id	sid	tid	token	lemma	pos
ap-1187	1	1	ap-3-10.dvi	ap-3-10.dvi	PROPN
ap-1187	1	2	acta	acta	PROPN
ap-1187	1	3	polytechnica	polytechnica	PROPN
ap-1187	1	4	vol	vol	NOUN
ap-1187	1	5	.	.	PROPN
ap-1187	2	1	50	50	NUM
ap-1187	2	2	no	no	NOUN
ap-1187	2	3	.	.	PUNCT
ap-1187	3	1	3/2010	3/2010	NUM
ap-1187	3	2	lorentz	lorentz	PROPN
ap-1187	3	3	and	and	CCONJ
ap-1187	3	4	su	su	PROPN
ap-1187	3	5	(	(	PUNCT
ap-1187	3	6	3	3	X
ap-1187	3	7	)	)	PUNCT
ap-1187	3	8	groups	group	NOUN
ap-1187	3	9	derived	derive	VERB
ap-1187	3	10	from	from	ADP
ap-1187	3	11	cubic	cubic	ADJ
ap-1187	3	12	quark	quark	PROPN
ap-1187	3	13	algebra	algebra	PROPN
ap-1187	3	14	r.	r.	PROPN
ap-1187	3	15	kerner	kerner	PROPN
ap-1187	3	16	dedicated	dedicate	VERB
ap-1187	3	17	to	to	ADP
ap-1187	3	18	jǐŕı	jǐŕı	PROPN
ap-1187	3	19	niederle	niederle	NOUN
ap-1187	3	20	on	on	ADP
ap-1187	3	21	the	the	DET
ap-1187	3	22	occasion	occasion	NOUN
ap-1187	3	23	of	of	ADP
ap-1187	3	24	his	his	PRON
ap-1187	3	25	70	70	NUM
ap-1187	3	26	-	-	PUNCT
ap-1187	3	27	th	th	VERB
ap-1187	3	28	birthday	birthday	NOUN
ap-1187	3	29	abstract	abstract	NOUN
ap-1187	3	30	we	we	PRON
ap-1187	3	31	show	show	VERB
ap-1187	3	32	how	how	SCONJ
ap-1187	3	33	lorentz	lorentz	PROPN
ap-1187	3	34	and	and	CCONJ
ap-1187	3	35	su(3	su(3	PROPN
ap-1187	3	36	)	)	PUNCT
ap-1187	3	37	groups	group	NOUN
ap-1187	3	38	can	can	AUX
ap-1187	3	39	be	be	AUX
ap-1187	3	40	derived	derive	VERB
ap-1187	3	41	from	from	ADP
ap-1187	3	42	the	the	DET
ap-1187	3	43	covariance	covariance	NOUN
ap-1187	3	44	principle	principle	NOUN
ap-1187	3	45	conserving	conserve	VERB
ap-1187	3	46	a	a	DET
ap-1187	3	47	z3	z3	NOUN
ap-1187	3	48	-	-	PUNCT
ap-1187	3	49	graded	grade	VERB
ap-1187	3	50	three	three	NUM
ap-1187	3	51	-	-	PUNCT
ap-1187	3	52	form	form	NOUN
ap-1187	3	53	on	on	ADP
ap-1187	3	54	a	a	DET
ap-1187	3	55	z3	z3	NOUN
ap-1187	3	56	-	-	PUNCT
ap-1187	3	57	graded	grade	VERB
ap-1187	3	58	cubic	cubic	ADJ
ap-1187	3	59	algebra	algebra	NOUN
ap-1187	3	60	representing	represent	VERB
ap-1187	3	61	quarks	quark	NOUN
ap-1187	3	62	endowed	endow	VERB
ap-1187	3	63	with	with	ADP
ap-1187	3	64	non	non	ADJ
ap-1187	3	65	-	-	ADJ
ap-1187	3	66	standard	standard	ADJ
ap-1187	3	67	commutation	commutation	NOUN
ap-1187	3	68	laws	law	NOUN
ap-1187	3	69	.	.	PUNCT
ap-1187	4	1	this	this	DET
ap-1187	4	2	construction	construction	NOUN
ap-1187	4	3	suggests	suggest	VERB
ap-1187	4	4	that	that	SCONJ
ap-1187	4	5	the	the	DET
ap-1187	4	6	geometry	geometry	NOUN
ap-1187	4	7	of	of	ADP
ap-1187	4	8	space	space	NOUN
ap-1187	4	9	-	-	PUNCT
ap-1187	4	10	time	time	NOUN
ap-1187	4	11	can	can	AUX
ap-1187	4	12	be	be	AUX
ap-1187	4	13	considered	consider	VERB
ap-1187	4	14	as	as	ADP
ap-1187	4	15	a	a	DET
ap-1187	4	16	manifestation	manifestation	NOUN
ap-1187	4	17	of	of	ADP
ap-1187	4	18	symmetries	symmetry	NOUN
ap-1187	4	19	of	of	ADP
ap-1187	4	20	fundamental	fundamental	ADJ
ap-1187	4	21	matter	matter	NOUN
ap-1187	4	22	fields	field	NOUN
ap-1187	4	23	.	.	PUNCT
ap-1187	5	1	1	1	X
ap-1187	5	2	.	.	X
ap-1187	6	1	many	many	ADJ
ap-1187	6	2	fundamental	fundamental	ADJ
ap-1187	6	3	properties	property	NOUN
ap-1187	6	4	of	of	ADP
ap-1187	6	5	matter	matter	NOUN
ap-1187	6	6	at	at	ADP
ap-1187	6	7	the	the	DET
ap-1187	6	8	quantum	quantum	ADJ
ap-1187	6	9	level	level	NOUN
ap-1187	6	10	can	can	AUX
ap-1187	6	11	be	be	AUX
ap-1187	6	12	announced	announce	VERB
ap-1187	6	13	without	without	ADP
ap-1187	6	14	mentioning	mention	VERB
ap-1187	6	15	the	the	DET
ap-1187	6	16	space	space	NOUN
ap-1187	6	17	-	-	PUNCT
ap-1187	6	18	time	time	NOUN
ap-1187	6	19	realm	realm	NOUN
ap-1187	6	20	.	.	PUNCT
ap-1187	7	1	the	the	DET
ap-1187	7	2	pauli	pauli	PROPN
ap-1187	7	3	exclusion	exclusion	NOUN
ap-1187	7	4	principle	principle	NOUN
ap-1187	7	5	,	,	PUNCT
ap-1187	7	6	symmetry	symmetry	NOUN
ap-1187	7	7	between	between	ADP
ap-1187	7	8	particles	particle	NOUN
ap-1187	7	9	and	and	CCONJ
ap-1187	7	10	anti	anti	NOUN
ap-1187	7	11	-	-	ADJ
ap-1187	7	12	particles	particle	NOUN
ap-1187	7	13	,	,	PUNCT
ap-1187	7	14	electric	electric	ADJ
ap-1187	7	15	charge	charge	NOUN
ap-1187	7	16	and	and	CCONJ
ap-1187	7	17	baryonic	baryonic	NOUN
ap-1187	7	18	number	number	NOUN
ap-1187	7	19	conservation	conservation	NOUN
ap-1187	7	20	belong	belong	VERB
ap-1187	7	21	to	to	ADP
ap-1187	7	22	this	this	DET
ap-1187	7	23	category	category	NOUN
ap-1187	7	24	.	.	PUNCT
ap-1187	8	1	quantum	quantum	ADJ
ap-1187	8	2	mechanics	mechanic	NOUN
ap-1187	8	3	itself	itself	PRON
ap-1187	8	4	can	can	AUX
ap-1187	8	5	be	be	AUX
ap-1187	8	6	formulated	formulate	VERB
ap-1187	8	7	without	without	ADP
ap-1187	8	8	any	any	DET
ap-1187	8	9	mention	mention	NOUN
ap-1187	8	10	of	of	ADP
ap-1187	8	11	space	space	NOUN
ap-1187	8	12	,	,	PUNCT
ap-1187	8	13	as	as	SCONJ
ap-1187	8	14	was	be	AUX
ap-1187	8	15	shown	show	VERB
ap-1187	8	16	by	by	ADP
ap-1187	8	17	m.	m.	NOUN
ap-1187	8	18	born	bear	VERB
ap-1187	8	19	,	,	PUNCT
ap-1187	8	20	p.	p.	NOUN
ap-1187	8	21	jordan	jordan	PROPN
ap-1187	8	22	and	and	CCONJ
ap-1187	8	23	w.	w.	PROPN
ap-1187	8	24	heisenberg	heisenberg	PROPN
ap-1187	9	1	[	[	X
ap-1187	9	2	1	1	X
ap-1187	9	3	]	]	PUNCT
ap-1187	9	4	in	in	ADP
ap-1187	9	5	their	their	PRON
ap-1187	9	6	version	version	NOUN
ap-1187	9	7	of	of	ADP
ap-1187	9	8	matrix	matrix	NOUN
ap-1187	9	9	mechanics	mechanic	NOUN
ap-1187	9	10	,	,	PUNCT
ap-1187	9	11	or	or	CCONJ
ap-1187	9	12	in	in	ADP
ap-1187	9	13	j.	j.	PROPN
ap-1187	9	14	von	von	PROPN
ap-1187	9	15	neumann	neumann	PROPN
ap-1187	9	16	’s	’s	PART
ap-1187	9	17	[	[	X
ap-1187	9	18	2	2	NUM
ap-1187	9	19	]	]	PUNCT
ap-1187	9	20	formulation	formulation	NOUN
ap-1187	9	21	of	of	ADP
ap-1187	9	22	quantum	quantum	NOUN
ap-1187	9	23	theory	theory	NOUN
ap-1187	9	24	in	in	ADP
ap-1187	9	25	terms	term	NOUN
ap-1187	9	26	of	of	ADP
ap-1187	9	27	c∗	c∗	PROPN
ap-1187	9	28	algebras	algebra	NOUN
ap-1187	9	29	.	.	PUNCT
ap-1187	10	1	non	non	ADJ
ap-1187	10	2	-	-	ADJ
ap-1187	10	3	commutative	commutative	ADJ
ap-1187	10	4	geometry	geometry	NOUN
ap-1187	10	5	[	[	X
ap-1187	10	6	4	4	X
ap-1187	10	7	]	]	PUNCT
ap-1187	10	8	gives	give	VERB
ap-1187	10	9	another	another	DET
ap-1187	10	10	example	example	NOUN
ap-1187	10	11	of	of	ADP
ap-1187	10	12	interpreting	interpret	VERB
ap-1187	10	13	space	space	NOUN
ap-1187	10	14	-	-	PUNCT
ap-1187	10	15	time	time	NOUN
ap-1187	10	16	relationships	relationship	NOUN
ap-1187	10	17	in	in	ADP
ap-1187	10	18	pure	pure	ADJ
ap-1187	10	19	algebraic	algebraic	ADJ
ap-1187	10	20	terms	term	NOUN
ap-1187	10	21	.	.	PUNCT
ap-1187	11	1	einstein	einstein	PROPN
ap-1187	11	2	’s	’s	PART
ap-1187	11	3	dream	dream	NOUN
ap-1187	11	4	was	be	AUX
ap-1187	11	5	to	to	PART
ap-1187	11	6	be	be	AUX
ap-1187	11	7	able	able	ADJ
ap-1187	11	8	to	to	PART
ap-1187	11	9	derive	derive	VERB
ap-1187	11	10	the	the	DET
ap-1187	11	11	properties	property	NOUN
ap-1187	11	12	of	of	ADP
ap-1187	11	13	matter	matter	NOUN
ap-1187	11	14	,	,	PUNCT
ap-1187	11	15	and	and	CCONJ
ap-1187	11	16	perhaps	perhaps	ADV
ap-1187	11	17	its	its	PRON
ap-1187	11	18	very	very	ADJ
ap-1187	11	19	existence	existence	NOUN
ap-1187	11	20	,	,	PUNCT
ap-1187	11	21	from	from	ADP
ap-1187	11	22	the	the	DET
ap-1187	11	23	singularities	singularity	NOUN
ap-1187	11	24	of	of	ADP
ap-1187	11	25	fields	field	NOUN
ap-1187	11	26	defined	define	VERB
ap-1187	11	27	on	on	ADP
ap-1187	11	28	space	space	NOUN
ap-1187	11	29	-	-	PUNCT
ap-1187	11	30	time	time	NOUN
ap-1187	11	31	,	,	PUNCT
ap-1187	11	32	and	and	CCONJ
ap-1187	11	33	if	if	SCONJ
ap-1187	11	34	possible	possible	ADJ
ap-1187	11	35	,	,	PUNCT
ap-1187	11	36	from	from	ADP
ap-1187	11	37	the	the	DET
ap-1187	11	38	geometry	geometry	NOUN
ap-1187	11	39	and	and	CCONJ
ap-1187	11	40	topology	topology	NOUN
ap-1187	11	41	of	of	ADP
ap-1187	11	42	spacetime	spacetime	NOUN
ap-1187	11	43	itself	itself	PRON
ap-1187	11	44	.	.	PUNCT
ap-1187	12	1	a	a	DET
ap-1187	12	2	follower	follower	NOUN
ap-1187	12	3	of	of	ADP
ap-1187	12	4	maxwell	maxwell	PROPN
ap-1187	12	5	and	and	CCONJ
ap-1187	12	6	faraday	faraday	PROPN
ap-1187	12	7	,	,	PUNCT
ap-1187	12	8	he	he	PRON
ap-1187	12	9	believed	believe	VERB
ap-1187	12	10	in	in	ADP
ap-1187	12	11	the	the	DET
ap-1187	12	12	primary	primary	ADJ
ap-1187	12	13	role	role	NOUN
ap-1187	12	14	of	of	ADP
ap-1187	12	15	fields	field	NOUN
ap-1187	12	16	and	and	CCONJ
ap-1187	12	17	tried	try	VERB
ap-1187	12	18	to	to	PART
ap-1187	12	19	derive	derive	VERB
ap-1187	12	20	the	the	DET
ap-1187	12	21	equations	equation	NOUN
ap-1187	12	22	of	of	ADP
ap-1187	12	23	motion	motion	NOUN
ap-1187	12	24	as	as	ADP
ap-1187	12	25	characteristic	characteristic	ADJ
ap-1187	12	26	behavior	behavior	NOUN
ap-1187	12	27	of	of	ADP
ap-1187	12	28	field	field	NOUN
ap-1187	12	29	singularities	singularity	NOUN
ap-1187	12	30	,	,	PUNCT
ap-1187	12	31	or	or	CCONJ
ap-1187	12	32	singularities	singularity	NOUN
ap-1187	12	33	of	of	ADP
ap-1187	12	34	the	the	DET
ap-1187	12	35	space	space	NOUN
ap-1187	12	36	-	-	PUNCT
ap-1187	12	37	time	time	NOUN
ap-1187	12	38	(	(	PUNCT
ap-1187	12	39	see	see	VERB
ap-1187	12	40	[	[	X
ap-1187	12	41	3	3	NUM
ap-1187	12	42	]	]	NUM
ap-1187	12	43	)	)	PUNCT
ap-1187	12	44	.	.	PUNCT
ap-1187	13	1	one	one	PRON
ap-1187	13	2	can	can	AUX
ap-1187	13	3	defend	defend	VERB
ap-1187	13	4	an	an	DET
ap-1187	13	5	alternative	alternative	ADJ
ap-1187	13	6	point	point	NOUN
ap-1187	13	7	of	of	ADP
ap-1187	13	8	view	view	NOUN
ap-1187	13	9	supposing	suppose	VERB
ap-1187	13	10	that	that	SCONJ
ap-1187	13	11	the	the	DET
ap-1187	13	12	existence	existence	NOUN
ap-1187	13	13	of	of	ADP
ap-1187	13	14	matter	matter	NOUN
ap-1187	13	15	is	be	AUX
ap-1187	13	16	primary	primary	ADJ
ap-1187	13	17	with	with	ADP
ap-1187	13	18	respect	respect	NOUN
ap-1187	13	19	to	to	ADP
ap-1187	13	20	that	that	PRON
ap-1187	13	21	of	of	ADP
ap-1187	13	22	space	space	NOUN
ap-1187	13	23	-	-	PUNCT
ap-1187	13	24	time	time	NOUN
ap-1187	13	25	.	.	PUNCT
ap-1187	14	1	in	in	ADP
ap-1187	14	2	this	this	DET
ap-1187	14	3	light	light	NOUN
ap-1187	14	4	,	,	PUNCT
ap-1187	14	5	the	the	DET
ap-1187	14	6	idea	idea	NOUN
ap-1187	14	7	of	of	ADP
ap-1187	14	8	deriving	derive	VERB
ap-1187	14	9	the	the	DET
ap-1187	14	10	geometric	geometric	ADJ
ap-1187	14	11	properties	property	NOUN
ap-1187	14	12	of	of	ADP
ap-1187	14	13	space	space	NOUN
ap-1187	14	14	-	-	PUNCT
ap-1187	14	15	time	time	NOUN
ap-1187	14	16	,	,	PUNCT
ap-1187	14	17	and	and	CCONJ
ap-1187	14	18	perhaps	perhaps	ADV
ap-1187	14	19	its	its	PRON
ap-1187	14	20	very	very	ADJ
ap-1187	14	21	existence	existence	NOUN
ap-1187	14	22	,	,	PUNCT
ap-1187	14	23	from	from	ADP
ap-1187	14	24	fundamental	fundamental	ADJ
ap-1187	14	25	symmetries	symmetry	NOUN
ap-1187	14	26	and	and	CCONJ
ap-1187	14	27	interactions	interaction	NOUN
ap-1187	14	28	proper	proper	ADJ
ap-1187	14	29	to	to	PART
ap-1187	14	30	matter	matter	VERB
ap-1187	14	31	’s	’s	PART
ap-1187	14	32	most	most	ADV
ap-1187	14	33	fundamental	fundamental	ADJ
ap-1187	14	34	building	building	NOUN
ap-1187	14	35	blocks	block	NOUN
ap-1187	14	36	seems	seem	VERB
ap-1187	14	37	quite	quite	ADV
ap-1187	14	38	natural	natural	ADJ
ap-1187	14	39	.	.	PUNCT
ap-1187	15	1	if	if	SCONJ
ap-1187	15	2	the	the	DET
ap-1187	15	3	space	space	NOUN
ap-1187	15	4	-	-	PUNCT
ap-1187	15	5	time	time	NOUN
ap-1187	15	6	is	be	AUX
ap-1187	15	7	to	to	PART
ap-1187	15	8	be	be	AUX
ap-1187	15	9	derived	derive	VERB
ap-1187	15	10	from	from	ADP
ap-1187	15	11	the	the	DET
ap-1187	15	12	interactions	interaction	NOUN
ap-1187	15	13	of	of	ADP
ap-1187	15	14	fundamental	fundamental	ADJ
ap-1187	15	15	constituents	constituent	NOUN
ap-1187	15	16	of	of	ADP
ap-1187	15	17	matter	matter	NOUN
ap-1187	15	18	,	,	PUNCT
ap-1187	15	19	then	then	ADV
ap-1187	15	20	it	it	PRON
ap-1187	15	21	seems	seem	VERB
ap-1187	15	22	reasonable	reasonable	ADJ
ap-1187	15	23	to	to	PART
ap-1187	15	24	choose	choose	VERB
ap-1187	15	25	the	the	DET
ap-1187	15	26	strongest	strong	ADJ
ap-1187	15	27	ineractions	ineraction	NOUN
ap-1187	15	28	available	available	ADJ
ap-1187	15	29	,	,	PUNCT
ap-1187	15	30	which	which	PRON
ap-1187	15	31	are	be	AUX
ap-1187	15	32	the	the	DET
ap-1187	15	33	interactions	interaction	NOUN
ap-1187	15	34	between	between	ADP
ap-1187	15	35	quarks	quark	NOUN
ap-1187	15	36	.	.	PUNCT
ap-1187	16	1	the	the	DET
ap-1187	16	2	difficulty	difficulty	NOUN
ap-1187	16	3	resides	reside	VERB
ap-1187	16	4	in	in	ADP
ap-1187	16	5	the	the	DET
