PROPN
ap-1179	528	11	,	,	PUNCT
ap-1179	528	12	j.	j.	PROPN
ap-1179	528	13	m.	m.	PROPN
ap-1179	528	14	,	,	PUNCT
ap-1179	528	15	pérez	pérez	PROPN
ap-1179	528	16	bueno	bueno	PROPN
ap-1179	528	17	,	,	PUNCT
ap-1179	528	18	j.	j.	PROPN
ap-1179	528	19	c.	c.	PROPN
ap-1179	528	20	:	:	PUNCT
ap-1179	528	21	on	on	ADP
ap-1179	528	22	the	the	DET
ap-1179	528	23	higher	high	ADJ
ap-1179	528	24	-	-	PUNCT
ap-1179	528	25	order	order	NOUN
ap-1179	528	26	generalizations	generalization	NOUN
ap-1179	528	27	of	of	ADP
ap-1179	528	28	poisson	poisson	PROPN
ap-1179	528	29	structures	structure	NOUN
ap-1179	528	30	,	,	PUNCT
ap-1179	528	31	j.	j.	PROPN
ap-1179	528	32	phys	phys	PROPN
ap-1179	528	33	.	.	PUNCT
ap-1179	529	1	a30	a30	NOUN
ap-1179	529	2	,	,	PUNCT
ap-1179	529	3	l607	l607	PROPN
ap-1179	529	4	–	–	PUNCT
ap-1179	529	5	l616	l616	PROPN
ap-1179	529	6	(	(	PUNCT
ap-1179	529	7	1997	1997	NUM
ap-1179	529	8	)	)	PUNCT
ap-1179	529	9	,	,	PUNCT
ap-1179	529	10	hep	hep	NOUN
ap-1179	529	11	-	-	PUNCT
ap-1179	529	12	th/9703019	th/9703019	PROPN
ap-1179	529	13	.	.	PUNCT
ap-1179	530	1	[	[	X
ap-1179	530	2	16	16	NUM
ap-1179	530	3	]	]	X
ap-1179	530	4	awata	awata	PROPN
ap-1179	530	5	,	,	PUNCT
ap-1179	530	6	h.	h.	PROPN
ap-1179	530	7	,	,	PUNCT
ap-1179	530	8	li	li	PROPN
ap-1179	530	9	,	,	PUNCT
ap-1179	530	10	m.	m.	NOUN
ap-1179	530	11	,	,	PUNCT
ap-1179	530	12	minic	minic	PROPN
ap-1179	530	13	,	,	PUNCT
ap-1179	530	14	d.	d.	PROPN
ap-1179	530	15	,	,	PUNCT
ap-1179	530	16	yoneya	yoneya	PROPN
ap-1179	530	17	,	,	PUNCT
ap-1179	530	18	t.	t.	PROPN
ap-1179	530	19	:	:	PUNCT
ap-1179	530	20	on	on	ADP
ap-1179	530	21	the	the	DET
ap-1179	530	22	quantization	quantization	NOUN
ap-1179	530	23	of	of	ADP
ap-1179	530	24	nambu	nambu	NOUN
ap-1179	530	25	brackets	bracket	NOUN
ap-1179	530	26	,	,	PUNCT
ap-1179	530	27	jhep	jhep	ADJ
ap-1179	530	28	,	,	PUNCT
ap-1179	530	29	02	02	NUM
ap-1179	530	30	,	,	PUNCT
ap-1179	530	31	013	013	NUM
ap-1179	530	32	(	(	PUNCT
ap-1179	530	33	2001	2001	NUM
ap-1179	530	34	)	)	PUNCT
ap-1179	530	35	,	,	PUNCT
ap-1179	530	36	hep	hep	NOUN
ap-1179	530	37	-	-	PUNCT
ap-1179	530	38	th/9906248	th/9906248	PROPN
ap-1179	530	39	.	.	PUNCT
ap-1179	531	1	[	[	X
ap-1179	531	2	17	17	NUM
ap-1179	531	3	]	]	PUNCT
ap-1179	531	4	curtright	curtright	NOUN
ap-1179	531	5	,	,	PUNCT
ap-1179	531	6	t.	t.	PROPN
ap-1179	531	7	,	,	PUNCT