ap-1187	16	6	fact	fact	NOUN
ap-1187	16	7	that	that	SCONJ
ap-1187	16	8	we	we	PRON
ap-1187	16	9	should	should	AUX
ap-1187	16	10	define	define	VERB
ap-1187	16	11	these	these	DET
ap-1187	16	12	“	"	PUNCT
ap-1187	16	13	quarks	quark	NOUN
ap-1187	16	14	”	"	PUNCT
ap-1187	16	15	(	(	PUNCT
ap-1187	16	16	or	or	CCONJ
ap-1187	16	17	their	their	PRON
ap-1187	16	18	states	state	NOUN
ap-1187	16	19	)	)	PUNCT
ap-1187	16	20	without	without	ADP
ap-1187	16	21	any	any	DET
ap-1187	16	22	mention	mention	NOUN
ap-1187	16	23	of	of	ADP
ap-1187	16	24	space	space	NOUN
ap-1187	16	25	-	-	PUNCT
ap-1187	16	26	time	time	NOUN
ap-1187	16	27	.	.	PUNCT
ap-1187	17	1	the	the	DET
ap-1187	17	2	minimal	minimal	ADJ
ap-1187	17	3	requirements	requirement	NOUN
ap-1187	17	4	for	for	ADP
ap-1187	17	5	the	the	DET
ap-1187	17	6	definition	definition	NOUN
ap-1187	17	7	of	of	ADP
ap-1187	17	8	quarks	quarks	PROPN
ap-1187	17	9	at	at	ADP
ap-1187	17	10	the	the	DET
ap-1187	17	11	initial	initial	ADJ
ap-1187	17	12	stage	stage	NOUN
ap-1187	17	13	of	of	ADP
ap-1187	17	14	model	model	NOUN
ap-1187	17	15	building	building	NOUN
ap-1187	17	16	are	be	AUX
ap-1187	17	17	the	the	DET
ap-1187	17	18	following	following	NOUN
ap-1187	17	19	:	:	PUNCT
ap-1187	17	20	i	i	X
ap-1187	17	21	)	)	PUNCT
ap-1187	17	22	the	the	DET
ap-1187	17	23	mathematical	mathematical	ADJ
ap-1187	17	24	entities	entity	NOUN
ap-1187	17	25	representing	represent	VERB
ap-1187	17	26	quarks	quarks	NOUN
ap-1187	17	27	should	should	AUX
ap-1187	17	28	form	form	VERB
ap-1187	17	29	a	a	DET
ap-1187	17	30	linear	linear	ADJ
ap-1187	17	31	space	space	NOUN
ap-1187	17	32	over	over	ADP
ap-1187	17	33	complex	complex	ADJ
ap-1187	17	34	numbers	number	NOUN
ap-1187	17	35	,	,	PUNCT
ap-1187	17	36	so	so	SCONJ
ap-1187	17	37	that	that	SCONJ
ap-1187	17	38	we	we	PRON
ap-1187	17	39	could	could	AUX
ap-1187	17	40	produce	produce	VERB
ap-1187	17	41	their	their	PRON
ap-1187	17	42	linear	linear	ADJ
ap-1187	17	43	combinations	combination	NOUN
ap-1187	17	44	with	with	ADP
ap-1187	17	45	complex	complex	ADJ
ap-1187	17	46	coefficients	coefficient	NOUN
ap-1187	17	47	.	.	PUNCT
ap-1187	18	1	ii	ii	X
ap-1187	18	2	)	)	PUNCT
ap-1187	18	3	they	they	PRON
ap-1187	18	4	should	should	AUX
ap-1187	18	5	also	also	ADV
ap-1187	18	6	form	form	VERB
ap-1187	18	7	an	an	DET
ap-1187	18	8	associative	associative	ADJ
ap-1187	18	9	algebra	algebra	NOUN
ap-1187	18	10	,	,	PUNCT
ap-1187	18	11	so	so	SCONJ
ap-1187	18	12	that	that	SCONJ
ap-1187	18	13	their	their	PRON
ap-1187	18	14	multilinear	multilinear	NOUN
ap-1187	18	15	combinations	combination	NOUN
ap-1187	18	16	may	may	AUX
ap-1187	18	17	be	be	AUX
ap-1187	18	18	formed	form	VERB
ap-1187	18	19	;	;	PUNCT
ap-1187	18	20	iii	iii	X
ap-1187	18	21	)	)	PUNCT
ap-1187	18	22	there	there	PRON
ap-1187	18	23	should	should	AUX
ap-1187	18	24	exist	exist	VERB
ap-1187	18	25	two	two	NUM
ap-1187	18	26	isomorphic	isomorphic	ADJ
ap-1187	18	27	algebras	algebra	NOUN
ap-1187	18	28	of	of	ADP
ap-1187	18	29	this	this	DET
ap-1187	18	30	type	type	NOUN
ap-1187	18	31	corresponding	correspond	VERB
ap-1187	18	32	to	to	ADP
ap-1187	18	33	quarks	quarks	PROPN
ap-1187	18	34	and	and	CCONJ
ap-1187	18	35	anti	anti	ADJ
ap-1187	18	36	-	-	NOUN
ap-1187	18	37	quarks	quark	NOUN
ap-1187	18	38	,	,	PUNCT
ap-1187	18	39	and	and	CCONJ
ap-1187	18	40	the	the	DET
ap-1187	18	41	conjugation	conjugation	NOUN
ap-1187	18	42	transformation	transformation	NOUN
ap-1187	18	43	that	that	PRON
ap-1187	18	44	maps	map	VERB
ap-1187	18	45	one	one	NUM
ap-1187	18	46	of	of	ADP
ap-1187	18	47	these	these	DET
ap-1187	18	48	algebras	algebra	NOUN
ap-1187	18	49	onto	onto	ADP
ap-1187	18	50	another	another	PRON
ap-1187	18	51	,	,	PUNCT
ap-1187	18	52	a	a	DET
ap-1187	18	53	→	→	SYM
ap-1187	18	54	ā.	ā.	NOUN
ap-1187	18	55	iv	iv	X
ap-1187	18	56	)	)	PUNCT
ap-1187	18	57	the	the	DET
ap-1187	18	58	three	three	NUM
ap-1187	18	59	quark	quark	NOUN
ap-1187	18	60	(	(	PUNCT
ap-1187	18	61	or	or	CCONJ
ap-1187	18	62	three	three	NUM
ap-1187	18	63	anti	anti	ADJ
ap-1187	18	64	-	-	ADJ
ap-1187	18	65	quark	quark	NOUN
ap-1187	18	66	)	)	PUNCT
ap-1187	18	67	and	and	CCONJ
ap-1187	18	68	the	the	DET
ap-1187	18	69	quark	quark	PROPN
ap-1187	18	70	-	-	PUNCT
ap-1187	18	71	anti	anti	ADJ
ap-1187	18	72	-	-	ADJ
ap-1187	18	73	quark	quark	ADJ
ap-1187	18	74	combinations	combination	NOUN
ap-1187	18	75	should	should	AUX
ap-1187	18	76	be	be	AUX
ap-1187	18	77	distinguished	distinguish	VERB
ap-1187	18	78	in	in	ADP
ap-1187	18	79	a	a	DET
ap-1187	18	80	certain	certain	ADJ
ap-1187	18	81	way	way	NOUN
ap-1187	18	82	,	,	PUNCT
ap-1187	18	83	for	for	ADP
ap-1187	18	84	example	example	NOUN
ap-1187	18	85	,	,	PUNCT
ap-1187	18	86	they	they	PRON
ap-1187	18	87	should	should	AUX
ap-1187	18	88	form	form	VERB
ap-1187	18	89	a	a	DET
ap-1187	18	90	subalgebra	subalgebra	NOUN
ap-1187	18	91	in	in	ADP
ap-1187	18	92	the	the	DET
ap-1187	18	93	algebra	algebra	NOUN
ap-1187	18	94	spanned	span	VERB
ap-1187	18	95	by	by	ADP
ap-1187	18	96	the	the	DET
ap-1187	18	97	generators	generator	NOUN
ap-1187	18	98	.	.	PUNCT
ap-1187	19	1	with	with	ADP
ap-1187	19	2	this	this	PRON
ap-1187	19	3	in	in	ADP
ap-1187	19	4	mind	mind	NOUN
ap-1187	19	5	we	we	PRON
ap-1187	19	6	can	can	AUX
ap-1187	19	7	start	start	VERB
ap-1187	19	8	to	to	PART
ap-1187	19	9	explore	explore	VERB
ap-1187	19	10	the	the	DET
ap-1187	19	11	algebraic	algebraic	ADJ
ap-1187	19	12	properties	property	NOUN
ap-1187	19	13	of	of	ADP
ap-1187	19	14	quarks	quark	NOUN
ap-1187	19	15	that	that	PRON
ap-1187	19	16	would	would	AUX
ap-1187	19	17	lead	lead	VERB
ap-1187	19	18	to	to	ADP
ap-1187	19	19	more	more	ADJ
ap-1187	19	20	general	general	ADJ
ap-1187	19	21	symmetries	symmetry	NOUN
ap-1187	19	22	,	,	PUNCT
ap-1187	19	23	that	that	PRON
ap-1187	19	24	of	of	ADP
ap-1187	19	25	space	space	NOUN
ap-1187	19	26	and	and	CCONJ
ap-1187	19	27	time	time	NOUN
ap-1187	19	28	,	,	PUNCT
ap-1187	19	29	appearing	appear	VERB
ap-1187	19	30	as	as	ADP
ap-1187	19	31	a	a	DET
ap-1187	19	32	consequence	consequence	NOUN
ap-1187	19	33	of	of	ADP
ap-1187	19	34	covariance	covariance	NOUN
ap-1187	19	35	requirements	requirement	NOUN
ap-1187	19	36	imposed	impose	VERB
ap-1187	19	37	on	on	ADP
ap-1187	19	38	the	the	DET
ap-1187	19	39	discrete	discrete	ADJ
ap-1187	19	40	relations	relation	NOUN
ap-1187	19	41	between	between	ADP
ap-1187	19	42	the	the	DET
ap-1187	19	43	generators	generator	NOUN
ap-1187	19	44	of	of	ADP
ap-1187	19	45	the	the	DET
ap-1187	19	46	quark	quark	PROPN
ap-1187	19	47	algebra	algebra	PROPN
ap-1187	19	48	.	.	PUNCT
ap-1187	20	1	2	2	X
ap-1187	20	2	.	.	X
ap-1187	20	3	at	at	ADP
ap-1187	20	4	present	present	ADJ
ap-1187	20	5	,	,	PUNCT
ap-1187	20	6	the	the	DET
ap-1187	20	7	most	most	ADV
ap-1187	20	8	successful	successful	ADJ
ap-1187	20	9	theoretical	theoretical	ADJ
ap-1187	20	10	descriptions	description	NOUN
ap-1187	20	11	of	of	ADP
ap-1187	20	12	fundamental	fundamental	ADJ
ap-1187	20	13	interactions	interaction	NOUN
ap-1187	20	14	are	be	AUX
ap-1187	20	15	based	base	VERB
ap-1187	20	16	on	on	ADP
ap-1187	20	17	the	the	DET
ap-1187	20	18	quark	quark	PROPN
ap-1187	20	19	model	model	NOUN
ap-1187	20	20	,	,	PUNCT
ap-1187	20	21	despite	despite	SCONJ
ap-1187	20	22	the	the	DET
ap-1187	20	23	fact	fact	NOUN
ap-1187	20	24	that	that	SCONJ
ap-1187	20	25	isolated	isolated	ADJ
ap-1187	20	26	quarks	quarks	NOUN
ap-1187	20	27	can	can	AUX
ap-1187	20	28	not	not	PART
ap-1187	20	29	be	be	AUX
ap-1187	20	30	observed	observe	VERB
ap-1187	20	31	.	.	PUNCT
ap-1187	21	1	the	the	DET
ap-1187	21	2	only	only	ADJ
ap-1187	21	3	experimentally	experimentally	ADV
ap-1187	21	4	accessible	accessible	ADJ
ap-1187	21	5	states	state	NOUN
ap-1187	21	6	are	be	AUX
ap-1187	21	7	either	either	CCONJ
ap-1187	21	8	three	three	NUM
ap-1187	21	9	-	-	PUNCT
ap-1187	21	10	quark	quark	NOUN
ap-1187	21	11	or	or	CCONJ
ap-1187	21	12	three	three	NUM
ap-1187	21	13	-	-	PUNCT
ap-1187	21	14	anti	anti	ADJ
ap-1187	21	15	-	-	ADJ
ap-1187	21	16	quark	quark	ADJ
ap-1187	21	17	combinations	combination	NOUN
ap-1187	21	18	(	(	PUNCT
ap-1187	21	19	fermions	fermion	NOUN
ap-1187	21	20	)	)	PUNCT
ap-1187	21	21	or	or	CCONJ
ap-1187	21	22	quark	quark	ADJ
ap-1187	21	23	-	-	PUNCT
ap-1187	21	24	anti	anti	ADJ
ap-1187	21	25	-	-	ADJ
ap-1187	21	26	quark	quark	ADJ
ap-1187	21	27	states	state	NOUN
ap-1187	21	28	(	(	PUNCT
ap-1187	21	29	bosons	boson	NOUN
ap-1187	21	30	)	)	PUNCT
ap-1187	21	31	.	.	PUNCT
ap-1187	22	1	whenever	whenever	SCONJ
ap-1187	22	2	one	one	PRON
ap-1187	22	3	has	have	VERB
ap-1187	22	4	to	to	PART
ap-1187	22	5	do	do	VERB
ap-1187	22	6	with	with	ADP
ap-1187	22	7	a	a	DET
ap-1187	22	8	tri	tri	ADJ
ap-1187	22	9	-	-	ADJ
ap-1187	22	10	linear	linear	ADJ
ap-1187	22	11	combination	combination	NOUN
ap-1187	22	12	of	of	ADP
ap-1187	22	13	fields	field	NOUN
ap-1187	22	14	(	(	PUNCT
ap-1187	22	15	or	or	CCONJ
ap-1187	22	16	operators	operator	NOUN
ap-1187	22	17	)	)	PUNCT
ap-1187	22	18	,	,	PUNCT
ap-1187	22	19	one	one	PRON
ap-1187	22	20	must	must	AUX
ap-1187	22	21	investigate	investigate	VERB
ap-1187	22	22	the	the	DET
ap-1187	22	23	behavior	behavior	NOUN
ap-1187	22	24	of	of	ADP
ap-1187	22	25	such	such	ADJ
ap-1187	22	26	states	state	NOUN
ap-1187	22	27	under	under	ADP
ap-1187	22	28	permutations	permutation	NOUN
ap-1187	22	29	.	.	PUNCT
ap-1187	23	1	let	let	VERB
ap-1187	23	2	us	we	PRON
ap-1187	23	3	introduce	introduce	VERB
ap-1187	23	4	n	n	DET
ap-1187	23	5	generators	generator	NOUN
ap-1187	23	6	spanning	span	VERB
ap-1187	23	7	a	a	DET
ap-1187	23	8	linear	linear	ADJ
ap-1187	23	9	space	space	NOUN
ap-1187	23	10	over	over	ADP
ap-1187	23	11	complex	complex	ADJ
ap-1187	23	12	numbers	number	NOUN
ap-1187	23	13	,	,	PUNCT
ap-1187	23	14	satisfying	satisfy	VERB
ap-1187	23	15	the	the	DET
ap-1187	23	16	following	follow	VERB
ap-1187	23	17	relations	relation	NOUN
ap-1187	23	18	which	which	PRON
ap-1187	23	19	are	be	AUX
ap-1187	23	20	a	a	DET
ap-1187	23	21	cubic	cubic	ADJ
ap-1187	23	22	generalization	generalization	NOUN
ap-1187	23	23	of	of	ADP
ap-1187	23	24	anti	anti	NOUN
ap-1187	23	25	-	-	NOUN
ap-1187	23	26	commutation	commutation	NOUN
ap-1187	23	27	in	in	ADP
ap-1187	23	28	the	the	DET
ap-1187	23	29	ususal	ususal	ADJ
ap-1187	23	30	(	(	PUNCT
ap-1187	23	31	binary	binary	ADJ
ap-1187	23	32	)	)	PUNCT
ap-1187	23	33	case	case	NOUN
ap-1187	23	34	(	(	PUNCT
ap-1187	23	35	see	see	VERB
ap-1187	24	1	e.g.	e.g.	ADV
ap-1187	24	2	[	[	X
ap-1187	24	3	5	5	NUM
ap-1187	24	4	,	,	PUNCT
ap-1187	24	5	6	6	NUM
ap-1187	24	6	]	]	PUNCT
ap-1187	24	7	):	):	PUNCT
ap-1187	24	8	θaθbθc	θaθbθc	PROPN
ap-1187	24	9	=	=	PUNCT
ap-1187	24	10	j	j	PROPN
ap-1187	24	11	θbθcθa	θbθcθa	X
ap-1187	24	12	=	=	SYM
ap-1187	24	13	j2	j2	PROPN
ap-1187	24	14	θcθaθb	θcθaθb	NUM
ap-1187	24	15	,	,	PUNCT
ap-1187	24	16	(	(	PUNCT
ap-1187	24	17	1	1	X
ap-1187	24	18	)	)	PUNCT
ap-1187	24	19	with	with	ADP
ap-1187	24	20	j	j	PROPN
ap-1187	24	21	=	=	SYM
ap-1187	24	22	eiπ/3	eiπ/3	PROPN
ap-1187	24	23	,	,	PUNCT
ap-1187	24	24	the	the	DET
ap-1187	24	25	primitive	primitive	ADJ
ap-1187	24	26	cubic	cubic	ADJ
ap-1187	24	27	root	root	NOUN
ap-1187	24	28	of	of	ADP
ap-1187	24	29	1	1	NUM
ap-1187	24	30	.	.	PUNCT
ap-1187	25	1	we	we	PRON
ap-1187	25	2	have	have	VERB
ap-1187	25	3	j̄	j̄	PROPN
ap-1187	25	4	=	=	SYM
ap-1187	25	5	j2	j2	PROPN
ap-1187	25	6	and	and	CCONJ
ap-1187	25	7	1	1	NUM
ap-1187	25	8	+	+	CCONJ
ap-1187	25	9	j	j	PROPN
ap-1187	25	10	+	+	CCONJ
ap-1187	25	11	j2	j2	PROPN
ap-1187	25	12	=	=	SYM
ap-1187	25	13	0	0	PROPN
ap-1187	25	14	.	.	PUNCT
ap-1187	26	1	we	we	PRON
ap-1187	26	2	shall	shall	AUX
ap-1187	26	3	also	also	ADV
ap-1187	26	4	introduce	introduce	VERB
ap-1187	26	5	a	a	DET
ap-1187	26	6	similar	similar	ADJ
ap-1187	26	7	set	set	NOUN
ap-1187	26	8	of	of	ADP
ap-1187	26	9	conjugate	conjugate	ADJ
ap-1187	26	10	generators	generator	NOUN
ap-1187	26	11	,	,	PUNCT
ap-1187	26	12	θ̄ȧ	θ̄ȧ	PROPN
ap-1187	26	13	,	,	PUNCT
ap-1187	26	14	ȧ	ȧ	PROPN
ap-1187	26	15	,	,	PUNCT
ap-1187	26	16	ḃ	ḃ	PROPN
ap-1187	26	17	,	,	PUNCT
ap-1187	26	18	.	.	PUNCT
ap-1187	26	19	.	.	PUNCT
ap-1187	26	20	.	.	PUNCT
ap-1187	27	1	=	=	PUNCT
ap-1187	27	2	1	1	NUM
ap-1187	27	3	,	,	PUNCT
ap-1187	27	4	2	2	NUM
ap-1187	27	5	,	,	PUNCT
ap-1187	27	6	.	.	PUNCT
ap-1187	27	7	.	.	PUNCT
ap-1187	28	1	.	.	PUNCT
ap-1187	29	1	,	,	PUNCT
ap-1187	29	2	n	n	X
ap-1187	29	3	,	,	PUNCT
ap-1187	29	4	satisfying	satisfy	VERB
ap-1187	29	5	a	a	DET
ap-1187	29	6	similar	similar	ADJ
ap-1187	29	7	condition	condition	NOUN
ap-1187	29	8	with	with	ADP
ap-1187	29	9	j2	j2	PROPN
ap-1187	29	10	replacing	replace	VERB
ap-1187	29	11	j	j	PROPN
ap-1187	29	12	:	:	PUNCT
ap-1187	29	13	θ̄ȧθ̄ḃ	θ̄ȧθ̄ḃ	PROPN
ap-1187	29	14	θ̄ċ	θ̄ċ	PUNCT
ap-1187	30	1	=	=	PROPN
ap-1187	30	2	j2	j2	PROPN
ap-1187	30	3	θ̄ḃ	θ̄ḃ	PROPN
ap-1187	30	4	θ̄ċ	θ̄ċ	PUNCT
ap-1187	31	1	θ̄ȧ	θ̄ȧ	PROPN
ap-1187	32	1	=	=	PUNCT
ap-1187	32	2	j	j	PROPN
ap-1187	32	3	θ̄ċ	θ̄ċ	ADP
ap-1187	32	4	θ̄ȧθ̄ḃ	θ̄ȧθ̄ḃ	PROPN
ap-1187	32	5	,	,	PUNCT
ap-1187	32	6	(	(	PUNCT
ap-1187	32	7	2	2	X
ap-1187	32	8	)	)	PUNCT
ap-1187	32	9	let	let	VERB
ap-1187	32	10	us	we	PRON
ap-1187	32	11	denote	denote	VERB
ap-1187	32	12	this	this	DET
ap-1187	32	13	algebra	algebra	NOUN
ap-1187	32	14	by	by	ADP
ap-1187	32	15	a.	a.	NOUN
ap-1187	32	16	we	we	PRON
ap-1187	32	17	shall	shall	AUX
ap-1187	32	18	endow	endow	VERB
ap-1187	32	19	this	this	DET
ap-1187	32	20	algebra	algebra	NOUN
ap-1187	32	21	with	with	ADP
ap-1187	32	22	a	a	DET
ap-1187	32	23	natural	natural	ADJ
ap-1187	32	24	z3	z3	NOUN
ap-1187	32	25	grading	grading	NOUN
ap-1187	32	26	,	,	PUNCT
ap-1187	32	27	considering	consider	VERB
ap-1187	32	28	the	the	DET
ap-1187	32	29	37	37	NUM
ap-1187	32	30	acta	acta	PROPN
ap-1187	32	31	polytechnica	polytechnica	PROPN
ap-1187	32	32	vol	vol	NOUN
ap-1187	32	33	.	.	PROPN
ap-1187	33	1	50	50	NUM
ap-1187	33	2	no	no	NOUN
ap-1187	33	3	.	.	PUNCT
ap-1187	34	1	3/2010	3/2010	NUM
ap-1187	34	2	generators	generator	NOUN
ap-1187	34	3	θa	θa	ADP
ap-1187	34	4	as	as	ADP
ap-1187	34	5	grade	grade	NOUN
ap-1187	34	6	1	1	NUM
ap-1187	34	7	elements	element	NOUN
ap-1187	34	8	,	,	PUNCT
ap-1187	34	9	and	and	CCONJ
ap-1187	34	10	their	their	PRON
ap-1187	34	11	conjugates	conjugate	NOUN
ap-1187	34	12	θ̄ȧ	θ̄ȧ	PUNCT
ap-1187	34	13	being	be	AUX
ap-1187	34	14	of	of	ADP
ap-1187	34	15	grade	grade	NOUN
ap-1187	34	16	2	2	NUM
ap-1187	34	17	.	.	PUNCT
ap-1187	35	1	the	the	DET
ap-1187	35	2	grades	grade	NOUN
ap-1187	35	3	add	add	VERB
ap-1187	35	4	up	up	ADP
ap-1187	35	5	modulo	modulo	NOUN
ap-1187	35	6	3	3	NUM
ap-1187	35	7	,	,	PUNCT
ap-1187	35	8	so	so	SCONJ
ap-1187	35	9	that	that	SCONJ
ap-1187	35	10	the	the	DET
ap-1187	35	11	products	product	NOUN
ap-1187	35	12	θaθb	θaθb	NOUN
ap-1187	35	13	span	span	VERB
ap-1187	35	14	a	a	DET
ap-1187	35	15	linear	linear	ADJ
ap-1187	35	16	subspace	subspace	NOUN
ap-1187	35	17	of	of	ADP
ap-1187	35	18	grade	grade	NOUN
ap-1187	35	19	2	2	NUM
ap-1187	35	20	,	,	PUNCT
ap-1187	35	21	and	and	CCONJ
ap-1187	35	22	the	the	DET
ap-1187	35	23	cubic	cubic	ADJ
ap-1187	35	24	products	product	NOUN
ap-1187	35	25	θaθbθc	θaθbθc	NOUN
ap-1187	35	26	are	be	AUX
ap-1187	35	27	of	of	ADP
ap-1187	35	28	grade	grade	NOUN
ap-1187	35	29	0	0	NUM
ap-1187	35	30	.	.	PUNCT
ap-1187	36	1	similarly	similarly	ADV
ap-1187	36	2	,	,	PUNCT
ap-1187	36	3	all	all	DET
ap-1187	36	4	quadratic	quadratic	ADJ
ap-1187	36	5	expressions	expression	NOUN
ap-1187	36	6	in	in	ADP
ap-1187	36	7	conjugate	conjugate	ADJ
ap-1187	36	8	generators	generator	NOUN
ap-1187	36	9	,	,	PUNCT
ap-1187	36	10	θ̄ȧθ̄ḃ	θ̄ȧθ̄ḃ	PROPN
ap-1187	36	11	are	be	AUX
ap-1187	36	12	of	of	ADP
ap-1187	36	13	grade	grade	NOUN
ap-1187	36	14	2	2	NUM
ap-1187	36	15	+	+	NUM
ap-1187	36	16	2	2	NUM
ap-1187	36	17	=	=	SYM
ap-1187	36	18	4mod	4mod	NUM
ap-1187	36	19	3	3	NUM
ap-1187	36	20	=	=	SYM
ap-1187	36	21	1	1	NUM
ap-1187	36	22	,	,	PUNCT
ap-1187	36	23	whereas	whereas	SCONJ
ap-1187	36	24	their	their	PRON
ap-1187	36	25	cubic	cubic	ADJ
ap-1187	36	26	products	product	NOUN
ap-1187	36	27	are	be	AUX
ap-1187	36	28	again	again	ADV
ap-1187	36	29	of	of	ADP
ap-1187	36	30	grade	grade	NOUN
ap-1187	36	31	0	0	NUM
ap-1187	36	32	,	,	PUNCT
ap-1187	36	33	like	like	ADP
ap-1187	36	34	the	the	DET
ap-1187	36	35	cubic	cubic	ADJ
ap-1187	36	36	products	product	NOUN
ap-1187	36	37	of	of	ADP
ap-1187	36	38	θa	θa	PRON
ap-1187	36	39	’s	’s	PART
ap-1187	36	40	.	.	PUNCT
ap-1187	37	1	combined	combine	VERB
ap-1187	37	2	with	with	ADP
ap-1187	37	3	the	the	DET
ap-1187	37	4	associativity	associativity	NOUN
ap-1187	37	5	,	,	PUNCT
ap-1187	37	6	these	these	DET
ap-1187	37	7	cubic	cubic	ADJ
ap-1187	37	8	relations	relation	NOUN
ap-1187	37	9	impose	impose	VERB
ap-1187	37	10	a	a	DET
ap-1187	37	11	finite	finite	ADJ
ap-1187	37	12	dimension	dimension	NOUN
ap-1187	37	13	on	on	ADP
ap-1187	37	14	the	the	DET
ap-1187	37	15	algebra	algebra	NOUN
ap-1187	37	16	generated	generate	VERB
ap-1187	37	17	by	by	ADP
ap-1187	37	18	z3	z3	PROPN
ap-1187	37	19	graded	grade	VERB
ap-1187	37	20	generators	generator	NOUN
ap-1187	37	21	.	.	PUNCT
ap-1187	38	1	as	as	ADP
ap-1187	38	2	a	a	DET
ap-1187	38	3	matter	matter	NOUN
ap-1187	38	4	of	of	ADP
ap-1187	38	5	fact	fact	NOUN
ap-1187	38	6	,	,	PUNCT
ap-1187	38	7	cubic	cubic	ADJ
ap-1187	38	8	expressions	expression	NOUN
ap-1187	38	9	are	be	AUX
ap-1187	38	10	the	the	DET
ap-1187	38	11	highest	high	ADJ
ap-1187	38	12	order	order	NOUN
ap-1187	38	13	that	that	PRON
ap-1187	38	14	does	do	AUX
ap-1187	38	15	not	not	PART
ap-1187	38	16	vanish	vanish	VERB
ap-1187	38	17	identically	identically	ADV
ap-1187	38	18	.	.	PUNCT
ap-1187	39	1	the	the	DET
ap-1187	39	2	proof	proof	NOUN
ap-1187	39	3	is	be	AUX
ap-1187	39	4	immediate	immediate	ADJ
ap-1187	39	5	:	:	PUNCT
ap-1187	39	6	θaθbθcθd	θaθbθcθd	PROPN
ap-1187	39	7	=	=	SYM
ap-1187	39	8	j	j	PROPN
ap-1187	39	9	θbθcθaθd	θbθcθaθd	PROPN
ap-1187	39	10	=	=	SYM
ap-1187	39	11	j2	j2	PROPN
ap-1187	39	12	θbθaθdθc	θbθaθdθc	PROPN
ap-1187	39	13	=	=	PROPN
ap-1187	39	14	j3	j3	PROPN
ap-1187	39	15	θaθdθbθc	θaθdθbθc	VERB
ap-1187	39	16	=	=	PROPN
ap-1187	39	17	j4	j4	PROPN
ap-1187	39	18	θaθbθcθd	θaθbθcθd	PROPN
ap-1187	39	19	and	and	CCONJ
ap-1187	39	20	because	because	SCONJ
ap-1187	39	21	j4	j4	PROPN
ap-1187	39	22	=	=	PROPN
ap-1187	39	23	j	j	PROPN
ap-1187	39	24	�	�	PROPN
ap-1187	39	25	=	=	SYM
ap-1187	39	26	1	1	NUM
ap-1187	39	27	,	,	PUNCT
ap-1187	39	28	the	the	DET
ap-1187	39	29	only	only	ADJ
ap-1187	39	30	solution	solution	NOUN
ap-1187	39	31	is	be	AUX
ap-1187	39	32	θaθbθcθd	θaθbθcθd	PROPN
ap-1187	39	33	=	=	PUNCT
ap-1187	39	34	0	0	X
ap-1187	39	35	.	.	PUNCT
ap-1187	40	1	(	(	PUNCT
ap-1187	40	2	3	3	X
ap-1187	40	3	)	)	PUNCT
ap-1187	40	4	therefore	therefore	ADV
ap-1187	40	5	the	the	DET
ap-1187	40	6	total	total	ADJ
ap-1187	40	7	dimension	dimension	NOUN
ap-1187	40	8	of	of	ADP
ap-1187	40	9	the	the	DET
ap-1187	40	10	algebra	algebra	NOUN
ap-1187	40	11	defined	define	VERB
ap-1187	40	12	via	via	ADP
ap-1187	40	13	the	the	DET
ap-1187	40	14	cubic	cubic	ADJ
ap-1187	40	15	relations	relation	NOUN
ap-1187	40	16	(	(	PUNCT
ap-1187	40	17	1	1	X
ap-1187	40	18	)	)	PUNCT
ap-1187	40	19	is	be	AUX
ap-1187	40	20	equal	equal	ADJ
ap-1187	40	21	to	to	ADP
ap-1187	40	22	n	n	DET
ap-1187	40	23	+	+	ADJ
ap-1187	40	24	n2+(n3−	n2+(n3−	ADJ
ap-1187	40	25	n)/3	n)/3	PROPN
ap-1187	40	26	:	:	PUNCT
ap-1187	40	27	the	the	DET
ap-1187	40	28	n	n	PRON
ap-1187	40	29	generators	generator	NOUN
ap-1187	40	30	of	of	ADP
ap-1187	40	31	grade	grade	NOUN
ap-1187	40	32	1	1	NUM
ap-1187	40	33	,	,	PUNCT
ap-1187	40	34	the	the	DET
ap-1187	40	35	n2	n2	ADJ
ap-1187	40	36	independent	independent	ADJ
ap-1187	40	37	products	product	NOUN
ap-1187	40	38	of	of	ADP
ap-1187	40	39	two	two	NUM
ap-1187	40	40	generators	generator	NOUN
ap-1187	40	41	,	,	PUNCT
ap-1187	40	42	and	and	CCONJ
ap-1187	40	43	(	(	PUNCT
ap-1187	40	44	n3	n3	NOUN
ap-1187	40	45	−	−	PROPN
ap-1187	40	46	n)/3	n)/3	PROPN
ap-1187	40	47	independent	independent	ADJ
ap-1187	40	48	cubic	cubic	ADJ
ap-1187	40	49	expressions	expression	NOUN
ap-1187	40	50	,	,	PUNCT
ap-1187	40	51	because	because	SCONJ
ap-1187	40	52	the	the	DET
ap-1187	40	53	cube	cube	NOUN
ap-1187	40	54	of	of	ADP
ap-1187	40	55	any	any	DET
ap-1187	40	56	generator	generator	NOUN
ap-1187	40	57	must	must	AUX
ap-1187	40	58	be	be	AUX
ap-1187	40	59	zero	zero	NUM
ap-1187	40	60	,	,	PUNCT
ap-1187	40	61	and	and	CCONJ
ap-1187	40	62	the	the	DET
ap-1187	40	63	remaining	remain	VERB
ap-1187	40	64	n3	n3	NOUN
ap-1187	40	65	−	−	PROPN
ap-1187	40	66	n	n	CCONJ
ap-1187	40	67	ternary	ternary	ADJ
ap-1187	40	68	products	product	NOUN
ap-1187	40	69	are	be	AUX
ap-1187	40	70	divided	divide	VERB
ap-1187	40	71	by	by	ADP
ap-1187	40	72	3	3	NUM
ap-1187	40	73	,	,	PUNCT
ap-1187	40	74	by	by	ADP
ap-1187	40	75	virtue	virtue	NOUN
ap-1187	40	76	of	of	ADP
ap-1187	40	77	the	the	DET
ap-1187	40	78	constitutive	constitutive	ADJ
ap-1187	40	79	relations	relation	NOUN
ap-1187	40	80	(	(	PUNCT
ap-1187	40	81	1	1	NUM
ap-1187	40	82	)	)	PUNCT
ap-1187	40	83	.	.	PUNCT
ap-1187	41	1	the	the	DET
ap-1187	41	2	conjugate	conjugate	ADJ
ap-1187	41	3	generators	generator	NOUN
ap-1187	41	4	θ̄ḃ	θ̄ḃ	PROPN
ap-1187	41	5	span	span	VERB
ap-1187	41	6	an	an	DET
ap-1187	41	7	algebra	algebra	NOUN
ap-1187	41	8	ā	ā	NOUN
ap-1187	41	9	isomorphic	isomorphic	ADJ
ap-1187	41	10	with	with	ADP
ap-1187	41	11	a.	a.	NOUN
ap-1187	41	12	both	both	DET
ap-1187	41	13	algebras	algebra	NOUN
ap-1187	41	14	split	split	VERB
ap-1187	41	15	quite	quite	ADV
ap-1187	41	16	naturally	naturally	ADV
ap-1187	41	17	into	into	ADP
ap-1187	41	18	sums	sum	NOUN
ap-1187	41	19	of	of	ADP
ap-1187	41	20	linear	linear	ADJ
ap-1187	41	21	subspaces	subspace	NOUN
ap-1187	41	22	with	with	ADP
ap-1187	41	23	definite	definite	ADJ
ap-1187	41	24	grades	grade	NOUN
ap-1187	41	25	:	:	PUNCT
ap-1187	41	26	a	a	DET
ap-1187	41	27	=	=	PROPN
ap-1187	41	28	a0	a0	PROPN
ap-1187	41	29	⊕a1	⊕a1	NUM
ap-1187	41	30	⊕a2	⊕a2	NOUN
ap-1187	41	31	,	,	PUNCT
ap-1187	41	32	ā	ā	NOUN
ap-1187	41	33	=	=	SYM
ap-1187	41	34	ā0	ā0	PROPN
ap-1187	41	35	⊕	⊕	PROPN
ap-1187	41	36	ā1	ā1	PROPN
ap-1187	41	37	⊕	⊕	PROPN
ap-1187	41	38	ā2	ā2	PROPN
ap-1187	41	39	,	,	PUNCT
ap-1187	41	40	the	the	DET
ap-1187	41	41	subspaces	subspace	NOUN
ap-1187	41	42	a0	a0	NOUN
ap-1187	41	43	and	and	CCONJ
ap-1187	41	44	ā0	ā0	ADV
ap-1187	41	45	form	form	VERB
ap-1187	41	46	zero	zero	NUM
ap-1187	41	47	-	-	PUNCT
ap-1187	41	48	graded	grade	VERB
ap-1187	41	49	subalgebras	subalgebra	NOUN
ap-1187	41	50	.	.	PUNCT
ap-1187	42	1	these	these	DET
ap-1187	42	2	algebras	algebra	NOUN
ap-1187	42	3	can	can	AUX
ap-1187	42	4	be	be	AUX
ap-1187	42	5	made	make	VERB
ap-1187	42	6	unital	unital	ADJ
ap-1187	42	7	if	if	SCONJ
ap-1187	42	8	we	we	PRON
ap-1187	42	9	add	add	VERB
ap-1187	42	10	to	to	ADP
ap-1187	42	11	each	each	PRON
ap-1187	42	12	of	of	ADP
ap-1187	42	13	them	they	PRON
ap-1187	42	14	the	the	DET
ap-1187	42	15	unit	unit	NOUN
ap-1187	42	16	element	element	NOUN
ap-1187	42	17	1	1	NUM
ap-1187	42	18	acting	act	VERB
ap-1187	42	19	as	as	ADP
ap-1187	42	20	identity	identity	NOUN
ap-1187	42	21	and	and	CCONJ
ap-1187	42	22	considered	consider	VERB
ap-1187	42	23	as	as	ADP
ap-1187	42	24	being	be	AUX
ap-1187	42	25	of	of	ADP
ap-1187	42	26	grade	grade	NOUN
ap-1187	42	27	0	0	NUM
ap-1187	42	28	.	.	PUNCT
ap-1187	43	1	if	if	SCONJ
ap-1187	43	2	we	we	PRON
ap-1187	43	3	want	want	VERB
ap-1187	43	4	the	the	DET
ap-1187	43	5	products	product	NOUN
ap-1187	43	6	between	between	ADP
ap-1187	43	7	the	the	DET
ap-1187	43	8	generators	generator	NOUN
ap-1187	43	9	θa	θa	NUM
ap-1187	43	10	and	and	CCONJ
ap-1187	43	11	their	their	PRON
ap-1187	43	12	conjugates	conjugate	NOUN
ap-1187	43	13	θ̄ḃ	θ̄ḃ	VERB
ap-1187	43	14	to	to	PART
ap-1187	43	15	be	be	AUX
ap-1187	43	16	included	include	VERB
ap-1187	43	17	into	into	ADP
ap-1187	43	18	the	the	DET
ap-1187	43	19	greater	great	ADJ
ap-1187	43	20	algebra	algebra	NOUN
ap-1187	43	21	spanned	span	VERB
ap-1187	43	22	by	by	ADP
ap-1187	43	23	both	both	DET
ap-1187	43	24	types	type	NOUN
ap-1187	43	25	of	of	ADP
ap-1187	43	26	generators	generator	NOUN
ap-1187	43	27	,	,	PUNCT
ap-1187	43	28	we	we	PRON
ap-1187	43	29	should	should	AUX
ap-1187	43	30	consider	consider	VERB
ap-1187	43	31	all	all	DET
ap-1187	43	32	possible	possible	ADJ
ap-1187	43	33	products	product	NOUN
ap-1187	43	34	,	,	PUNCT
ap-1187	43	35	which	which	PRON
ap-1187	43	36	will	will	AUX
ap-1187	43	37	be	be	AUX
ap-1187	43	38	included	include	VERB
ap-1187	43	39	in	in	ADP
ap-1187	43	40	the	the	DET
ap-1187	43	41	linear	linear	ADJ
ap-1187	43	42	subspaces	subspace	NOUN
ap-1187	43	43	with	with	ADP
ap-1187	43	44	a	a	DET
ap-1187	43	45	definite	definite	ADJ
ap-1187	43	46	grade	grade	NOUN
ap-1187	43	47	.	.	PUNCT
ap-1187	44	1	of	of	ADP
ap-1187	44	2	the	the	DET
ap-1187	44	3	resulting	result	VERB
ap-1187	44	4	algebra	algebra	NOUN