ap-1179	531	8	zachos	zachos	PROPN
ap-1179	531	9	,	,	PUNCT
ap-1179	531	10	c.	c.	NOUN
ap-1179	531	11	:	:	PUNCT
ap-1179	531	12	classical	classical	ADJ
ap-1179	531	13	and	and	CCONJ
ap-1179	531	14	quantum	quantum	NOUN
ap-1179	531	15	nambu	nambu	NOUN
ap-1179	531	16	mechanics	mechanic	NOUN
ap-1179	531	17	,	,	PUNCT
ap-1179	531	18	phys	phy	NOUN
ap-1179	531	19	.	.	PUNCT
ap-1179	532	1	rev	rev	PROPN
ap-1179	532	2	.	.	PROPN
ap-1179	532	3	d68	d68	PROPN
ap-1179	532	4	,	,	PUNCT
ap-1179	532	5	085001	085001	NUM
ap-1179	532	6	(	(	PUNCT
ap-1179	532	7	2003	2003	NUM
ap-1179	532	8	)	)	PUNCT
ap-1179	532	9	,	,	PUNCT
ap-1179	532	10	ep	ep	PROPN
ap-1179	532	11	-	-	PUNCT
ap-1179	532	12	th/0212267	th/0212267	PROPN
ap-1179	532	13	.	.	PUNCT
ap-1179	533	1	[	[	X
ap-1179	533	2	18	18	NUM
ap-1179	533	3	]	]	X
ap-1179	533	4	gerstenhaber	gerstenhaber	NOUN
ap-1179	533	5	,	,	PUNCT
ap-1179	533	6	m.	m.	NOUN
ap-1179	533	7	:	:	PUNCT
ap-1179	533	8	on	on	ADP
ap-1179	533	9	the	the	DET
ap-1179	533	10	deformation	deformation	NOUN
ap-1179	533	11	of	of	ADP
ap-1179	533	12	rings	ring	NOUN
ap-1179	533	13	and	and	CCONJ
ap-1179	533	14	algebras	algebra	NOUN
ap-1179	533	15	,	,	PUNCT
ap-1179	533	16	annals	annal	VERB
ap-1179	533	17	math	math	NOUN
ap-1179	533	18	.	.	PUNCT
ap-1179	534	1	79	79	NUM
ap-1179	534	2	,	,	PUNCT
ap-1179	534	3	59–103	59–103	NUM
ap-1179	534	4	(	(	PUNCT
ap-1179	534	5	1964	1964	NUM
ap-1179	534	6	)	)	PUNCT
ap-1179	534	7	.	.	PUNCT
ap-1179	535	1	[	[	X
ap-1179	535	2	19	19	NUM
ap-1179	535	3	]	]	X
ap-1179	535	4	gautheron	gautheron	NOUN
ap-1179	535	5	,	,	PUNCT
ap-1179	535	6	p.	p.	NOUN
ap-1179	535	7	:	:	PUNCT
ap-1179	536	1	some	some	DET
ap-1179	536	2	remarks	remark	NOUN
ap-1179	536	3	concerning	concern	VERB
ap-1179	536	4	nambu	nambu	NOUN
ap-1179	536	5	mechanics	mechanic	NOUN
ap-1179	536	6	,	,	PUNCT
ap-1179	536	7	lett	lett	PROPN
ap-1179	536	8	.	.	PUNCT
ap-1179	536	9	math	math	NOUN
ap-1179	536	10	.	.	PUNCT
ap-1179	537	1	phys	phy	NOUN
ap-1179	537	2	.	.	PUNCT
ap-1179	538	1	37	37	NUM
ap-1179	538	2	,	,	PUNCT
ap-1179	538	3	103–116	103–116	NUM
ap-1179	538	4	(	(	PUNCT
ap-1179	538	5	1996	1996	NUM
ap-1179	538	6	)	)	PUNCT
ap-1179	538	7	.	.	PUNCT
ap-1179	539	1	[	[	X
ap-1179	539	2	20	20	NUM
ap-1179	539	3	]	]	PUNCT
ap-1179	539	4	rotkiewicz	rotkiewicz	NOUN
ap-1179	539	5	,	,	PUNCT
ap-1179	539	6	m.	m.	NOUN
ap-1179	539	7	:	:	PUNCT