ap-1187	44	5	a	a	DET
ap-1187	44	6	⊗	⊗	PROPN
ap-1187	44	7	ā.	ā.	PUNCT
ap-1187	44	8	in	in	ADP
ap-1187	44	9	order	order	NOUN
ap-1187	44	10	to	to	PART
ap-1187	44	11	decide	decide	VERB
ap-1187	44	12	which	which	DET
ap-1187	44	13	expressions	expression	NOUN
ap-1187	44	14	are	be	AUX
ap-1187	44	15	linearly	linearly	ADV
ap-1187	44	16	dependent	dependent	ADJ
ap-1187	44	17	,	,	PUNCT
ap-1187	44	18	and	and	CCONJ
ap-1187	44	19	what	what	PRON
ap-1187	44	20	is	be	AUX
ap-1187	44	21	the	the	DET
ap-1187	44	22	overall	overall	ADJ
ap-1187	44	23	dimension	dimension	NOUN
ap-1187	44	24	of	of	ADP
ap-1187	44	25	the	the	DET
ap-1187	44	26	enlarged	enlarge	VERB
ap-1187	44	27	algebra	algebra	NOUN
ap-1187	44	28	generated	generate	VERB
ap-1187	44	29	by	by	ADP
ap-1187	44	30	θa	θa	NOUN
ap-1187	44	31	’s	’	NOUN
ap-1187	44	32	and	and	CCONJ
ap-1187	44	33	their	their	PRON
ap-1187	44	34	conjugate	conjugate	ADJ
ap-1187	44	35	variables	variable	NOUN
ap-1187	44	36	θ̄ḋ	θ̄ḋ	VERB
ap-1187	44	37	’s	’s	ADV
ap-1187	44	38	,	,	PUNCT
ap-1187	44	39	we	we	PRON
ap-1187	44	40	must	must	AUX
ap-1187	44	41	impose	impose	VERB
ap-1187	44	42	some	some	DET
ap-1187	44	43	binary	binary	ADJ
ap-1187	44	44	commutation	commutation	NOUN
ap-1187	44	45	relations	relation	NOUN
ap-1187	44	46	on	on	ADP
ap-1187	44	47	their	their	PRON
ap-1187	44	48	products	product	NOUN
ap-1187	44	49	.	.	PUNCT
ap-1187	45	1	the	the	DET
ap-1187	45	2	fact	fact	NOUN
ap-1187	45	3	that	that	SCONJ
ap-1187	45	4	conjugate	conjugate	ADJ
ap-1187	45	5	generators	generator	NOUN
ap-1187	45	6	are	be	AUX
ap-1187	45	7	of	of	ADP
ap-1187	45	8	grade	grade	NOUN
ap-1187	45	9	2	2	NUM
ap-1187	45	10	may	may	AUX
ap-1187	45	11	suggest	suggest	VERB
ap-1187	45	12	that	that	SCONJ
ap-1187	45	13	they	they	PRON
ap-1187	45	14	behave	behave	VERB
ap-1187	45	15	like	like	ADP
ap-1187	45	16	products	product	NOUN
ap-1187	45	17	of	of	ADP
ap-1187	45	18	two	two	NUM
ap-1187	45	19	ordinary	ordinary	ADJ
ap-1187	45	20	generators	generator	NOUN
ap-1187	45	21	θaθb	θaθb	NOUN
ap-1187	45	22	.	.	PUNCT
ap-1187	46	1	such	such	DET
ap-1187	46	2	a	a	DET
ap-1187	46	3	choice	choice	NOUN
ap-1187	46	4	often	often	ADV
ap-1187	46	5	was	be	AUX
ap-1187	46	6	made	make	VERB
ap-1187	46	7	(	(	PUNCT
ap-1187	46	8	see	see	VERB
ap-1187	46	9	,	,	PUNCT
ap-1187	46	10	e.g.	e.g.	ADV
ap-1187	46	11	,	,	PUNCT
ap-1187	46	12	[	[	X
ap-1187	46	13	5	5	NUM
ap-1187	46	14	,	,	PUNCT
ap-1187	46	15	9	9	NUM
ap-1187	46	16	,	,	PUNCT
ap-1187	46	17	6	6	NUM
ap-1187	46	18	]	]	NUM
ap-1187	46	19	)	)	PUNCT
ap-1187	46	20	.	.	PUNCT
ap-1187	47	1	however	however	ADV
ap-1187	47	2	,	,	PUNCT
ap-1187	47	3	this	this	PRON
ap-1187	47	4	does	do	AUX
ap-1187	47	5	not	not	PART
ap-1187	47	6	enable	enable	VERB
ap-1187	47	7	one	one	NUM
ap-1187	47	8	to	to	PART
ap-1187	47	9	make	make	VERB
ap-1187	47	10	a	a	DET
ap-1187	47	11	distinction	distinction	NOUN
ap-1187	47	12	between	between	ADP
ap-1187	47	13	conjugate	conjugate	ADJ
ap-1187	47	14	generators	generator	NOUN
ap-1187	47	15	and	and	CCONJ
ap-1187	47	16	the	the	DET
ap-1187	47	17	products	product	NOUN
ap-1187	47	18	of	of	ADP
ap-1187	47	19	two	two	NUM
ap-1187	47	20	ordinary	ordinary	ADJ
ap-1187	47	21	generators	generator	NOUN
ap-1187	47	22	,	,	PUNCT
ap-1187	47	23	and	and	CCONJ
ap-1187	47	24	it	it	PRON
ap-1187	47	25	would	would	AUX
ap-1187	47	26	be	be	AUX
ap-1187	47	27	better	well	ADJ
ap-1187	47	28	to	to	PART
ap-1187	47	29	be	be	AUX
ap-1187	47	30	able	able	ADJ
ap-1187	47	31	to	to	PART
ap-1187	47	32	make	make	VERB
ap-1187	47	33	the	the	DET
ap-1187	47	34	difference	difference	NOUN
ap-1187	47	35	.	.	PUNCT
ap-1187	48	1	due	due	ADP
ap-1187	48	2	to	to	ADP
ap-1187	48	3	the	the	DET
ap-1187	48	4	binary	binary	ADJ
ap-1187	48	5	nature	nature	NOUN
ap-1187	48	6	of	of	ADP
ap-1187	48	7	“	"	PUNCT
ap-1187	48	8	mixed	mixed	ADJ
ap-1187	48	9	”	"	PUNCT
ap-1187	48	10	products	product	NOUN
ap-1187	48	11	,	,	PUNCT
ap-1187	48	12	another	another	DET
ap-1187	48	13	choice	choice	NOUN
ap-1187	48	14	is	be	AUX
ap-1187	48	15	possible	possible	ADJ
ap-1187	48	16	,	,	PUNCT
ap-1187	48	17	namely	namely	ADV
ap-1187	48	18	,	,	PUNCT
ap-1187	48	19	to	to	PART
ap-1187	48	20	impose	impose	VERB
ap-1187	48	21	the	the	DET
ap-1187	48	22	following	follow	VERB
ap-1187	48	23	relations	relation	NOUN
ap-1187	48	24	:	:	PUNCT
ap-1187	48	25	θaθ̄ḃ	θaθ̄ḃ	PROPN
ap-1187	48	26	=	=	PUNCT
ap-1187	48	27	−j	−j	NOUN
ap-1187	48	28	θ̄ḃθa	θ̄ḃθa	ADJ
ap-1187	48	29	,	,	PUNCT
ap-1187	48	30	θ̄ḃθa	θ̄ḃθa	PUNCT
ap-1187	49	1	=	=	SYM
ap-1187	49	2	−j2	−j2	NUM
ap-1187	49	3	θaθ̄ḃ	θaθ̄ḃ	PROPN
ap-1187	49	4	,	,	PUNCT
ap-1187	49	5	(	(	PUNCT
ap-1187	49	6	4	4	NUM
ap-1187	49	7	)	)	PUNCT
ap-1187	49	8	in	in	ADP
ap-1187	49	9	what	what	PRON
ap-1187	49	10	follows	follow	VERB
ap-1187	49	11	,	,	PUNCT
ap-1187	49	12	we	we	PRON
ap-1187	49	13	shall	shall	AUX
ap-1187	49	14	deal	deal	VERB
ap-1187	49	15	with	with	ADP
ap-1187	49	16	the	the	DET
ap-1187	49	17	first	first	ADJ
ap-1187	49	18	two	two	NUM
ap-1187	49	19	simplest	simple	ADJ
ap-1187	49	20	realizations	realization	NOUN
ap-1187	49	21	of	of	ADP
ap-1187	49	22	such	such	ADJ
ap-1187	49	23	algebras	algebra	NOUN
ap-1187	49	24	,	,	PUNCT
ap-1187	49	25	spanned	span	VERB
ap-1187	49	26	by	by	ADP
ap-1187	49	27	two	two	NUM
ap-1187	49	28	or	or	CCONJ
ap-1187	49	29	three	three	NUM
ap-1187	49	30	generators	generator	NOUN
ap-1187	49	31	.	.	PUNCT
ap-1187	50	1	consider	consider	VERB
ap-1187	50	2	the	the	DET
ap-1187	50	3	case	case	NOUN
ap-1187	50	4	when	when	SCONJ
ap-1187	50	5	a	a	DET
ap-1187	50	6	,	,	PUNCT
ap-1187	50	7	b	b	NOUN
ap-1187	50	8	,	,	PUNCT
ap-1187	50	9	.	.	PUNCT
ap-1187	50	10	.	.	PUNCT
ap-1187	50	11	.	.	PUNCT
ap-1187	51	1	=	=	PUNCT
ap-1187	51	2	1	1	NUM
ap-1187	51	3	,	,	PUNCT
ap-1187	51	4	2	2	NUM
ap-1187	51	5	.	.	PUNCT
ap-1187	52	1	the	the	DET
ap-1187	52	2	algebra	algebra	NOUN
ap-1187	52	3	a	a	DET
ap-1187	52	4	contains	contain	NOUN
ap-1187	52	5	numbers	number	NOUN
ap-1187	52	6	,	,	PUNCT
ap-1187	52	7	two	two	NUM
ap-1187	52	8	generators	generator	NOUN
ap-1187	52	9	of	of	ADP
ap-1187	52	10	grade	grade	NOUN
ap-1187	52	11	1	1	NUM
ap-1187	52	12	,	,	PUNCT
ap-1187	52	13	θ1	θ1	NOUN
ap-1187	52	14	and	and	CCONJ
ap-1187	52	15	θ2	θ2	PROPN
ap-1187	52	16	,	,	PUNCT
ap-1187	52	17	their	their	PRON
ap-1187	52	18	four	four	NUM
ap-1187	52	19	independent	independent	ADJ
ap-1187	52	20	products	product	NOUN
ap-1187	52	21	(	(	PUNCT
ap-1187	52	22	of	of	ADP
ap-1187	52	23	grade	grade	NOUN
ap-1187	52	24	2	2	NUM
ap-1187	52	25	)	)	PUNCT
ap-1187	52	26	,	,	PUNCT
ap-1187	52	27	and	and	CCONJ
ap-1187	52	28	two	two	NUM
ap-1187	52	29	independent	independent	ADJ
ap-1187	52	30	cubic	cubic	ADJ
ap-1187	52	31	expressions	expression	NOUN
ap-1187	52	32	,	,	PUNCT
ap-1187	52	33	θ1θ2θ1	θ1θ2θ1	NOUN
ap-1187	52	34	and	and	CCONJ
ap-1187	52	35	θ2θ1θ2	θ2θ1θ2	ADJ
ap-1187	52	36	.	.	PUNCT
ap-1187	52	37	similar	similar	ADJ
ap-1187	52	38	expressions	expression	NOUN
ap-1187	52	39	can	can	AUX
ap-1187	52	40	be	be	AUX
ap-1187	52	41	produced	produce	VERB
ap-1187	52	42	with	with	ADP
ap-1187	52	43	conjugate	conjugate	ADJ
ap-1187	52	44	generators	generator	NOUN
ap-1187	52	45	θ̄ċ	θ̄ċ	NOUN
ap-1187	52	46	;	;	PUNCT
ap-1187	52	47	finally	finally	ADV
ap-1187	52	48	,	,	PUNCT
ap-1187	52	49	mixed	mixed	ADJ
ap-1187	52	50	expressions	expression	NOUN
ap-1187	52	51	appear	appear	VERB
ap-1187	52	52	,	,	PUNCT
ap-1187	52	53	like	like	ADP
ap-1187	52	54	four	four	NUM
ap-1187	52	55	independent	independent	ADJ
ap-1187	52	56	grade	grade	NOUN
ap-1187	52	57	0	0	NUM
ap-1187	52	58	terms	term	NOUN
ap-1187	52	59	θ1θ̄1̇	θ1θ̄1̇	PROPN
ap-1187	52	60	,	,	PUNCT
ap-1187	52	61	θ1θ̄2̇	θ1θ̄2̇	PROPN
ap-1187	52	62	,	,	PUNCT
ap-1187	52	63	θ2θ̄1̇	θ2θ̄1̇	NOUN
ap-1187	52	64	and	and	CCONJ
ap-1187	52	65	θ2θ̄2̇.	θ2θ̄2̇.	PROPN
ap-1187	53	1	3	3	X
ap-1187	53	2	.	.	PUNCT
ap-1187	53	3	let	let	VERB
ap-1187	53	4	us	we	PRON
ap-1187	53	5	consider	consider	VERB
ap-1187	53	6	multilinear	multilinear	NOUN
ap-1187	53	7	forms	form	NOUN
ap-1187	53	8	defined	define	VERB
ap-1187	53	9	on	on	ADP
ap-1187	53	10	the	the	DET
ap-1187	53	11	algebra	algebra	NOUN
ap-1187	53	12	a	a	DET
ap-1187	53	13	⊗	⊗	PROPN
ap-1187	53	14	ā.	ā.	PUNCT
ap-1187	53	15	because	because	SCONJ
ap-1187	53	16	only	only	ADV
ap-1187	53	17	cubic	cubic	ADJ
ap-1187	53	18	relations	relation	NOUN
ap-1187	53	19	are	be	AUX
ap-1187	53	20	imposed	impose	VERB
ap-1187	53	21	on	on	ADP
ap-1187	53	22	products	product	NOUN
ap-1187	53	23	in	in	ADP
ap-1187	53	24	a	a	PRON
ap-1187	53	25	and	and	CCONJ
ap-1187	53	26	in	in	ADP
ap-1187	53	27	ā	ā	NOUN
ap-1187	53	28	,	,	PUNCT
ap-1187	53	29	and	and	CCONJ
ap-1187	53	30	the	the	DET
ap-1187	53	31	binary	binary	ADJ
ap-1187	53	32	relations	relation	NOUN
ap-1187	53	33	on	on	ADP
ap-1187	53	34	the	the	DET
ap-1187	53	35	products	product	NOUN
ap-1187	53	36	of	of	ADP
ap-1187	53	37	ordinary	ordinary	ADJ
ap-1187	53	38	and	and	CCONJ
ap-1187	53	39	conjugate	conjugate	ADJ
ap-1187	53	40	elements	element	NOUN
ap-1187	53	41	,	,	PUNCT
ap-1187	53	42	we	we	PRON
ap-1187	53	43	shall	shall	AUX
ap-1187	53	44	fix	fix	VERB
ap-1187	53	45	our	our	PRON
ap-1187	53	46	attention	attention	NOUN
ap-1187	53	47	on	on	ADP
ap-1187	53	48	tri	tri	ADJ
ap-1187	53	49	-	-	ADJ
ap-1187	53	50	linear	linear	ADJ
ap-1187	53	51	and	and	CCONJ
ap-1187	53	52	bi	bi	ADJ
ap-1187	53	53	-	-	ADJ
ap-1187	53	54	linear	linear	ADJ
ap-1187	53	55	forms	form	NOUN
ap-1187	53	56	,	,	PUNCT
ap-1187	53	57	conceived	conceive	VERB
ap-1187	53	58	as	as	ADP
ap-1187	53	59	mappings	mapping	NOUN
ap-1187	53	60	of	of	ADP
ap-1187	53	61	a	a	DET
ap-1187	53	62	⊗	⊗	PROPN
ap-1187	53	63	ā	ā	NOUN
ap-1187	53	64	into	into	ADP
ap-1187	53	65	certain	certain	ADJ
ap-1187	53	66	linear	linear	ADJ
ap-1187	53	67	spaces	space	NOUN
ap-1187	53	68	over	over	ADP
ap-1187	53	69	complex	complex	ADJ
ap-1187	53	70	numbers	number	NOUN
ap-1187	53	71	.	.	PUNCT
ap-1187	54	1	let	let	VERB
ap-1187	54	2	us	we	PRON
ap-1187	54	3	consider	consider	VERB
ap-1187	54	4	a	a	DET
ap-1187	54	5	tri	tri	ADJ
ap-1187	54	6	-	-	ADJ
ap-1187	54	7	linear	linear	ADJ
ap-1187	54	8	form	form	NOUN
ap-1187	54	9	ρα	ρα	PROPN
ap-1187	54	10	abc	abc	PROPN
ap-1187	54	11	.	.	PUNCT
ap-1187	55	1	obviously	obviously	ADV
ap-1187	55	2	,	,	PUNCT
ap-1187	55	3	as	as	SCONJ
ap-1187	55	4	ρα	ρα	PROPN
ap-1187	55	5	abc	abc	PROPN
ap-1187	55	6	θaθbθc	θaθbθc	PROPN
ap-1187	55	7	=	=	PUNCT
ap-1187	56	1	ρα	ρα	PROPN
ap-1187	56	2	bca	bca	PROPN
ap-1187	56	3	θbθcθa	θbθcθa	PROPN
ap-1187	56	4	=	=	SYM
ap-1187	56	5	ρα	ρα	PROPN
ap-1187	56	6	cab	cab	NOUN
ap-1187	56	7	θcθaθb	θcθaθb	PRON
ap-1187	56	8	,	,	PUNCT
ap-1187	56	9	by	by	ADP
ap-1187	56	10	virtue	virtue	NOUN
ap-1187	56	11	of	of	ADP
ap-1187	56	12	the	the	DET
ap-1187	56	13	commutation	commutation	NOUN
ap-1187	56	14	relations	relation	NOUN
ap-1187	56	15	(	(	PUNCT
ap-1187	56	16	1	1	X
ap-1187	56	17	)	)	PUNCT
ap-1187	56	18	it	it	PRON
ap-1187	56	19	follows	follow	VERB
ap-1187	56	20	that	that	SCONJ
ap-1187	56	21	we	we	PRON
ap-1187	56	22	must	must	AUX
ap-1187	56	23	have	have	VERB
ap-1187	56	24	ρα	ρα	PROPN
ap-1187	56	25	abc	abc	PROPN
ap-1187	56	26	=	=	SYM
ap-1187	56	27	j2	j2	PROPN
ap-1187	56	28	ρα	ρα	PROPN
ap-1187	56	29	bca	bca	PROPN
ap-1187	56	30	=	=	PUNCT
ap-1187	56	31	j	j	PROPN
ap-1187	56	32	ρα	ρα	PROPN
ap-1187	56	33	cab	cab	PROPN
ap-1187	56	34	.	.	PUNCT
ap-1187	57	1	(	(	PUNCT
ap-1187	57	2	5	5	NUM
ap-1187	57	3	)	)	PUNCT
ap-1187	57	4	even	even	ADV
ap-1187	57	5	in	in	ADP
ap-1187	57	6	this	this	DET
ap-1187	57	7	minimal	minimal	ADJ
ap-1187	57	8	and	and	CCONJ
ap-1187	57	9	discrete	discrete	ADJ
ap-1187	57	10	case	case	NOUN
ap-1187	57	11	,	,	PUNCT
ap-1187	57	12	there	there	PRON
ap-1187	57	13	are	be	VERB
ap-1187	57	14	covariant	covariant	ADJ
ap-1187	57	15	and	and	CCONJ
ap-1187	57	16	contravariant	contravariant	ADJ
ap-1187	57	17	indices	index	NOUN
ap-1187	57	18	:	:	PUNCT
ap-1187	57	19	the	the	DET
ap-1187	57	20	lower	low	ADJ
ap-1187	57	21	case	case	NOUN
ap-1187	57	22	and	and	CCONJ
ap-1187	57	23	the	the	DET
ap-1187	57	24	upper	upper	ADJ
ap-1187	57	25	case	case	NOUN
ap-1187	57	26	indices	indice	VERB
ap-1187	57	27	display	display	VERB
ap-1187	57	28	inverse	inverse	NOUN
ap-1187	57	29	transformation	transformation	NOUN
ap-1187	57	30	properties	property	NOUN
ap-1187	57	31	.	.	PUNCT
ap-1187	58	1	if	if	SCONJ
ap-1187	58	2	a	a	DET
ap-1187	58	3	given	give	VERB
ap-1187	58	4	cyclic	cyclic	ADJ
ap-1187	58	5	permutation	permutation	NOUN
ap-1187	58	6	is	be	AUX
ap-1187	58	7	represented	represent	VERB
ap-1187	58	8	by	by	ADP
ap-1187	58	9	a	a	DET
ap-1187	58	10	multiplication	multiplication	NOUN
ap-1187	58	11	by	by	ADP
ap-1187	58	12	j	j	PROPN
ap-1187	58	13	for	for	ADP
ap-1187	58	14	the	the	DET
ap-1187	58	15	upper	upper	ADJ
ap-1187	58	16	indices	index	NOUN
ap-1187	58	17	,	,	PUNCT
ap-1187	58	18	the	the	DET
ap-1187	58	19	same	same	ADJ
ap-1187	58	20	permutation	permutation	NOUN
ap-1187	58	21	performed	perform	VERB
ap-1187	58	22	on	on	ADP
ap-1187	58	23	the	the	DET
ap-1187	58	24	lower	low	ADJ
ap-1187	58	25	indices	index	NOUN
ap-1187	58	26	is	be	AUX
ap-1187	58	27	represented	represent	VERB
ap-1187	58	28	by	by	ADP
ap-1187	58	29	multiplication	multiplication	NOUN
ap-1187	58	30	by	by	ADP
ap-1187	58	31	the	the	DET
ap-1187	58	32	inverse	inverse	NOUN
ap-1187	58	33	,	,	PUNCT
ap-1187	58	34	i.e.	i.e.	X
ap-1187	58	35	j2	j2	PROPN
ap-1187	58	36	,	,	PUNCT
ap-1187	58	37	so	so	SCONJ
ap-1187	58	38	that	that	SCONJ
ap-1187	58	39	they	they	PRON
ap-1187	58	40	compensate	compensate	VERB
ap-1187	58	41	each	each	DET
ap-1187	58	42	other	other	ADJ
ap-1187	58	43	.	.	PUNCT
ap-1187	59	1	similar	similar	ADJ
ap-1187	59	2	reasoning	reasoning	NOUN
ap-1187	59	3	leads	lead	VERB
ap-1187	59	4	to	to	ADP
ap-1187	59	5	the	the	DET
ap-1187	59	6	definition	definition	NOUN
ap-1187	59	7	of	of	ADP
ap-1187	59	8	the	the	DET
ap-1187	59	9	conjugate	conjugate	ADJ
ap-1187	59	10	forms	form	NOUN
ap-1187	59	11	ρα̇	ρα̇	ADJ
ap-1187	59	12	ċḃȧ	ċḃȧ	VERB
ap-1187	59	13	satisfying	satisfy	VERB
ap-1187	59	14	the	the	DET
ap-1187	59	15	relations	relation	NOUN
ap-1187	59	16	(	(	PUNCT
ap-1187	59	17	5	5	NUM
ap-1187	59	18	)	)	PUNCT
ap-1187	59	19	with	with	ADP
ap-1187	59	20	j	j	PROPN
ap-1187	59	21	replaced	replace	VERB
ap-1187	59	22	by	by	ADP
ap-1187	59	23	j2	j2	PROPN
ap-1187	59	24	:	:	PUNCT
ap-1187	59	25	ρ̄α̇	ρ̄α̇	ADJ
ap-1187	59	26	ȧḃċ	ȧḃċ	X
ap-1187	60	1	=	=	PUNCT
ap-1187	60	2	jρ̄α̇	jρ̄α̇	NOUN
ap-1187	60	3	ḃċȧ	ḃċȧ	NOUN
ap-1187	60	4	=	=	SYM
ap-1187	60	5	j2ρ̄α̇	j2ρ̄α̇	NUM
ap-1187	60	6	ċȧḃ	ċȧḃ	NOUN
ap-1187	60	7	(	(	PUNCT
ap-1187	60	8	6	6	NUM
ap-1187	60	9	)	)	PUNCT
ap-1187	60	10	in	in	ADP
ap-1187	60	11	the	the	DET
ap-1187	60	12	case	case	NOUN
ap-1187	60	13	of	of	ADP
ap-1187	60	14	two	two	NUM
ap-1187	60	15	generators	generator	NOUN
ap-1187	60	16	,	,	PUNCT
ap-1187	60	17	there	there	PRON
ap-1187	60	18	are	be	VERB
ap-1187	60	19	only	only	ADV
ap-1187	60	20	two	two	NUM
ap-1187	60	21	independent	independent	ADJ
ap-1187	60	22	sets	set	NOUN
ap-1187	60	23	of	of	ADP
ap-1187	60	24	indices	index	NOUN
ap-1187	60	25	.	.	PUNCT
ap-1187	61	1	therefore	therefore	ADV
ap-1187	61	2	the	the	DET
ap-1187	61	3	upper	upper	ADJ
ap-1187	61	4	indices	index	NOUN
ap-1187	61	5	α	α	X
ap-1187	61	6	,	,	PUNCT
ap-1187	61	7	β̇	β̇	PRON
ap-1187	61	8	take	take	VERB
ap-1187	61	9	on	on	ADP
ap-1187	61	10	the	the	DET
ap-1187	61	11	values	value	NOUN
ap-1187	61	12	1	1	NUM
ap-1187	61	13	or	or	CCONJ
ap-1187	61	14	2	2	NUM
ap-1187	61	15	.	.	X
ap-1187	62	1	we	we	PRON
ap-1187	62	2	choose	choose	VERB
ap-1187	62	3	the	the	DET
ap-1187	62	4	following	following	ADJ
ap-1187	62	5	notation	notation	NOUN
ap-1187	62	6	:	:	PUNCT
ap-1187	62	7	ρ1121	ρ1121	NUM
ap-1187	62	8	=	=	SYM
ap-1187	62	9	jρ1112	jρ1112	PROPN
ap-1187	62	10	=	=	SYM
ap-1187	62	11	j2ρ1211	j2ρ1211	PROPN
ap-1187	62	12	;	;	PUNCT
ap-1187	62	13	ρ2212	ρ2212	PROPN
ap-1187	62	14	=	=	SYM
ap-1187	62	15	jρ2221	jρ2221	NOUN
ap-1187	62	16	=	=	SYM
ap-1187	62	17	j2ρ2122	j2ρ2122	PROPN
ap-1187	62	18	,	,	PUNCT
ap-1187	62	19	(	(	PUNCT
ap-1187	62	20	7	7	X
ap-1187	62	21	)	)	PUNCT
ap-1187	62	22	all	all	DET
ap-1187	62	23	other	other	ADJ
ap-1187	62	24	components	component	NOUN
ap-1187	62	25	identically	identically	ADV
ap-1187	62	26	vanishing	vanish	VERB
ap-1187	62	27	.	.	PUNCT
ap-1187	63	1	the	the	DET
ap-1187	63	2	conjugate	conjugate	ADJ
ap-1187	63	3	matrices	matrix	NOUN
ap-1187	63	4	ρ̄α̇	ρ̄α̇	ADJ
ap-1187	63	5	ḃċȧ	ḃċȧ	NOUN
ap-1187	63	6	are	be	AUX
ap-1187	63	7	defined	define	VERB
ap-1187	63	8	by	by	ADP
ap-1187	63	9	the	the	DET
ap-1187	63	10	same	same	ADJ
ap-1187	63	11	formulae	formulae	NOUN
ap-1187	63	12	,	,	PUNCT
ap-1187	63	13	with	with	ADP
ap-1187	63	14	j	j	PROPN
ap-1187	63	15	replaced	replace	VERB
ap-1187	63	16	by	by	ADP
ap-1187	63	17	j2	j2	PROPN
ap-1187	63	18	and	and	CCONJ
ap-1187	63	19	vice	vice	NOUN
ap-1187	63	20	versa	versa	ADV
ap-1187	63	21	.	.	PUNCT
ap-1187	64	1	the	the	DET
ap-1187	64	2	constitutive	constitutive	ADJ
ap-1187	64	3	cubic	cubic	ADJ
ap-1187	64	4	relations	relation	NOUN
ap-1187	64	5	between	between	ADP
ap-1187	64	6	the	the	DET
ap-1187	64	7	generators	generator	NOUN
ap-1187	64	8	of	of	ADP
ap-1187	64	9	the	the	DET
ap-1187	64	10	z3	z3	PROPN
ap-1187	64	11	graded	grade	VERB
ap-1187	64	12	algebra	algebra	NOUN
ap-1187	64	13	can	can	AUX
ap-1187	64	14	be	be	AUX
ap-1187	64	15	considered	consider	VERB
ap-1187	64	16	as	as	ADP
ap-1187	64	17	intrinsic	intrinsic	ADJ
ap-1187	64	18	if	if	SCONJ
ap-1187	64	19	they	they	PRON
ap-1187	64	20	are	be	AUX
ap-1187	64	21	conserved	conserve	VERB
ap-1187	64	22	after	after	ADP
ap-1187	64	23	linear	linear	ADJ
ap-1187	64	24	transformations	transformation	NOUN
ap-1187	64	25	with	with	ADP
ap-1187	64	26	commuting	commuting	NOUN
ap-1187	64	27	(	(	PUNCT
ap-1187	64	28	pure	pure	ADJ
ap-1187	64	29	number	number	NOUN
ap-1187	64	30	)	)	PUNCT
ap-1187	64	31	coefficients	coefficient	NOUN
ap-1187	64	32	,	,	PUNCT
ap-1187	64	33	i.e.	i.e.	X
ap-1187	64	34	if	if	SCONJ
ap-1187	64	35	they	they	PRON
ap-1187	64	36	are	be	AUX
ap-1187	64	37	independent	independent	ADJ
ap-1187	64	38	of	of	ADP
ap-1187	64	39	the	the	DET
ap-1187	64	40	choice	choice	NOUN
ap-1187	64	41	of	of	ADP
ap-1187	64	42	the	the	DET
ap-1187	64	43	basis	basis	NOUN
ap-1187	64	44	.	.	PUNCT
ap-1187	65	1	let	let	VERB
ap-1187	65	2	38	38	NUM
ap-1187	65	3	acta	acta	PROPN
ap-1187	65	4	polytechnica	polytechnica	PROPN
ap-1187	65	5	vol	vol	NOUN
ap-1187	65	6	.	.	PROPN
ap-1187	66	1	50	50	NUM
ap-1187	66	2	no	no	NOUN
ap-1187	66	3	.	.	PUNCT
ap-1187	67	1	3/2010	3/2010	NUM
ap-1187	67	2	ua′	ua′	NOUN
ap-1187	67	3	a	a	DET
ap-1187	67	4	denote	denote	NOUN
ap-1187	67	5	a	a	DET
ap-1187	67	6	non	non	ADJ
ap-1187	67	7	-	-	ADJ
ap-1187	67	8	singular	singular	ADJ
ap-1187	67	9	n	n	ADP
ap-1187	67	10	×n	×n	ADJ
ap-1187	67	11	matrix	matrix	NOUN
ap-1187	67	12	,	,	PUNCT
ap-1187	67	13	transforming	transform	VERB
ap-1187	67	14	the	the	DET
ap-1187	67	15	generators	generator	NOUN
ap-1187	67	16	θa	θa	PRON
ap-1187	67	17	into	into	ADP
ap-1187	67	18	another	another	DET
ap-1187	67	19	set	set	NOUN
ap-1187	67	20	of	of	ADP
ap-1187	67	21	generators	generator	NOUN
ap-1187	67	22	,	,	PUNCT
ap-1187	67	23	θb′	θb′	NOUN
ap-1187	67	24	=	=	PUNCT
ap-1187	67	25	ub′	ub′	PROPN
ap-1187	67	26	b	b	SYM
ap-1187	67	27	θb	θb	PROPN
ap-1187	67	28	.	.	PUNCT
ap-1187	68	1	the	the	DET
ap-1187	68	2	primed	prime	VERB
ap-1187	68	3	indices	index	NOUN
ap-1187	68	4	run	run	VERB
ap-1187	68	5	over	over	ADP
ap-1187	68	6	the	the	DET
ap-1187	68	7	same	same	ADJ
ap-1187	68	8	range	range	NOUN
ap-1187	68	9	of	of	ADP
ap-1187	68	10	values	value	NOUN
ap-1187	68	11	,	,	PUNCT
ap-1187	68	12	i.e.	i.e.	X
ap-1187	68	13	from	from	ADP
ap-1187	68	14	1	1	NUM
ap-1187	68	15	to	to	ADP
ap-1187	68	16	2	2	NUM
ap-1187	68	17	;	;	PUNCT
ap-1187	68	18	the	the	DET
ap-1187	68	19	prime	prime	NOUN
ap-1187	68	20	is	be	AUX
ap-1187	68	21	there	there	PRON
ap-1187	68	22	just	just	ADV
ap-1187	68	23	to	to	PART
ap-1187	68	24	make	make	VERB
ap-1187	68	25	clear	clear	ADJ
ap-1187	68	26	we	we	PRON
ap-1187	68	27	are	be	AUX
ap-1187	68	28	referring	refer	VERB
ap-1187	68	29	to	to	ADP
ap-1187	68	30	a	a	DET
ap-1187	68	31	new	new	ADJ
ap-1187	68	32	basis	basis	NOUN
ap-1187	68	33	.	.	PUNCT
ap-1187	69	1	we	we	PRON
ap-1187	69	2	are	be	AUX
ap-1187	69	3	looking	look	VERB
ap-1187	69	4	for	for	ADP
ap-1187	69	5	the	the	DET
ap-1187	69	6	solution	solution	NOUN
ap-1187	69	7	of	of	ADP
ap-1187	69	8	the	the	DET
ap-1187	69	9	covariance	covariance	NOUN
ap-1187	69	10	condition	condition	NOUN
ap-1187	69	11	for	for	ADP
ap-1187	69	12	the	the	DET
ap-1187	69	13	ρ	ρ	NOUN
ap-1187	69	14	-	-	PUNCT
ap-1187	69	15	matrices	matrix	NOUN
ap-1187	69	16	:	:	PUNCT
ap-1187	69	17	λα′	λα′	ADP
ap-1187	69	18	β	β	X
ap-1187	69	19	ρβ	ρβ	PROPN
ap-1187	69	20	abc	abc	PROPN
ap-1187	69	21	=	=	SYM
ap-1187	69	22	ua′	ua′	PROPN
ap-1187	69	23	a	a	DET
ap-1187	69	24	ub′	ub′	PROPN
ap-1187	69	25	b	b	NOUN
ap-1187	69	26	uc′	uc′	NOUN
ap-1187	69	27	c	c	PROPN
ap-1187	69	28	ρα′	ρα′	ADV
ap-1187	69	29	a′b′c′	a′b′c′	PROPN
ap-1187	69	30	.	.	PUNCT
ap-1187	70	1	(	(	PUNCT
ap-1187	70	2	8)	8)	NUM
ap-1187	70	3	let	let	VERB
ap-1187	70	4	us	we	PRON
ap-1187	70	5	write	write	VERB
ap-1187	70	6	down	down	ADP
ap-1187	70	7	the	the	DET
ap-1187	70	8	explicit	explicit	ADJ
ap-1187	70	9	expression	expression	NOUN
ap-1187	70	10	,	,	PUNCT
ap-1187	70	11	with	with	ADP
ap-1187	70	12	fixed	fix	VERB
ap-1187	70	13	indices	index	NOUN
ap-1187	70	14	(	(	PUNCT
ap-1187	70	15	abc	abc	PROPN
ap-1187	70	16	)	)	PUNCT
ap-1187	70	17	on	on	ADP
ap-1187	70	18	the	the	DET
ap-1187	70	19	left	left	ADJ
ap-1187	70	20	-	-	PUNCT
ap-1187	70	21	hand	hand	NOUN
ap-1187	70	22	side	side	NOUN
ap-1187	70	23	.	.	PUNCT
ap-1187	71	1	let	let	VERB
ap-1187	71	2	us	we	PRON
ap-1187	71	3	choose	choose	VERB
ap-1187	71	4	one	one	NUM
ap-1187	71	5	of	of	ADP
ap-1187	71	6	the	the	DET
ap-1187	71	7	two	two	NUM
ap-1187	71	8	available	available	ADJ
ap-1187	71	9	combinations	combination	NOUN
ap-1187	71	10	of	of	ADP
ap-1187	71	11	indices	index	NOUN
ap-1187	71	12	,	,	PUNCT
ap-1187	71	13	(	(	PUNCT
ap-1187	71	14	abc	abc	PROPN
ap-1187	71	15	)	)	PUNCT
ap-1187	71	16	=	=	PUNCT
ap-1187	72	1	(	(	PUNCT
ap-1187	72	2	121	121	NUM
ap-1187	72	3	)	)	PUNCT
ap-1187	72	4	;	;	PUNCT
ap-1187	72	5	then	then	ADV
ap-1187	72	6	the	the	DET
ap-1187	72	7	upper	upper	ADJ
ap-1187	72	8	index	index	NOUN
ap-1187	72	9	of	of	ADP
ap-1187	72	10	the	the	DET
ap-1187	72	11	ρ	ρ	NOUN
ap-1187	72	12	-	-	PUNCT
ap-1187	72	13	matrix	matrix	NOUN
ap-1187	72	14	is	be	AUX
ap-1187	72	15	also	also	ADV
ap-1187	72	16	fixed	fix	VERB
ap-1187	72	17	and	and	CCONJ
ap-1187	72	18	equal	equal	ADJ
ap-1187	72	19	to	to	ADP
ap-1187	72	20	1	1	NUM
ap-1187	72	21	:	:	PUNCT
ap-1187	72	22	λα′	λα′	PROPN
ap-1187	72	23	1	1	NUM
ap-1187	72	24	ρ1121	ρ1121	NUM
ap-1187	72	25	=	=	SYM
ap-1187	72	26	ua′	ua′	PROPN
ap-1187	72	27	1	1	NUM
ap-1187	72	28	ub′	ub′	PROPN
ap-1187	72	29	2	2	NUM
ap-1187	72	30	uc′	uc′	NOUN
ap-1187	72	31	1	1	NUM
ap-1187	72	32	ρα′	ρα′	NOUN
ap-1187	72	33	a′b′c′	a′b′c′	NOUN
ap-1187	72	34	.	.	PUNCT
ap-1187	73	1	(	(	PUNCT
ap-1187	73	2	9	9	X
ap-1187	73	3	)	)	PUNCT
ap-1187	73	4	now	now	ADV
ap-1187	73	5	,	,	PUNCT
ap-1187	73	6	ρ1121	ρ1121	PROPN
ap-1187	73	7	=	=	SYM
ap-1187	73	8	1	1	NUM
ap-1187	73	9	,	,	PUNCT
ap-1187	73	10	and	and	CCONJ
ap-1187	73	11	we	we	PRON
ap-1187	73	12	have	have	VERB
ap-1187	73	13	two	two	NUM
ap-1187	73	14	equations	equation	NOUN
ap-1187	73	15	corresponding	correspond	VERB
ap-1187	73	16	to	to	ADP
ap-1187	73	17	the	the	DET
ap-1187	73	18	choice	choice	NOUN
ap-1187	73	19	of	of	ADP
ap-1187	73	20	values	value	NOUN
ap-1187	73	21	of	of	ADP
ap-1187	73	22	the	the	DET
ap-1187	73	23	index	index	NOUN
ap-1187	73	24	α′	α′	NUM
ap-1187	73	25	equal	equal	ADJ
ap-1187	73	26	to	to	ADP
ap-1187	73	27	1	1	NUM
ap-1187	73	28	or	or	CCONJ
ap-1187	73	29	2	2	NUM
ap-1187	73	30	.	.	PUNCT
ap-1187	74	1	for	for	ADP
ap-1187	74	2	α′	α′	NUM
ap-1187	74	3	=	=	SYM
ap-1187	74	4	1′	1′	NUM
ap-1187	74	5	the	the	DET
ap-1187	74	6	ρ	ρ	NOUN
ap-1187	74	7	-	-	NOUN
ap-1187	74	8	matrix	matrix	NOUN
ap-1187	74	9	on	on	ADP
ap-1187	74	10	the	the	DET
ap-1187	74	11	right	right	ADJ
ap-1187	74	12	-	-	PUNCT
ap-1187	74	13	hand	hand	NOUN
ap-1187	74	14	side	side	NOUN
ap-1187	74	15	is	be	AUX
ap-1187	74	16	ρ1	ρ1	NOUN
ap-1187	74	17	′	′	NUM
ap-1187	74	18	a′b′c′	a′b′c′	NOUN
ap-1187	74	19	,	,	PUNCT
ap-1187	74	20	which	which	PRON
ap-1187	74	21	has	have	VERB
ap-1187	74	22	only	only	ADV
ap-1187	74	23	three	three	NUM
ap-1187	74	24	components	component	NOUN
ap-1187	74	25	,	,	PUNCT
ap-1187	74	26	ρ1	ρ1	NOUN
ap-1187	74	27	′	′	NOUN
ap-1187	74	28	1′2′1′	1′2′1′	NUM
ap-1187	74	29	=	=	SYM
ap-1187	74	30	1	1	NUM
ap-1187	74	31	,	,	PUNCT