ap-1179	539	8	cohomology	cohomology	NOUN
ap-1179	539	9	ring	ring	NOUN
ap-1179	539	10	of	of	ADP
ap-1179	539	11	n	n	CCONJ
ap-1179	539	12	-	-	PUNCT
ap-1179	539	13	lie	lie	NOUN
ap-1179	539	14	algebras	algebra	NOUN
ap-1179	539	15	,	,	PUNCT
ap-1179	539	16	extracta	extracta	PROPN
ap-1179	539	17	math	math	PROPN
ap-1179	539	18	.	.	PROPN
ap-1179	540	1	20	20	NUM
ap-1179	540	2	,	,	PUNCT
ap-1179	540	3	219–232	219–232	NUM
ap-1179	540	4	(	(	PUNCT
ap-1179	540	5	2005	2005	NUM
ap-1179	540	6	)	)	PUNCT
ap-1179	540	7	.	.	PUNCT
ap-1179	541	1	[	[	X
ap-1179	541	2	21	21	NUM
ap-1179	541	3	]	]	X
ap-1179	541	4	de	de	X
ap-1179	541	5	azcárraga	azcárraga	PROPN
ap-1179	541	6	,	,	PUNCT
ap-1179	541	7	j.	j.	PROPN
ap-1179	541	8	a.	a.	PROPN
ap-1179	541	9	,	,	PUNCT
ap-1179	541	10	izquierdo	izquierdo	PROPN
ap-1179	541	11	,	,	PUNCT
ap-1179	541	12	j.	j.	PROPN
ap-1179	541	13	m.	m.	PROPN
ap-1179	541	14	:	:	PUNCT
ap-1179	541	15	cohomology	cohomology	NOUN
ap-1179	541	16	of	of	ADP
ap-1179	541	17	filippov	filippov	PROPN
ap-1179	541	18	algebras	algebra	NOUN
ap-1179	541	19	and	and	CCONJ
ap-1179	541	20	an	an	DET
ap-1179	541	21	analogue	analogue	NOUN
ap-1179	541	22	of	of	ADP
ap-1179	541	23	whitehead	whitehead	PROPN
ap-1179	541	24	’s	’s	PART
ap-1179	541	25	lemma	lemma	PROPN
ap-1179	541	26	,	,	PUNCT
ap-1179	541	27	j.	j.	PROPN
ap-1179	541	28	phys	phys	PROPN
ap-1179	541	29	.	.	PUNCT
ap-1179	541	30	conf	conf	PROPN
ap-1179	541	31	.	.	PUNCT
ap-1179	542	1	ser	ser	PROPN
ap-1179	542	2	.	.	PROPN
ap-1179	542	3	175	175	NUM
ap-1179	542	4	,	,	PUNCT
ap-1179	542	5	012001	012001	NUM
ap-1179	542	6	(	(	PUNCT
ap-1179	542	7	2009	2009	NUM
ap-1179	542	8	)	)	PUNCT
ap-1179	542	9	,	,	PUNCT
ap-1179	542	10	arxiv:0905.3083[math	arxiv:0905.3083[math	NOUN
ap-1179	542	11	-	-	PUNCT
ap-1179	542	12	ph	ph	NOUN
ap-1179	542	13	]	]	X
ap-1179	542	14	.	.	PUNCT
ap-1179	543	1	[	[	X
ap-1179	543	2	22	22	NUM
ap-1179	543	3	]	]	PUNCT
ap-1179	543	4	loday	loday	ADV
ap-1179	543	5	,	,	PUNCT
ap-1179	543	6	j.-l	j.-l	PROPN
ap-1179	543	7	.	.	PUNCT
ap-1179	543	8	:	:	PUNCT
ap-1179	544	1	une	une	PROPN
ap-1179	544	2	version	version	PROPN
ap-1179	544	3	non	non	ADJ
ap-1179	544	4	-	-	ADJ
ap-1179	544	5	commutative	commutative	ADJ
ap-1179	544	6	des	des	PROPN
ap-1179	544	7	algèbres	algèbre	NOUN
ap-1179	544	8	de	de	X
ap-1179	544	9	lie	lie	NOUN
ap-1179	544	10	,	,	PUNCT