ap-1187	74	32	ρ1	ρ1	NOUN
ap-1187	74	33	′	′	NUM
ap-1187	74	34	2′1′1′	2′1′1′	NUM
ap-1187	74	35	=	=	SYM
ap-1187	74	36	j2	j2	PROPN
ap-1187	74	37	,	,	PUNCT
ap-1187	74	38	ρ1	ρ1	NOUN
ap-1187	74	39	′	′	NUM
ap-1187	74	40	1′1′2′	1′1′2′	NUM
ap-1187	74	41	=	=	SYM
ap-1187	74	42	j	j	PROPN
ap-1187	74	43	,	,	PUNCT
ap-1187	74	44	which	which	PRON
ap-1187	74	45	leads	lead	VERB
ap-1187	74	46	to	to	ADP
ap-1187	74	47	the	the	DET
ap-1187	74	48	following	follow	VERB
ap-1187	74	49	equation	equation	NOUN
ap-1187	74	50	:	:	PUNCT
ap-1187	74	51	λ1	λ1	ADJ
ap-1187	74	52	′	′	NOUN
ap-1187	74	53	1	1	NUM
ap-1187	74	54	=	=	SYM
ap-1187	74	55	u1	u1	NOUN
ap-1187	74	56	′	′	NOUN
ap-1187	74	57	1	1	NUM
ap-1187	74	58	u2	u2	NOUN
ap-1187	74	59	′	′	ADJ
ap-1187	74	60	2	2	NUM
ap-1187	74	61	u1	u1	NOUN
ap-1187	74	62	′	′	NOUN
ap-1187	74	63	1	1	NUM
ap-1187	75	1	+	+	CCONJ
ap-1187	75	2	j2	j2	PROPN
ap-1187	75	3	u2	u2	PROPN
ap-1187	75	4	′	′	NOUN
ap-1187	75	5	1	1	NUM
ap-1187	75	6	u1	u1	NOUN
ap-1187	75	7	′	′	NUM
ap-1187	75	8	2	2	NUM
ap-1187	75	9	u1	u1	NOUN
ap-1187	75	10	′	′	NOUN
ap-1187	75	11	1	1	NUM
ap-1187	76	1	+	+	CCONJ
ap-1187	76	2	j	j	PROPN
ap-1187	76	3	u1	u1	NOUN
ap-1187	76	4	′	′	NOUN
ap-1187	76	5	1	1	NUM
ap-1187	76	6	u1	u1	NOUN
ap-1187	76	7	′	′	NOUN
ap-1187	76	8	2	2	NUM
ap-1187	76	9	u2	u2	NOUN
ap-1187	76	10	′	′	NOUN
ap-1187	76	11	1	1	NUM
ap-1187	76	12	=	=	SYM
ap-1187	76	13	=	=	SYM
ap-1187	76	14	u1	u1	NOUN
ap-1187	76	15	′	′	NOUN
ap-1187	76	16	1	1	NUM
ap-1187	76	17	(	(	PUNCT
ap-1187	76	18	u	u	NOUN
ap-1187	76	19	2′	2′	NUM
ap-1187	76	20	2	2	NUM
ap-1187	76	21	u1	u1	NOUN
ap-1187	76	22	′	′	NOUN
ap-1187	76	23	1	1	NUM
ap-1187	76	24	−	−	PROPN
ap-1187	77	1	u2	u2	NOUN
ap-1187	77	2	′	′	NOUN
ap-1187	77	3	1	1	NUM
ap-1187	77	4	u1	u1	NOUN
ap-1187	77	5	′	′	NOUN
ap-1187	77	6	2	2	NUM
ap-1187	77	7	)	)	PUNCT
ap-1187	77	8	=	=	NOUN
ap-1187	77	9	u1	u1	NOUN
ap-1187	77	10	′	′	NOUN
ap-1187	77	11	1	1	NUM
ap-1187	78	1	[	[	X
ap-1187	78	2	det(u	det(u	NOUN
ap-1187	78	3	)	)	PUNCT
ap-1187	78	4	]	]	PUNCT
ap-1187	78	5	,	,	PUNCT
ap-1187	78	6	(	(	PUNCT
ap-1187	78	7	10	10	NUM
ap-1187	78	8	)	)	PUNCT
ap-1187	78	9	because	because	SCONJ
ap-1187	78	10	j2+j	j2+j	PROPN
ap-1187	78	11	=	=	PUNCT
ap-1187	78	12	−1	−1	NOUN
ap-1187	78	13	.	.	PUNCT
ap-1187	79	1	for	for	ADP
ap-1187	79	2	the	the	DET
ap-1187	79	3	alternative	alternative	ADJ
ap-1187	79	4	choice	choice	NOUN
ap-1187	79	5	α′	α′	ADV
ap-1187	79	6	=	=	SYM
ap-1187	79	7	2′	2′	NUM
ap-1187	79	8	the	the	DET
ap-1187	79	9	ρ	ρ	NOUN
ap-1187	79	10	-	-	NOUN
ap-1187	79	11	matrix	matrix	NOUN
ap-1187	79	12	on	on	ADP
ap-1187	79	13	the	the	DET
ap-1187	79	14	right	right	ADJ
ap-1187	79	15	-	-	PUNCT
ap-1187	79	16	hand	hand	NOUN
ap-1187	79	17	side	side	NOUN
ap-1187	79	18	is	be	AUX
ap-1187	79	19	ρ2	ρ2	NOUN
ap-1187	79	20	′	′	NUM
ap-1187	79	21	a′b′c′	a′b′c′	NOUN
ap-1187	79	22	,	,	PUNCT
ap-1187	79	23	whose	whose	DET
ap-1187	79	24	three	three	NUM
ap-1187	79	25	non	non	ADJ
ap-1187	79	26	-	-	ADJ
ap-1187	79	27	vanishing	vanishing	ADJ
ap-1187	79	28	components	component	NOUN
ap-1187	79	29	are	be	AUX
ap-1187	79	30	ρ2	ρ2	ADJ
ap-1187	79	31	′	′	NUM
ap-1187	79	32	2′1′2′	2′1′2′	NUM
ap-1187	79	33	=	=	SYM
ap-1187	79	34	1	1	NUM
ap-1187	79	35	,	,	PUNCT
ap-1187	79	36	ρ2	ρ2	VERB
ap-1187	79	37	′	′	NOUN
ap-1187	79	38	1′2′2′	1′2′2′	NUM
ap-1187	79	39	=	=	SYM
ap-1187	79	40	j2	j2	PROPN
ap-1187	79	41	,	,	PUNCT
ap-1187	79	42	ρ2	ρ2	VERB
ap-1187	79	43	′	′	NOUN
ap-1187	79	44	2′2′1′	2′2′1′	NUM
ap-1187	80	1	=	=	PUNCT
ap-1187	80	2	j.	j.	PROPN
ap-1187	81	1	the	the	DET
ap-1187	81	2	corresponding	correspond	VERB
ap-1187	81	3	equation	equation	NOUN
ap-1187	81	4	gives	give	VERB
ap-1187	81	5	:	:	PUNCT
ap-1187	81	6	λ2	λ2	NOUN
ap-1187	81	7	′	′	NOUN
ap-1187	81	8	1	1	NUM
ap-1187	81	9	=	=	SYM
ap-1187	81	10	−u2	−u2	NOUN
ap-1187	81	11	′	′	NOUN
ap-1187	81	12	1	1	NUM
ap-1187	81	13	[	[	X
ap-1187	81	14	det(u	det(u	NOUN
ap-1187	81	15	)	)	PUNCT
ap-1187	81	16	]	]	PUNCT
ap-1187	81	17	,	,	PUNCT
ap-1187	81	18	(	(	PUNCT
ap-1187	81	19	11	11	NUM
ap-1187	81	20	)	)	PUNCT
ap-1187	81	21	the	the	DET
ap-1187	81	22	remaining	remain	VERB
ap-1187	81	23	two	two	NUM
ap-1187	81	24	equations	equation	NOUN
ap-1187	81	25	are	be	AUX
ap-1187	81	26	obtained	obtain	VERB
ap-1187	81	27	in	in	ADP
ap-1187	81	28	a	a	DET
ap-1187	81	29	similar	similar	ADJ
ap-1187	81	30	manner	manner	NOUN
ap-1187	81	31	,	,	PUNCT
ap-1187	81	32	resulting	result	VERB
ap-1187	81	33	in	in	ADP
ap-1187	81	34	the	the	DET
ap-1187	81	35	following	following	NOUN
ap-1187	81	36	:	:	PUNCT
ap-1187	82	1	λ1	λ1	ADJ
ap-1187	82	2	′	′	NOUN
ap-1187	82	3	2	2	NUM
ap-1187	82	4	=	=	SYM
ap-1187	82	5	−u1	−u1	NOUN
ap-1187	82	6	′	′	NOUN
ap-1187	82	7	2	2	NUM
ap-1187	83	1	[	[	X
ap-1187	83	2	det(u	det(u	NOUN
ap-1187	83	3	)	)	PUNCT
ap-1187	83	4	]	]	PUNCT
ap-1187	83	5	,	,	PUNCT
ap-1187	83	6	λ2	λ2	NOUN
ap-1187	83	7	′	′	NOUN
ap-1187	83	8	2	2	NUM
ap-1187	83	9	=	=	SYM
ap-1187	83	10	u2	u2	NOUN
ap-1187	83	11	′	′	NOUN
ap-1187	83	12	2	2	NUM
ap-1187	84	1	[	[	X
ap-1187	84	2	det(u	det(u	NOUN
ap-1187	84	3	)	)	PUNCT
ap-1187	84	4	]	]	PUNCT
ap-1187	84	5	.	.	PUNCT
ap-1187	85	1	(	(	PUNCT
ap-1187	85	2	12	12	NUM
ap-1187	85	3	)	)	PUNCT
ap-1187	85	4	the	the	DET
ap-1187	85	5	determinant	determinant	NOUN
ap-1187	85	6	of	of	ADP
ap-1187	85	7	the	the	DET
ap-1187	85	8	2×	2×	NUM
ap-1187	85	9	2	2	NUM
ap-1187	85	10	complex	complex	ADJ
ap-1187	85	11	matrix	matrix	NOUN
ap-1187	85	12	ua′	ua′	ADP
ap-1187	86	1	b	b	NOUN
ap-1187	86	2	appears	appear	VERB
ap-1187	86	3	everywhere	everywhere	ADV
ap-1187	86	4	on	on	ADP
ap-1187	86	5	the	the	DET
ap-1187	86	6	right	right	ADJ
ap-1187	86	7	-	-	PUNCT
ap-1187	86	8	hand	hand	NOUN
ap-1187	86	9	side	side	NOUN
ap-1187	86	10	.	.	PUNCT
ap-1187	87	1	taking	take	VERB
ap-1187	87	2	the	the	DET
ap-1187	87	3	determinant	determinant	NOUN
ap-1187	87	4	of	of	ADP
ap-1187	87	5	the	the	DET
ap-1187	87	6	matrix	matrix	NOUN
ap-1187	87	7	λα′	λα′	ADP
ap-1187	87	8	β	β	X
ap-1187	87	9	one	one	NOUN
ap-1187	87	10	gets	get	VERB
ap-1187	87	11	immediately	immediately	ADV
ap-1187	87	12	det(λ	det(λ	NUM
ap-1187	87	13	)	)	PUNCT
ap-1187	87	14	=	=	PUNCT
ap-1187	88	1	[	[	X
ap-1187	88	2	det(u)]3	det(u)]3	NOUN
ap-1187	88	3	.	.	PUNCT
ap-1187	89	1	(	(	PUNCT
ap-1187	89	2	13	13	X
ap-1187	89	3	)	)	PUNCT
ap-1187	89	4	taking	take	VERB
ap-1187	89	5	into	into	ADP
ap-1187	89	6	account	account	NOUN
ap-1187	89	7	that	that	SCONJ
ap-1187	89	8	the	the	DET
ap-1187	89	9	inverse	inverse	NOUN
ap-1187	89	10	transformation	transformation	NOUN
ap-1187	89	11	should	should	AUX
ap-1187	89	12	exist	exist	VERB
ap-1187	89	13	and	and	CCONJ
ap-1187	89	14	have	have	VERB
ap-1187	89	15	the	the	DET
ap-1187	89	16	same	same	ADJ
ap-1187	89	17	properties	property	NOUN
ap-1187	89	18	,	,	PUNCT
ap-1187	89	19	we	we	PRON
ap-1187	89	20	arrive	arrive	VERB
ap-1187	89	21	at	at	ADP
ap-1187	89	22	the	the	DET
ap-1187	89	23	conclusion	conclusion	NOUN
ap-1187	89	24	that	that	SCONJ
ap-1187	89	25	detλ	detλ	NOUN
ap-1187	89	26	=	=	SYM
ap-1187	89	27	1	1	NUM
ap-1187	89	28	,	,	PUNCT
ap-1187	89	29	det(λα′	det(λα′	ADJ
ap-1187	89	30	β	β	X
ap-1187	89	31	)	)	PUNCT
ap-1187	90	1	=	=	PUNCT
ap-1187	90	2	λ	λ	NOUN
ap-1187	90	3	1′	1′	NUM
ap-1187	90	4	1	1	NUM
ap-1187	90	5	λ	λ	NOUN
ap-1187	90	6	2′	2′	NUM
ap-1187	90	7	2	2	NUM
ap-1187	90	8	−	−	NOUN
ap-1187	90	9	λ2	λ2	NOUN
ap-1187	90	10	′	′	NOUN
ap-1187	90	11	1	1	NUM
ap-1187	90	12	λ	λ	NOUN
ap-1187	90	13	1′	1′	NUM
ap-1187	90	14	2	2	NUM
ap-1187	90	15	=	=	SYM
ap-1187	90	16	1	1	NUM
ap-1187	90	17	(	(	PUNCT
ap-1187	90	18	14	14	NUM
ap-1187	90	19	)	)	PUNCT
ap-1187	90	20	which	which	PRON
ap-1187	90	21	defines	define	VERB
ap-1187	90	22	the	the	DET
ap-1187	90	23	sl(2,c	sl(2,c	NOUN
ap-1187	90	24	)	)	PUNCT
ap-1187	90	25	group	group	NOUN
ap-1187	90	26	,	,	PUNCT
ap-1187	90	27	the	the	DET
ap-1187	90	28	covering	covering	NOUN
ap-1187	90	29	group	group	NOUN
ap-1187	90	30	of	of	ADP
ap-1187	90	31	the	the	DET
ap-1187	90	32	lorentz	lorentz	PROPN
ap-1187	90	33	group	group	NOUN
ap-1187	90	34	.	.	PUNCT
ap-1187	91	1	however	however	ADV
ap-1187	91	2	,	,	PUNCT
ap-1187	91	3	the	the	DET
ap-1187	91	4	u	u	NOUN
ap-1187	91	5	-matrices	-matrice	NOUN
ap-1187	91	6	on	on	ADP
ap-1187	91	7	the	the	DET
ap-1187	91	8	right	right	ADJ
ap-1187	91	9	-	-	PUNCT
ap-1187	91	10	hand	hand	NOUN
ap-1187	91	11	side	side	NOUN
ap-1187	91	12	are	be	AUX
ap-1187	91	13	defined	define	VERB
ap-1187	91	14	only	only	ADV
ap-1187	91	15	up	up	ADP
ap-1187	91	16	to	to	ADP
ap-1187	91	17	the	the	DET
ap-1187	91	18	phase	phase	NOUN
ap-1187	91	19	,	,	PUNCT
ap-1187	91	20	which	which	PRON
ap-1187	91	21	due	due	ADP
ap-1187	91	22	to	to	ADP
ap-1187	91	23	the	the	DET
ap-1187	91	24	cubic	cubic	ADJ
ap-1187	91	25	character	character	NOUN
ap-1187	91	26	of	of	ADP
ap-1187	91	27	the	the	DET
ap-1187	91	28	relations	relation	NOUN
ap-1187	91	29	(	(	PUNCT
ap-1187	91	30	10–12	10–12	NUM
ap-1187	91	31	)	)	PUNCT
ap-1187	91	32	,	,	PUNCT
ap-1187	91	33	and	and	CCONJ
ap-1187	91	34	they	they	PRON
ap-1187	91	35	can	can	AUX
ap-1187	91	36	take	take	VERB
ap-1187	91	37	on	on	ADP
ap-1187	91	38	three	three	NUM
ap-1187	91	39	different	different	ADJ
ap-1187	91	40	values	value	NOUN
ap-1187	91	41	:	:	PUNCT
ap-1187	91	42	1	1	NUM
ap-1187	91	43	,	,	PUNCT
ap-1187	91	44	j	j	PROPN
ap-1187	91	45	or	or	CCONJ
ap-1187	91	46	j2	j2	PROPN
ap-1187	91	47	,	,	PUNCT
ap-1187	91	48	i.e.	i.e.	X
ap-1187	91	49	the	the	DET
ap-1187	91	50	matrices	matrix	NOUN
ap-1187	91	51	j	j	PROPN
ap-1187	91	52	ua′	ua′	PROPN
ap-1187	91	53	b	b	PROPN
ap-1187	91	54	or	or	CCONJ
ap-1187	91	55	j2	j2	PROPN
ap-1187	91	56	ua′	ua′	PROPN
ap-1187	91	57	b	b	AUX
ap-1187	91	58	satisfy	satisfy	VERB
ap-1187	91	59	the	the	DET
ap-1187	91	60	same	same	ADJ
ap-1187	91	61	relations	relation	NOUN
ap-1187	91	62	as	as	ADP
ap-1187	91	63	the	the	DET
ap-1187	91	64	matrices	matrix	NOUN
ap-1187	92	1	ua′	ua′	ADP
ap-1187	92	2	b	b	NOUN
ap-1187	92	3	defined	define	VERB
ap-1187	92	4	above	above	ADV
ap-1187	92	5	.	.	PUNCT
ap-1187	93	1	the	the	DET
ap-1187	93	2	determinant	determinant	NOUN
ap-1187	93	3	of	of	ADP
ap-1187	93	4	u	u	NOUN
ap-1187	93	5	can	can	AUX
ap-1187	93	6	take	take	VERB
ap-1187	93	7	on	on	ADP
ap-1187	93	8	the	the	DET
ap-1187	93	9	values	value	NOUN
ap-1187	93	10	1	1	NUM
ap-1187	93	11	,	,	PUNCT
ap-1187	93	12	j	j	PROPN
ap-1187	93	13	or	or	CCONJ
ap-1187	93	14	j2	j2	PROPN
ap-1187	93	15	while	while	SCONJ
ap-1187	93	16	det(λ	det(λ	PROPN
ap-1187	93	17	)	)	PUNCT
ap-1187	93	18	=	=	SYM
ap-1187	94	1	1	1	NUM
ap-1187	94	2	let	let	VERB
ap-1187	94	3	us	we	PRON
ap-1187	94	4	then	then	ADV
ap-1187	94	5	choose	choose	VERB
ap-1187	94	6	the	the	DET
ap-1187	94	7	matrices	matrix	NOUN
ap-1187	94	8	λα′	λα′	ADP
ap-1187	94	9	β	β	NOUN
ap-1187	94	10	to	to	PART
ap-1187	94	11	be	be	AUX
ap-1187	94	12	the	the	DET
ap-1187	94	13	usual	usual	ADJ
ap-1187	94	14	spinor	spinor	NOUN
ap-1187	94	15	representation	representation	NOUN
ap-1187	94	16	of	of	ADP
ap-1187	94	17	the	the	DET
ap-1187	94	18	sl(2,c	sl(2,c	NOUN
ap-1187	94	19	)	)	PUNCT
ap-1187	94	20	group	group	NOUN
ap-1187	94	21	,	,	PUNCT
ap-1187	94	22	while	while	SCONJ
ap-1187	94	23	the	the	DET
ap-1187	94	24	matrices	matrix	NOUN
ap-1187	94	25	ua′	ua′	ADP
ap-1187	94	26	b	b	NOUN
ap-1187	94	27	will	will	AUX
ap-1187	94	28	be	be	AUX
ap-1187	94	29	defined	define	VERB
ap-1187	94	30	as	as	SCONJ
ap-1187	94	31	follows	follow	VERB
ap-1187	94	32	:	:	PUNCT
ap-1187	94	33	u1	u1	NOUN
ap-1187	94	34	′	′	NOUN
ap-1187	94	35	1	1	NUM
ap-1187	94	36	=	=	SYM
ap-1187	94	37	jλ1	jλ1	PROPN
ap-1187	94	38	′	′	NUM
ap-1187	94	39	1	1	NUM
ap-1187	94	40	,	,	PUNCT
ap-1187	94	41	u1	u1	VERB
ap-1187	94	42	′	′	NOUN
ap-1187	94	43	2	2	NUM
ap-1187	95	1	=	=	SYM
ap-1187	95	2	−jλ1	−jλ1	PROPN
ap-1187	95	3	′	′	NUM
ap-1187	95	4	2	2	NUM
ap-1187	95	5	,	,	PUNCT
ap-1187	95	6	u2	u2	NOUN
ap-1187	95	7	′	′	NOUN
ap-1187	95	8	1	1	NUM
ap-1187	95	9	=	=	SYM
ap-1187	95	10	−jλ2	−jλ2	PROPN
ap-1187	95	11	′	′	NUM
ap-1187	95	12	1	1	NUM
ap-1187	95	13	,	,	PUNCT
ap-1187	95	14	u2	u2	NOUN
ap-1187	95	15	′	′	NOUN
ap-1187	95	16	2	2	NUM
ap-1187	95	17	=	=	SYM
ap-1187	95	18	jλ2	jλ2	NOUN
ap-1187	95	19	′	′	NUM
ap-1187	95	20	2	2	NUM
ap-1187	95	21	,	,	PUNCT
ap-1187	95	22	(	(	PUNCT
ap-1187	95	23	15	15	NUM
ap-1187	95	24	)	)	PUNCT
ap-1187	95	25	the	the	DET
ap-1187	95	26	determinant	determinant	NOUN
ap-1187	95	27	of	of	ADP
ap-1187	95	28	u	u	PRON
ap-1187	95	29	being	be	AUX