ap-1179	544	11	l’ens	l’ens	PROPN
ap-1179	544	12	.	.	PUNCT
ap-1179	544	13	math	math	NOUN
ap-1179	544	14	.	.	PUNCT
ap-1179	545	1	39	39	NUM
ap-1179	545	2	,	,	PUNCT
ap-1179	545	3	269–293	269–293	NUM
ap-1179	545	4	(	(	PUNCT
ap-1179	545	5	1993	1993	NUM
ap-1179	545	6	)	)	PUNCT
ap-1179	545	7	.	.	PUNCT
ap-1179	546	1	[	[	X
ap-1179	546	2	23	23	NUM
ap-1179	546	3	]	]	X
ap-1179	546	4	daletskii	daletskii	ADV
ap-1179	546	5	,	,	PUNCT
ap-1179	546	6	y.	y.	PROPN
ap-1179	546	7	l.	l.	PROPN
ap-1179	546	8	,	,	PUNCT
ap-1179	546	9	takhtajan	takhtajan	PROPN
ap-1179	546	10	,	,	PUNCT
ap-1179	546	11	l.	l.	PROPN
ap-1179	546	12	:	:	PUNCT
ap-1179	546	13	leibniz	leibniz	PROPN
ap-1179	546	14	and	and	CCONJ
ap-1179	546	15	lie	lie	VERB
ap-1179	546	16	algebra	algebra	NOUN
ap-1179	546	17	structures	structure	NOUN
ap-1179	546	18	for	for	ADP
ap-1179	546	19	nambu	nambu	NOUN
ap-1179	546	20	algebra	algebra	PROPN
ap-1179	546	21	,	,	PUNCT
ap-1179	546	22	lett	lett	PROPN
ap-1179	546	23	.	.	PUNCT
ap-1179	546	24	math	math	NOUN
ap-1179	546	25	.	.	PUNCT
ap-1179	547	1	phys	phy	NOUN
ap-1179	547	2	.	.	PUNCT
ap-1179	548	1	39	39	NUM
ap-1179	548	2	,	,	PUNCT
ap-1179	548	3	127–141	127–141	NUM
ap-1179	548	4	(	(	PUNCT
ap-1179	548	5	1997	1997	NUM
ap-1179	548	6	)	)	PUNCT
ap-1179	548	7	.	.	PUNCT
ap-1179	549	1	[	[	X
ap-1179	549	2	24	24	NUM
ap-1179	549	3	]	]	X
ap-1179	549	4	casas	casas	PROPN
ap-1179	549	5	,	,	PUNCT
ap-1179	549	6	j.	j.	PROPN
ap-1179	549	7	m.	m.	PROPN
ap-1179	549	8	,	,	PUNCT
ap-1179	549	9	loday	loday	ADV
ap-1179	549	10	,	,	PUNCT
ap-1179	549	11	j.-l	j.-l	PROPN
ap-1179	549	12	.	.	PUNCT
ap-1179	549	13	,	,	PUNCT
ap-1179	549	14	pirashvili	pirashvili	NOUN
ap-1179	549	15	,	,	PUNCT
ap-1179	549	16	t.	t.	PROPN
ap-1179	549	17	:	:	PUNCT
ap-1179	549	18	leibniz	leibniz	PROPN
ap-1179	549	19	n	n	CCONJ
ap-1179	549	20	-	-	PUNCT
ap-1179	549	21	algebras	algebras	PROPN
ap-1179	549	22	,	,	PUNCT
ap-1179	549	23	forum	forum	PROPN
ap-1179	549	24	math	math	NOUN
ap-1179	549	25	.	.	PUNCT
ap-1179	550	1	14	14	NUM
ap-1179	550	2	,	,	PUNCT
ap-1179	550	3	189–207	189–207	NUM
ap-1179	550	4	(	(	PUNCT
ap-1179	550	5	2002	2002	NUM
ap-1179	550	6	)	)	PUNCT
ap-1179	550	7	.	.	PUNCT
ap-1179	551	1	[	[	X
ap-1179	551	2	25	25	NUM
ap-1179	551	3	]	]	PUNCT
ap-1179	551	4	loday	loday	ADV
ap-1179	551	5	,	,	PUNCT
ap-1179	551	6	j.-l	j.-l	PROPN
ap-1179	551	7	.	.	PUNCT
ap-1179	551	8	,	,	PUNCT
ap-1179	551	9	pirashvili	pirashvili	NOUN
ap-1179	551	10	,	,	PUNCT
ap-1179	551	11	t.	t.	PROPN
ap-1179	551	12	:	:	PUNCT
ap-1179	551	13	universal	universal	ADJ
ap-1179	551	14	enveloping	enveloping	NOUN
ap-1179	551	15	algebras	algebra	NOUN
ap-1179	551	16	of	of	ADP
ap-1179	551	17	leibniz	leibniz	PROPN
ap-1179	551	18	algebras	algebras	PROPN
ap-1179	551	19	and	and	CCONJ
ap-1179	551	20	(	(	PUNCT
ap-1179	551	21	co)homology	co)homology	NOUN
ap-1179	551	22	,	,	PUNCT
ap-1179	551	23	mat	mat	NOUN
ap-1179	551	24	.	.	PUNCT
ap-1179	551	25	annalen	annalen	PROPN
ap-1179	551	26	296	296	NUM
ap-1179	551	27	,	,	PUNCT
ap-1179	551	28	139–158	139–158	NUM
ap-1179	551	29	(	(	PUNCT
ap-1179	551	30	1993	1993	NUM
ap-1179	551	31	)	)	PUNCT
ap-1179	551	32	.	.	PUNCT
ap-1179	552	1	[	[	X
ap-1179	552	2	26	26	NUM
ap-1179	552	3	]	]	PUNCT
ap-1179	552	4	fialowski	fialowski	NOUN
ap-1179	552	5	,	,	PUNCT
ap-1179	552	6	a.	a.	NOUN
ap-1179	552	7	,	,	PUNCT
ap-1179	552	8	mandal	mandal	PROPN
ap-1179	552	9	,	,	PUNCT
ap-1179	552	10	a.	a.	NOUN
ap-1179	552	11	:	:	PUNCT
ap-1179	552	12	leibniz	leibniz	PROPN
ap-1179	552	13	algebra	algebra	PROPN
ap-1179	552	14	deformations	deformation	NOUN
ap-1179	552	15	of	of	ADP
ap-1179	552	16	a	a	DET
ap-1179	552	17	lie	lie	NOUN
ap-1179	552	18	algebra	algebra	NOUN
ap-1179	552	19	,	,	PUNCT
ap-1179	552	20	j.	j.	PROPN
ap-1179	552	21	math	math	PROPN
ap-1179	552	22	.	.	PUNCT
ap-1179	553	1	phys	phy	NOUN
ap-1179	553	2	.	.	PUNCT
ap-1179	554	1	49	49	NUM
ap-1179	554	2	,	,	PUNCT
ap-1179	554	3	093511	093511	NUM
ap-1179	554	4	(	(	PUNCT
ap-1179	554	5	2008	2008	NUM
ap-1179	554	6	)	)	PUNCT
ap-1179	554	7	,	,	PUNCT
ap-1179	554	8	arxiv:0802.1263	arxiv:0802.1263	X
ap-1179	555	1	[	[	X
ap-1179	555	2	math.kt	math.kt	X
ap-1179	555	3	]	]	X
ap-1179	555	4	.	.	PUNCT
ap-1179	556	1	[	[	X
ap-1179	556	2	27	27	NUM
ap-1179	556	3	]	]	X
ap-1179	556	4	figueroa	figueroa	PROPN
ap-1179	556	5	-	-	PUNCT
ap-1179	556	6	o’farrill	o’farrill	PROPN
ap-1179	556	7	,	,	PUNCT
ap-1179	556	8	j.	j.	PROPN
ap-1179	556	9	m.	m.	PROPN
ap-1179	556	10	:	:	PUNCT
ap-1179	556	11	three	three	NUM
ap-1179	556	12	lectures	lecture	NOUN
ap-1179	556	13	on	on	ADP
ap-1179	556	14	3algebras	3algebras	NUM
ap-1179	556	15	,	,	PUNCT
ap-1179	556	16	arxiv:0812.2865	arxiv:0812.2865	PRON
ap-1179	556	17	[	[	PUNCT
ap-1179	556	18	hep	hep	NOUN