ap-1187	95	30	equal	equal	ADJ
ap-1187	95	31	to	to	ADP
ap-1187	95	32	j2	j2	PROPN
ap-1187	95	33	.	.	PUNCT
ap-1187	96	1	obviously	obviously	ADV
ap-1187	96	2	,	,	PUNCT
ap-1187	96	3	the	the	DET
ap-1187	96	4	same	same	ADJ
ap-1187	96	5	reasoning	reasoning	NOUN
ap-1187	96	6	leads	lead	VERB
ap-1187	96	7	to	to	ADP
ap-1187	96	8	the	the	DET
ap-1187	96	9	conjugate	conjugate	ADJ
ap-1187	96	10	cubic	cubic	ADJ
ap-1187	96	11	representation	representation	NOUN
ap-1187	96	12	of	of	ADP
ap-1187	96	13	sl(2,c	sl(2,c	NOUN
ap-1187	96	14	)	)	PUNCT
ap-1187	96	15	if	if	SCONJ
ap-1187	96	16	we	we	PRON
ap-1187	96	17	require	require	VERB
ap-1187	96	18	the	the	DET
ap-1187	96	19	covariance	covariance	NOUN
ap-1187	96	20	of	of	ADP
ap-1187	96	21	the	the	DET
ap-1187	96	22	conjugate	conjugate	ADJ
ap-1187	96	23	tensor	tensor	NOUN
ap-1187	96	24	ρ̄β̇	ρ̄β̇	NOUN
ap-1187	96	25	ḋėḟ	ḋėḟ	NOUN
ap-1187	96	26	=	=	SYM
ap-1187	96	27	j	j	PROPN
ap-1187	96	28	ρ̄β̇	ρ̄β̇	NOUN
ap-1187	96	29	ėḟ	ėḟ	PUNCT
ap-1187	97	1	ḋ	ḋ	PROPN
ap-1187	97	2	=	=	SYM
ap-1187	97	3	j2	j2	PROPN
ap-1187	97	4	ρ̄β̇	ρ̄β̇	NOUN
ap-1187	97	5	ḟ	ḟ	VERB
ap-1187	97	6	ḋė	ḋė	PRON
ap-1187	97	7	,	,	PUNCT
ap-1187	97	8	by	by	ADP
ap-1187	97	9	imposing	impose	VERB
ap-1187	97	10	the	the	DET
ap-1187	97	11	equation	equation	NOUN
ap-1187	97	12	similar	similar	ADJ
ap-1187	97	13	to	to	ADP
ap-1187	97	14	(	(	PUNCT
ap-1187	97	15	8)	8)	NUM
ap-1187	97	16	λα̇′	λα̇′	PROPN
ap-1187	97	17	β̇	β̇	PROPN
ap-1187	97	18	ρ̄β̇	ρ̄β̇	NOUN
ap-1187	97	19	ȧḃċ	ȧḃċ	X
ap-1187	98	1	=	=	SYM
ap-1187	98	2	ρ̄α̇′	ρ̄α̇′	NOUN
ap-1187	98	3	ȧ′ḃ′ċ′ū	ȧ′ḃ′ċ′ū	PROPN
ap-1187	98	4	ȧ′	ȧ′	VERB
ap-1187	98	5	ȧ	ȧ	PROPN
ap-1187	98	6	ū	ū	NOUN
ap-1187	98	7	ḃ′	ḃ′	VERB
ap-1187	98	8	ḃ	ḃ	PROPN
ap-1187	98	9	ū	ū	NOUN
ap-1187	98	10	ċ′	ċ′	ADJ
ap-1187	98	11	ċ	ċ	PROPN
ap-1187	98	12	.	.	PUNCT
ap-1187	99	1	(	(	PUNCT
ap-1187	99	2	16	16	NUM
ap-1187	99	3	)	)	PUNCT
ap-1187	99	4	matrix	matrix	NOUN
ap-1187	99	5	ū	ū	NOUN
ap-1187	99	6	is	be	AUX
ap-1187	99	7	the	the	DET
ap-1187	99	8	complex	complex	ADJ
ap-1187	99	9	conjugate	conjugate	NOUN
ap-1187	99	10	of	of	ADP
ap-1187	99	11	matrix	matrix	NOUN
ap-1187	99	12	u	u	NOUN
ap-1187	99	13	,	,	PUNCT
ap-1187	99	14	and	and	CCONJ
ap-1187	99	15	det(ū	det(ū	PROPN
ap-1187	99	16	)	)	PUNCT
ap-1187	99	17	is	be	AUX
ap-1187	99	18	equal	equal	ADJ
ap-1187	99	19	to	to	ADP
ap-1187	99	20	j.	j.	PROPN
ap-1187	99	21	moreover	moreover	PROPN
ap-1187	99	22	,	,	PUNCT
ap-1187	99	23	the	the	DET
ap-1187	99	24	two	two	NUM
ap-1187	99	25	-	-	PUNCT
ap-1187	99	26	component	component	NOUN
ap-1187	99	27	entities	entity	NOUN
ap-1187	99	28	obtained	obtain	VERB
ap-1187	99	29	as	as	ADP
ap-1187	99	30	images	image	NOUN
ap-1187	99	31	of	of	ADP
ap-1187	99	32	cubic	cubic	ADJ
ap-1187	99	33	combinations	combination	NOUN
ap-1187	99	34	of	of	ADP
ap-1187	99	35	quarks	quark	NOUN
ap-1187	99	36	,	,	PUNCT
ap-1187	99	37	ψα	ψα	ADP
ap-1187	99	38	=	=	PUNCT
ap-1187	99	39	ρα	ρα	PROPN
ap-1187	99	40	abcθaθbθc	abcθaθbθc	NOUN
ap-1187	99	41	and	and	CCONJ
ap-1187	99	42	ψ̄β̇	ψ̄β̇	NOUN
ap-1187	99	43	=	=	SYM
ap-1187	99	44	ρ̄β̇	ρ̄β̇	NOUN
ap-1187	99	45	ḋėḟ	ḋėḟ	ADJ
ap-1187	99	46	θ̄ḋ	θ̄ḋ	NOUN
ap-1187	99	47	θ̄ė	θ̄ė	NOUN
ap-1187	99	48	θ̄ḟ	θ̄ḟ	NOUN
ap-1187	99	49	should	should	AUX
ap-1187	99	50	anticommute	anticommute	VERB
ap-1187	99	51	,	,	PUNCT
ap-1187	99	52	because	because	SCONJ
ap-1187	99	53	their	their	PRON
ap-1187	99	54	arguments	argument	NOUN
ap-1187	99	55	do	do	VERB
ap-1187	99	56	so	so	ADV
ap-1187	99	57	,	,	PUNCT
ap-1187	99	58	by	by	ADP
ap-1187	99	59	virtue	virtue	NOUN
ap-1187	99	60	of	of	ADP
ap-1187	99	61	(	(	PUNCT
ap-1187	99	62	4	4	NUM
ap-1187	99	63	):	):	PUNCT
ap-1187	99	64	(	(	PUNCT
ap-1187	99	65	θaθbθc)(θ̄ḋ	θaθbθc)(θ̄ḋ	NOUN
ap-1187	99	66	θ̄ė	θ̄ė	NOUN
ap-1187	99	67	θ̄ḟ	θ̄ḟ	NOUN
ap-1187	99	68	)	)	PUNCT
ap-1187	100	1	=	=	PUNCT
ap-1187	100	2	−(θ̄ḋθ̄ė	−(θ̄ḋθ̄ė	ADV
ap-1187	100	3	θ̄ḟ	θ̄ḟ	NOUN
ap-1187	100	4	)	)	PUNCT
ap-1187	100	5	(	(	PUNCT
ap-1187	100	6	θaθbθc	θaθbθc	PROPN
ap-1187	100	7	)	)	PUNCT
ap-1187	100	8	we	we	PRON
ap-1187	100	9	have	have	AUX
ap-1187	100	10	found	find	VERB
ap-1187	100	11	the	the	DET
ap-1187	100	12	way	way	NOUN
ap-1187	100	13	to	to	PART
ap-1187	100	14	derive	derive	VERB
ap-1187	100	15	the	the	DET
ap-1187	100	16	covering	covering	NOUN
ap-1187	100	17	group	group	NOUN
ap-1187	100	18	of	of	ADP
ap-1187	100	19	the	the	DET
ap-1187	100	20	lorentz	lorentz	PROPN
ap-1187	100	21	group	group	NOUN
ap-1187	100	22	acting	act	VERB
ap-1187	100	23	on	on	ADP
ap-1187	100	24	spinors	spinor	NOUN
ap-1187	100	25	via	via	ADP
ap-1187	100	26	the	the	DET
ap-1187	100	27	usual	usual	ADJ
ap-1187	100	28	spinorial	spinorial	ADJ
ap-1187	100	29	representation	representation	NOUN
ap-1187	100	30	.	.	PUNCT
ap-1187	101	1	the	the	DET
ap-1187	101	2	spinors	spinor	NOUN
ap-1187	101	3	are	be	AUX
ap-1187	101	4	obtained	obtain	VERB
ap-1187	101	5	as	as	ADP
ap-1187	101	6	the	the	DET
ap-1187	101	7	homomorphic	homomorphic	ADJ
ap-1187	101	8	image	image	NOUN
ap-1187	101	9	of	of	ADP
ap-1187	101	10	a	a	DET
ap-1187	101	11	tri	tri	ADJ
ap-1187	101	12	-	-	ADJ
ap-1187	101	13	linear	linear	ADJ
ap-1187	101	14	combination	combination	NOUN
ap-1187	101	15	of	of	ADP
ap-1187	101	16	three	three	NUM
ap-1187	101	17	quarks	quark	NOUN
ap-1187	101	18	(	(	PUNCT
ap-1187	101	19	or	or	CCONJ
ap-1187	101	20	anti	anti	ADJ
ap-1187	101	21	-	-	NOUN
ap-1187	101	22	quarks	quark	NOUN
ap-1187	101	23	)	)	PUNCT
ap-1187	101	24	.	.	PUNCT
ap-1187	102	1	the	the	DET
ap-1187	102	2	quarks	quarks	PROPN
ap-1187	102	3	transform	transform	VERB
ap-1187	102	4	with	with	ADP
ap-1187	102	5	matrices	matrix	NOUN
ap-1187	102	6	u	u	NOUN
ap-1187	102	7	(	(	PUNCT
ap-1187	102	8	or	or	CCONJ
ap-1187	102	9	ū	ū	NOUN
ap-1187	102	10	for	for	ADP
ap-1187	102	11	the	the	DET
ap-1187	102	12	anti	anti	ADJ
ap-1187	102	13	-	-	NOUN
ap-1187	102	14	quarks	quark	NOUN
ap-1187	102	15	)	)	PUNCT
ap-1187	102	16	,	,	PUNCT
ap-1187	102	17	but	but	CCONJ
ap-1187	102	18	these	these	DET
ap-1187	102	19	matrices	matrix	NOUN
ap-1187	102	20	are	be	AUX
ap-1187	102	21	not	not	PART
ap-1187	102	22	unitary	unitary	ADJ
ap-1187	102	23	:	:	PUNCT
ap-1187	102	24	their	their	PRON
ap-1187	102	25	determinants	determinant	NOUN
ap-1187	102	26	are	be	AUX
ap-1187	102	27	equal	equal	ADJ
ap-1187	102	28	to	to	ADP
ap-1187	102	29	j2	j2	PROPN
ap-1187	102	30	or	or	CCONJ
ap-1187	102	31	j	j	PROPN
ap-1187	102	32	,	,	PUNCT
ap-1187	102	33	respectively	respectively	ADV
ap-1187	102	34	.	.	PUNCT
ap-1187	103	1	so	so	ADV
ap-1187	103	2	,	,	PUNCT
ap-1187	103	3	quarks	quarks	PROPN
ap-1187	103	4	can	can	AUX
ap-1187	103	5	not	not	PART
ap-1187	103	6	be	be	AUX
ap-1187	103	7	put	put	VERB
ap-1187	103	8	on	on	ADP
ap-1187	103	9	the	the	DET
ap-1187	103	10	same	same	ADJ
ap-1187	103	11	footing	footing	NOUN
ap-1187	103	12	as	as	ADP
ap-1187	103	13	classical	classical	ADJ
ap-1187	103	14	spinors	spinor	NOUN
ap-1187	103	15	;	;	PUNCT
ap-1187	103	16	they	they	PRON
ap-1187	103	17	transform	transform	VERB
ap-1187	103	18	under	under	ADP
ap-1187	103	19	a	a	DET
ap-1187	103	20	z3	z3	NOUN
ap-1187	103	21	-	-	PUNCT
ap-1187	103	22	covering	covering	NOUN
ap-1187	103	23	of	of	ADP
ap-1187	103	24	the	the	DET
ap-1187	103	25	sl(2,c	sl(2,c	NOUN
ap-1187	103	26	)	)	PUNCT
ap-1187	103	27	group	group	NOUN
ap-1187	103	28	.	.	PUNCT
ap-1187	104	1	a	a	DET
ap-1187	104	2	similar	similar	ADJ
ap-1187	104	3	covariance	covariance	NOUN
ap-1187	104	4	requirement	requirement	NOUN
ap-1187	104	5	can	can	AUX
ap-1187	104	6	be	be	AUX
ap-1187	104	7	formulated	formulate	VERB
ap-1187	104	8	with	with	ADP
ap-1187	104	9	respect	respect	NOUN
ap-1187	104	10	to	to	ADP
ap-1187	104	11	the	the	DET
ap-1187	104	12	set	set	NOUN
ap-1187	104	13	of	of	ADP
ap-1187	104	14	2	2	NUM
ap-1187	104	15	-	-	PUNCT
ap-1187	104	16	forms	form	NOUN
ap-1187	104	17	mapping	map	VERB
ap-1187	104	18	the	the	DET
ap-1187	104	19	quadratic	quadratic	ADJ
ap-1187	104	20	quark	quark	ADJ
ap-1187	104	21	-	-	PUNCT
ap-1187	104	22	anti	anti	ADJ
ap-1187	104	23	-	-	ADJ
ap-1187	104	24	quark	quark	ADJ
ap-1187	104	25	combinations	combination	NOUN
ap-1187	104	26	into	into	ADP
ap-1187	104	27	a	a	DET
ap-1187	104	28	fourdimensional	fourdimensional	ADJ
ap-1187	104	29	linear	linear	ADJ
ap-1187	104	30	real	real	ADJ
ap-1187	104	31	space	space	NOUN
ap-1187	104	32	.	.	PUNCT
ap-1187	105	1	as	as	SCONJ
ap-1187	105	2	we	we	PRON
ap-1187	105	3	saw	see	VERB
ap-1187	105	4	already	already	ADV
ap-1187	105	5	,	,	PUNCT
ap-1187	105	6	the	the	DET
ap-1187	105	7	symmetry	symmetry	NOUN
ap-1187	105	8	(	(	PUNCT
ap-1187	105	9	4	4	X
ap-1187	105	10	)	)	PUNCT
ap-1187	105	11	imposed	impose	VERB
ap-1187	105	12	on	on	ADP
ap-1187	105	13	these	these	DET
ap-1187	105	14	expressions	expression	NOUN
ap-1187	105	15	reduces	reduce	VERB
ap-1187	105	16	their	their	PRON
ap-1187	105	17	number	number	NOUN
ap-1187	105	18	to	to	ADP
ap-1187	105	19	four	four	NUM
ap-1187	105	20	.	.	PUNCT
ap-1187	106	1	let	let	VERB
ap-1187	106	2	us	we	PRON
ap-1187	106	3	define	define	VERB
ap-1187	106	4	two	two	NUM
ap-1187	106	5	quadratic	quadratic	ADJ
ap-1187	106	6	forms	form	NOUN
ap-1187	106	7	,	,	PUNCT
ap-1187	106	8	πμ	πμ	VERB
ap-1187	106	9	aḃ	aḃ	PRON
ap-1187	106	10	and	and	CCONJ
ap-1187	106	11	conjugate	conjugate	VERB
ap-1187	106	12	π̄μ	π̄μ	NUM
ap-1187	106	13	ḃa	ḃa	NOUN
ap-1187	106	14	with	with	ADP
ap-1187	106	15	the	the	DET
ap-1187	106	16	following	follow	VERB
ap-1187	106	17	symmetry	symmetry	NOUN
ap-1187	106	18	requirement	requirement	NOUN
ap-1187	106	19	πμ	πμ	VERB
ap-1187	106	20	aḃ	aḃ	PRON
ap-1187	106	21	θaθ̄ḃ	θaθ̄ḃ	NOUN
ap-1187	107	1	=	=	SYM
ap-1187	107	2	π̄μ	π̄μ	VERB
ap-1187	107	3	ḃa	ḃa	NOUN
ap-1187	107	4	θ̄ḃθa	θ̄ḃθa	ADJ
ap-1187	107	5	.	.	PUNCT
ap-1187	108	1	(	(	PUNCT
ap-1187	108	2	17	17	NUM
ap-1187	108	3	)	)	PUNCT
ap-1187	108	4	the	the	DET
ap-1187	108	5	greek	greek	NOUN
ap-1187	108	6	indices	indice	VERB
ap-1187	108	7	μ	μ	PROPN
ap-1187	108	8	,	,	PUNCT
ap-1187	108	9	ν	ν	PROPN
ap-1187	108	10	,	,	PUNCT
ap-1187	108	11	.	.	PUNCT
ap-1187	108	12	.	.	PUNCT
ap-1187	109	1	.	.	PUNCT
ap-1187	110	1	take	take	VERB
ap-1187	110	2	on	on	ADP
ap-1187	110	3	four	four	NUM
ap-1187	110	4	values	value	NOUN
ap-1187	110	5	,	,	PUNCT
ap-1187	110	6	and	and	CCONJ
ap-1187	110	7	we	we	PRON
ap-1187	110	8	shall	shall	AUX
ap-1187	110	9	label	label	VERB
ap-1187	110	10	them	they	PRON
ap-1187	110	11	0	0	NUM
ap-1187	110	12	,	,	PUNCT
ap-1187	110	13	1	1	NUM
ap-1187	110	14	,	,	PUNCT
ap-1187	110	15	2	2	NUM
ap-1187	110	16	,	,	PUNCT
ap-1187	110	17	3	3	NUM
ap-1187	110	18	.	.	PUNCT
ap-1187	111	1	it	it	PRON
ap-1187	111	2	follows	follow	VERB
ap-1187	111	3	immediately	immediately	ADV
ap-1187	111	4	from	from	ADP
ap-1187	111	5	(	(	PUNCT
ap-1187	111	6	4	4	NUM
ap-1187	111	7	)	)	PUNCT
ap-1187	111	8	that	that	PRON
ap-1187	111	9	πμ	πμ	VERB
ap-1187	111	10	aḃ	aḃ	PRON
ap-1187	111	11	=	=	PUNCT
ap-1187	111	12	−j2	−j2	PROPN
ap-1187	111	13	π̄μ	π̄μ	NUM
ap-1187	111	14	ḃa	ḃa	NOUN
ap-1187	111	15	.	.	PUNCT
ap-1187	112	1	(	(	PUNCT
ap-1187	112	2	18	18	NUM
ap-1187	112	3	)	)	PUNCT
ap-1187	112	4	39	39	NUM
ap-1187	112	5	acta	acta	PROPN
ap-1187	112	6	polytechnica	polytechnica	PROPN
ap-1187	112	7	vol	vol	NOUN
ap-1187	112	8	.	.	PROPN
ap-1187	113	1	50	50	NUM
ap-1187	113	2	no	no	NOUN
ap-1187	113	3	.	.	PUNCT
ap-1187	114	1	3/2010	3/2010	NUM
ap-1187	114	2	such	such	ADJ
ap-1187	114	3	matrices	matrix	NOUN
ap-1187	114	4	are	be	AUX
ap-1187	114	5	non	non	ADJ
ap-1187	114	6	-	-	ADJ
ap-1187	114	7	hermitian	hermitian	ADJ
ap-1187	114	8	,	,	PUNCT
ap-1187	114	9	and	and	CCONJ
ap-1187	114	10	they	they	PRON
ap-1187	114	11	can	can	AUX
ap-1187	114	12	be	be	AUX
ap-1187	114	13	realized	realize	VERB
ap-1187	114	14	by	by	ADP
ap-1187	114	15	the	the	DET
ap-1187	114	16	following	follow	VERB
ap-1187	114	17	substitution	substitution	NOUN
ap-1187	114	18	:	:	PUNCT
ap-1187	114	19	πμ	πμ	VERB
ap-1187	114	20	aḃ	aḃ	DET
ap-1187	114	21	=	=	SYM
ap-1187	114	22	j2	j2	PROPN
ap-1187	115	1	i	i	PRON
ap-1187	115	2	σμ	σμ	VERB
ap-1187	115	3	aḃ	aḃ	PRON
ap-1187	115	4	,	,	PUNCT
ap-1187	115	5	π̄μ	π̄μ	NUM
ap-1187	115	6	ḃa	ḃa	NOUN
ap-1187	115	7	=	=	PUNCT
ap-1187	115	8	−j	−j	NOUN
ap-1187	115	9	i	i	PRON
ap-1187	115	10	σμ	σμ	VERB
ap-1187	115	11	ḃa	ḃa	PROPN
ap-1187	115	12	(	(	PUNCT
ap-1187	115	13	19	19	NUM
ap-1187	115	14	)	)	PUNCT
ap-1187	115	15	where	where	SCONJ
ap-1187	115	16	σμ	σμ	PROPN
ap-1187	115	17	aḃ	aḃ	PRON