ap-1179	556	19	-	-	PUNCT
ap-1179	556	20	th	th	X
ap-1179	556	21	]	]	PUNCT
ap-1179	556	22	.	.	PUNCT
ap-1179	557	1	[	[	X
ap-1179	557	2	28	28	NUM
ap-1179	557	3	]	]	X
ap-1179	557	4	de	de	X
ap-1179	557	5	azcárraga	azcárraga	PROPN
ap-1179	557	6	,	,	PUNCT
ap-1179	557	7	j.	j.	PROPN
ap-1179	557	8	a.	a.	PROPN
ap-1179	557	9	,	,	PUNCT
ap-1179	557	10	izquierdo	izquierdo	PROPN
ap-1179	557	11	,	,	PUNCT
ap-1179	557	12	j.	j.	PROPN
ap-1179	557	13	m.	m.	PROPN
ap-1179	557	14	:	:	PUNCT
ap-1179	557	15	on	on	ADP
ap-1179	557	16	leibniz	leibniz	NOUN
ap-1179	557	17	deformations	deformation	NOUN
ap-1179	557	18	and	and	CCONJ
ap-1179	557	19	rigidity	rigidity	NOUN
ap-1179	557	20	of	of	ADP
ap-1179	557	21	simple	simple	ADJ
ap-1179	557	22	n	n	CCONJ
ap-1179	557	23	-	-	PUNCT
ap-1179	557	24	lie	lie	NOUN
ap-1179	557	25	algebras	algebra	NOUN
ap-1179	557	26	,	,	PUNCT
ap-1179	557	27	to	to	PART
ap-1179	557	28	be	be	AUX
ap-1179	557	29	published	publish	VERB
ap-1179	557	30	.	.	PUNCT
ap-1179	558	1	j.	j.	PROPN
ap-1179	558	2	a.	a.	PROPN
ap-1179	558	3	de	de	PROPN
ap-1179	558	4	azcárraga	azcárraga	PROPN
ap-1179	558	5	departamento	departamento	NOUN
ap-1179	558	6	de	de	PROPN
ap-1179	558	7	f́ısica	f́ısica	PROPN
ap-1179	558	8	teórica	teórica	PROPN
ap-1179	558	9	and	and	CCONJ
ap-1179	558	10	ific	ific	PROPN
ap-1179	558	11	(	(	PUNCT
ap-1179	558	12	csic	csic	NOUN
ap-1179	558	13	-	-	PUNCT
ap-1179	558	14	uveg	uveg	NOUN
ap-1179	558	15	)	)	PUNCT
ap-1179	558	16	univ	univ	PROPN
ap-1179	558	17	.	.	PUNCT
ap-1179	559	1	de	de	PROPN
ap-1179	559	2	valencia	valencia	PROPN
ap-1179	559	3	46100	46100	NUM
ap-1179	559	4	-	-	PUNCT
ap-1179	559	5	burjassot	burjassot	NOUN
ap-1179	559	6	(	(	PUNCT
ap-1179	559	7	valencia	valencia	PROPN
ap-1179	559	8	)	)	PUNCT
ap-1179	559	9	,	,	PUNCT
ap-1179	559	10	spain	spain	PROPN
ap-1179	559	11	j.	j.	PROPN
ap-1179	559	12	m.	m.	PROPN
ap-1179	559	13	izquierdo	izquierdo	PROPN
ap-1179	559	14	departamento	departamento	PROPN
ap-1179	559	15	de	de	PROPN
ap-1179	559	16	f́ısica	f́ısica	PROPN
ap-1179	559	17	teórica	teórica	PROPN
ap-1179	559	18	universidad	universidad	PROPN
ap-1179	559	19	de	de	PROPN
ap-1179	559	20	valladolid	valladolid	PROPN
ap-1179	559	21	47011	47011	NUM
ap-1179	559	22	-	-	SYM
ap-1179	559	23	valladolid	valladolid	PROPN
ap-1179	559	24	,	,	PUNCT
ap-1179	559	25	spain	spain	PROPN
ap-1179	559	26	13	13	NUM