ap-1187	115	18	are	be	AUX
ap-1187	115	19	the	the	DET
ap-1187	115	20	unit	unit	NOUN
ap-1187	115	21	2	2	NUM
ap-1187	115	22	matrix	matrix	NOUN
ap-1187	115	23	for	for	ADP
ap-1187	115	24	μ	μ	PROPN
ap-1187	115	25	=	=	SYM
ap-1187	115	26	0	0	NUM
ap-1187	115	27	,	,	PUNCT
ap-1187	115	28	and	and	CCONJ
ap-1187	115	29	the	the	DET
ap-1187	115	30	three	three	NUM
ap-1187	115	31	hermitian	hermitian	ADJ
ap-1187	115	32	pauli	pauli	PROPN
ap-1187	115	33	matrices	matrix	NOUN
ap-1187	115	34	for	for	ADP
ap-1187	115	35	μ	μ	PROPN
ap-1187	115	36	=	=	SYM
ap-1187	115	37	1	1	NUM
ap-1187	115	38	,	,	PUNCT
ap-1187	115	39	2	2	NUM
ap-1187	115	40	,	,	PUNCT
ap-1187	115	41	3	3	NUM
ap-1187	115	42	.	.	PUNCT
ap-1187	115	43	again	again	ADV
ap-1187	115	44	,	,	PUNCT
ap-1187	115	45	we	we	PRON
ap-1187	115	46	want	want	VERB
ap-1187	115	47	to	to	PART
ap-1187	115	48	get	get	VERB
ap-1187	115	49	the	the	DET
ap-1187	115	50	same	same	ADJ
ap-1187	115	51	form	form	NOUN
ap-1187	115	52	of	of	ADP
ap-1187	115	53	these	these	DET
ap-1187	115	54	four	four	NUM
ap-1187	115	55	matrices	matrix	NOUN
ap-1187	115	56	in	in	ADP
ap-1187	115	57	another	another	DET
ap-1187	115	58	basis	basis	NOUN
ap-1187	115	59	.	.	PUNCT
ap-1187	116	1	knowing	know	VERB
ap-1187	116	2	that	that	SCONJ
ap-1187	116	3	the	the	DET
ap-1187	116	4	lower	low	ADJ
ap-1187	116	5	indices	index	NOUN
ap-1187	116	6	a	a	PRON
ap-1187	116	7	and	and	CCONJ
ap-1187	116	8	ḃ	ḃ	PROPN
ap-1187	116	9	undergo	undergo	VERB
ap-1187	116	10	the	the	DET
ap-1187	116	11	transformation	transformation	NOUN
ap-1187	116	12	with	with	ADP
ap-1187	116	13	matrices	matrix	NOUN
ap-1187	116	14	ua′	ua′	PROPN
ap-1187	116	15	b	b	NOUN
ap-1187	116	16	and	and	CCONJ
ap-1187	116	17	ū	ū	NOUN
ap-1187	116	18	ȧ′	ȧ′	VERB
ap-1187	116	19	ḃ	ḃ	PROPN
ap-1187	116	20	,	,	PUNCT
ap-1187	116	21	we	we	PRON
ap-1187	116	22	demand	demand	VERB
ap-1187	116	23	that	that	SCONJ
ap-1187	116	24	there	there	PRON
ap-1187	116	25	exist	exist	VERB
ap-1187	116	26	some	some	DET
ap-1187	116	27	4	4	NUM
ap-1187	116	28	×	×	NOUN
ap-1187	116	29	4	4	NUM
ap-1187	116	30	matrices	matrix	NOUN
ap-1187	116	31	λμ′	λμ′	NOUN
ap-1187	116	32	ν	ν	NOUN
ap-1187	116	33	representing	represent	VERB
ap-1187	116	34	the	the	DET
ap-1187	116	35	transformation	transformation	NOUN
ap-1187	116	36	of	of	ADP
ap-1187	116	37	lower	low	ADJ
ap-1187	116	38	indices	index	NOUN
ap-1187	116	39	by	by	ADP
ap-1187	116	40	the	the	DET
ap-1187	116	41	matrices	matrix	NOUN
ap-1187	116	42	u	u	NOUN
ap-1187	116	43	and	and	CCONJ
ap-1187	116	44	ū	ū	NOUN
ap-1187	116	45	:	:	PUNCT
ap-1187	116	46	λμ′	λμ′	X
ap-1187	116	47	ν	ν	NOUN
ap-1187	116	48	πν	πν	ADP
ap-1187	116	49	aḃ	aḃ	PRON
ap-1187	116	50	=	=	X
ap-1187	117	1	ua′	ua′	ADP
ap-1187	117	2	a	a	DET
ap-1187	117	3	ū	ū	NOUN
ap-1187	117	4	ḃ′	ḃ′	VERB
ap-1187	117	5	ḃ	ḃ	PROPN
ap-1187	117	6	πμ′	πμ′	X
ap-1187	117	7	a′ḃ′	a′ḃ′	X
ap-1187	117	8	,	,	PUNCT
ap-1187	117	9	(	(	PUNCT
ap-1187	117	10	20	20	NUM
ap-1187	117	11	)	)	PUNCT
ap-1187	117	12	and	and	CCONJ
ap-1187	117	13	this	this	PRON
ap-1187	117	14	defines	define	VERB
ap-1187	117	15	the	the	DET
ap-1187	117	16	vector	vector	NOUN
ap-1187	117	17	(	(	PUNCT
ap-1187	117	18	4	4	NUM
ap-1187	117	19	×	×	NOUN
ap-1187	117	20	4	4	NUM
ap-1187	117	21	)	)	PUNCT
ap-1187	117	22	representation	representation	NOUN
ap-1187	117	23	of	of	ADP
ap-1187	117	24	the	the	DET
ap-1187	117	25	lorentz	lorentz	PROPN
ap-1187	117	26	group	group	NOUN
ap-1187	117	27	.	.	PUNCT
ap-1187	118	1	introducing	introduce	VERB
ap-1187	118	2	the	the	DET
ap-1187	118	3	invariant	invariant	ADJ
ap-1187	118	4	“	"	PUNCT
ap-1187	118	5	spinorial	spinorial	ADJ
ap-1187	118	6	metric	metric	NOUN
ap-1187	118	7	”	"	PUNCT
ap-1187	118	8	in	in	ADP
ap-1187	118	9	two	two	NUM
ap-1187	118	10	complex	complex	ADJ
ap-1187	118	11	dimensions	dimension	NOUN
ap-1187	118	12	,	,	PUNCT
ap-1187	118	13	εab	εab	PROPN
ap-1187	118	14	and	and	CCONJ
ap-1187	118	15	εȧḃ	εȧḃ	NOUN
ap-1187	118	16	such	such	ADJ
ap-1187	118	17	that	that	SCONJ
ap-1187	118	18	ε12	ε12	NOUN
ap-1187	118	19	=	=	SYM
ap-1187	118	20	−ε21	−ε21	X
ap-1187	118	21	=	=	SYM
ap-1187	118	22	1	1	NUM
ap-1187	118	23	and	and	CCONJ
ap-1187	118	24	ε1̇2̇	ε1̇2̇	NOUN
ap-1187	118	25	=	=	SYM
ap-1187	118	26	−ε2̇1̇	−ε2̇1̇	PROPN
ap-1187	118	27	,	,	PUNCT
ap-1187	118	28	we	we	PRON
ap-1187	118	29	can	can	AUX
ap-1187	118	30	define	define	VERB
ap-1187	118	31	the	the	DET
ap-1187	118	32	contravariant	contravariant	ADJ
ap-1187	118	33	components	component	NOUN
ap-1187	118	34	πν	πν	ADP
ap-1187	118	35	aḃ.	aḃ.	VERB
ap-1187	118	36	it	it	PRON
ap-1187	118	37	is	be	AUX
ap-1187	118	38	easy	easy	ADJ
ap-1187	118	39	to	to	PART
ap-1187	118	40	show	show	VERB
ap-1187	118	41	that	that	SCONJ
ap-1187	118	42	the	the	DET
ap-1187	118	43	minkowskian	minkowskian	PROPN
ap-1187	118	44	space	space	NOUN
ap-1187	118	45	-	-	PUNCT
ap-1187	118	46	time	time	NOUN
ap-1187	118	47	metric	metric	ADJ
ap-1187	118	48	,	,	PUNCT
ap-1187	118	49	invariant	invariant	ADJ
ap-1187	118	50	under	under	ADP
ap-1187	118	51	the	the	DET
ap-1187	118	52	lorentz	lorentz	PROPN
ap-1187	118	53	transformations	transformation	NOUN
ap-1187	118	54	,	,	PUNCT
ap-1187	118	55	can	can	AUX
ap-1187	118	56	be	be	AUX
ap-1187	118	57	defined	define	VERB
ap-1187	118	58	as	as	ADP
ap-1187	118	59	gμν	gμν	NOUN
ap-1187	118	60	=	=	NOUN
ap-1187	118	61	1	1	NUM
ap-1187	118	62	2	2	NUM
ap-1187	118	63	[	[	PUNCT
ap-1187	118	64	πμ	πμ	NOUN
ap-1187	118	65	aḃ	aḃ	PRON
ap-1187	118	66	πν	πν	ADP
ap-1187	118	67	aḃ	aḃ	PRON
ap-1187	118	68	]	]	PUNCT
ap-1187	119	1	=	=	PUNCT
ap-1187	119	2	diag	diag	NOUN
ap-1187	119	3	(	(	PUNCT
ap-1187	119	4	+	+	ADV
ap-1187	119	5	,	,	PUNCT
ap-1187	119	6	−,−,−	−,−,−	NOUN
ap-1187	119	7	)	)	PUNCT
ap-1187	119	8	(	(	PUNCT
ap-1187	119	9	21	21	NUM
ap-1187	119	10	)	)	PUNCT
ap-1187	119	11	together	together	ADV
ap-1187	119	12	with	with	ADP
ap-1187	119	13	the	the	DET
ap-1187	119	14	anti	anti	ADJ
ap-1187	119	15	-	-	ADJ
ap-1187	119	16	commuting	commuting	ADJ
ap-1187	119	17	spinors	spinor	NOUN
ap-1187	119	18	ψα	ψα	ADP
ap-1187	119	19	the	the	DET
ap-1187	119	20	four	four	NUM
ap-1187	119	21	real	real	ADJ
ap-1187	119	22	coefficients	coefficient	NOUN
ap-1187	119	23	defining	define	VERB
ap-1187	119	24	a	a	DET
ap-1187	119	25	lorentz	lorentz	PROPN
ap-1187	119	26	vector	vector	NOUN
ap-1187	119	27	,	,	PUNCT
ap-1187	119	28	xμ	xμ	PUNCT
ap-1187	120	1	=	=	PUNCT
ap-1187	120	2	πμ	πμ	VERB
ap-1187	120	3	aḃ	aḃ	DET
ap-1187	120	4	θaθ̄ḃ	θaθ̄ḃ	PROPN
ap-1187	120	5	,	,	PUNCT
ap-1187	120	6	can	can	AUX
ap-1187	120	7	now	now	ADV
ap-1187	120	8	generate	generate	VERB
ap-1187	120	9	the	the	DET
ap-1187	120	10	supersymmetry	supersymmetry	NOUN
ap-1187	120	11	via	via	ADP
ap-1187	120	12	standard	standard	ADJ
ap-1187	120	13	definitions	definition	NOUN
ap-1187	120	14	of	of	ADP
ap-1187	120	15	super	super	NOUN
ap-1187	120	16	-	-	NOUN
ap-1187	120	17	derivations	derivation	NOUN
ap-1187	120	18	.	.	PUNCT
ap-1187	121	1	4	4	X
ap-1187	121	2	.	.	X
ap-1187	121	3	consider	consider	VERB
ap-1187	121	4	now	now	ADV
ap-1187	121	5	three	three	NUM
ap-1187	121	6	generators	generator	NOUN
ap-1187	121	7	,	,	PUNCT
ap-1187	121	8	qa	qa	INTJ
ap-1187	121	9	,	,	PUNCT
ap-1187	121	10	a	a	PRON
ap-1187	121	11	=	=	SYM
ap-1187	121	12	1	1	NUM
ap-1187	121	13	,	,	PUNCT
ap-1187	121	14	2	2	NUM
ap-1187	121	15	,	,	PUNCT
ap-1187	121	16	3	3	NUM
ap-1187	121	17	,	,	PUNCT
ap-1187	121	18	and	and	CCONJ
ap-1187	121	19	their	their	PRON
ap-1187	121	20	conjugates	conjugate	NOUN
ap-1187	121	21	q̄ḃ	q̄ḃ	PRON
ap-1187	121	22	satisfying	satisfy	VERB
ap-1187	121	23	similar	similar	ADJ
ap-1187	121	24	cubic	cubic	ADJ
ap-1187	121	25	commutation	commutation	NOUN
ap-1187	121	26	relations	relation	NOUN
ap-1187	121	27	as	as	ADP
ap-1187	121	28	in	in	ADP
ap-1187	121	29	the	the	DET
ap-1187	121	30	two	two	NUM
ap-1187	121	31	-	-	PUNCT
ap-1187	121	32	dimensional	dimensional	ADJ
ap-1187	121	33	case	case	NOUN
ap-1187	121	34	:	:	PUNCT
ap-1187	121	35	qaqbqc	qaqbqc	NOUN
ap-1187	121	36	=	=	PUNCT
ap-1187	121	37	j	j	PROPN
ap-1187	121	38	qbqcqa	qbqcqa	NOUN
ap-1187	121	39	=	=	SYM
ap-1187	121	40	j2qcqaqb	j2qcqaqb	NOUN
ap-1187	121	41	,	,	PUNCT
ap-1187	121	42	q̄ȧq̄ḃq̄ċ	q̄ȧq̄ḃq̄ċ	NOUN
ap-1187	121	43	=	=	SYM
ap-1187	122	1	j2	j2	PROPN
ap-1187	122	2	q̄ḃq̄ċq̄ȧ	q̄ḃq̄ċq̄ȧ	PROPN
ap-1187	122	3	=	=	SYM
ap-1187	123	1	j	j	PROPN
ap-1187	123	2	q̄ċq̄ȧq̄ḃ	q̄ċq̄ȧq̄ḃ	PROPN
ap-1187	123	3	,	,	PUNCT
ap-1187	123	4	qa	qa	INTJ
ap-1187	123	5	q̄ḃ	q̄ḃ	PROPN
ap-1187	124	1	=	=	SYM
ap-1187	124	2	−jq̄ḃ	−jq̄ḃ	PROPN
ap-1187	124	3	qa	qa	INTJ
ap-1187	124	4	.	.	PUNCT
ap-1187	125	1	with	with	ADP
ap-1187	125	2	the	the	DET
ap-1187	125	3	indices	index	NOUN
ap-1187	125	4	a	a	DET
ap-1187	125	5	,	,	PUNCT
ap-1187	125	6	b	b	PROPN
ap-1187	125	7	,	,	PUNCT
ap-1187	125	8	c	c	NOUN
ap-1187	125	9	,	,	PUNCT
ap-1187	125	10	.	.	PUNCT
ap-1187	125	11	.	.	PUNCT
ap-1187	125	12	.	.	PUNCT
ap-1187	126	1	ranging	range	VERB
ap-1187	126	2	from	from	ADP
ap-1187	126	3	1	1	NUM
ap-1187	126	4	to	to	PART
ap-1187	126	5	3	3	NUM
ap-1187	126	6	we	we	PRON
ap-1187	126	7	get	get	VERB
ap-1187	126	8	eight	eight	NUM
ap-1187	126	9	linearly	linearly	ADV
ap-1187	126	10	independent	independent	ADJ
ap-1187	126	11	combinations	combination	NOUN
ap-1187	126	12	of	of	ADP
ap-1187	126	13	three	three	NUM
ap-1187	126	14	undotted	undotted	ADJ
ap-1187	126	15	indices	index	NOUN
ap-1187	126	16	,	,	PUNCT
ap-1187	126	17	and	and	CCONJ
ap-1187	126	18	the	the	DET
ap-1187	126	19	same	same	ADJ
ap-1187	126	20	number	number	NOUN
ap-1187	126	21	of	of	ADP
ap-1187	126	22	combinations	combination	NOUN
ap-1187	126	23	of	of	ADP
ap-1187	126	24	dotted	dotted	ADJ
ap-1187	126	25	ones	one	NOUN
ap-1187	126	26	.	.	PUNCT
ap-1187	127	1	they	they	PRON
ap-1187	127	2	can	can	AUX
ap-1187	127	3	be	be	AUX
ap-1187	127	4	arranged	arrange	VERB
ap-1187	127	5	as	as	SCONJ
ap-1187	127	6	follows	follow	VERB
ap-1187	127	7	:	:	PUNCT
ap-1187	128	1	q3q2q3	q3q2q3	NOUN
ap-1187	128	2	,	,	PUNCT
ap-1187	128	3	q2q3q2	q2q3q2	NOUN
ap-1187	128	4	,	,	PUNCT
ap-1187	128	5	q1q2q1	q1q2q1	NOUN
ap-1187	128	6	,	,	PUNCT
ap-1187	128	7	q3q1q3	q3q1q3	PROPN
ap-1187	128	8	,	,	PUNCT
ap-1187	128	9	q1q2q1	q1q2q1	NOUN
ap-1187	128	10	,	,	PUNCT
ap-1187	128	11	q2q1q2	q2q1q2	NOUN
ap-1187	128	12	,	,	PUNCT
ap-1187	128	13	q1q2q3	q1q2q3	ADJ
ap-1187	128	14	,	,	PUNCT
ap-1187	128	15	q3q2q1	q3q2q1	NOUN
ap-1187	128	16	,	,	PUNCT
ap-1187	128	17	while	while	SCONJ
ap-1187	128	18	the	the	DET
ap-1187	128	19	quadratic	quadratic	ADJ
ap-1187	128	20	expressions	expression	NOUN
ap-1187	128	21	of	of	ADP
ap-1187	128	22	grade	grade	NOUN
ap-1187	128	23	0	0	NUM
ap-1187	128	24	,	,	PUNCT
ap-1187	128	25	qa	qa	PROPN
ap-1187	128	26	q̄ḃ	q̄ḃ	PROPN
ap-1187	128	27	span	span	VERB
ap-1187	128	28	a	a	DET
ap-1187	128	29	9	9	NUM
ap-1187	128	30	-	-	PUNCT
ap-1187	128	31	dimensional	dimensional	ADJ
ap-1187	128	32	subspace	subspace	NOUN
ap-1187	128	33	in	in	ADP
ap-1187	128	34	the	the	DET
ap-1187	128	35	finite	finite	PROPN
ap-1187	128	36	algebra	algebra	PROPN
ap-1187	128	37	generaterd	generaterd	NOUN
ap-1187	128	38	by	by	ADP
ap-1187	128	39	qa	qa	PROPN
ap-1187	128	40	’s	’s	PART
ap-1187	128	41	.	.	PUNCT
ap-1187	129	1	the	the	DET
ap-1187	129	2	invariant	invariant	ADJ
ap-1187	129	3	3	3	NUM
ap-1187	129	4	-	-	PUNCT
ap-1187	129	5	form	form	NOUN
ap-1187	129	6	mapping	mapping	NOUN
ap-1187	129	7	these	these	DET
ap-1187	129	8	combinations	combination	NOUN
ap-1187	129	9	onto	onto	ADP
ap-1187	129	10	some	some	DET
ap-1187	129	11	eight	eight	NUM
ap-1187	129	12	-	-	PUNCT
ap-1187	129	13	dimensional	dimensional	ADJ
ap-1187	129	14	space	space	NOUN
ap-1187	129	15	must	must	AUX
ap-1187	129	16	also	also	ADV
ap-1187	129	17	have	have	VERB
ap-1187	129	18	eight	eight	NUM
ap-1187	129	19	independent	independent	ADJ
ap-1187	129	20	components	component	NOUN
ap-1187	129	21	(	(	PUNCT
ap-1187	129	22	over	over	ADP
ap-1187	129	23	real	real	ADJ
ap-1187	129	24	numbers	number	NOUN
ap-1187	129	25	)	)	PUNCT
ap-1187	129	26	.	.	PUNCT
ap-1187	130	1	the	the	DET
ap-1187	130	2	three	three	NUM
ap-1187	130	3	-	-	PUNCT
ap-1187	130	4	dimensional	dimensional	ADJ
ap-1187	130	5	“	"	PUNCT
ap-1187	130	6	cubic	cubic	ADJ
ap-1187	130	7	matrices	matrix	NOUN
ap-1187	130	8	”	"	PUNCT
ap-1187	130	9	are	be	AUX
ap-1187	130	10	then	then	ADV
ap-1187	130	11	as	as	SCONJ
ap-1187	130	12	follows	follow	VERB
ap-1187	130	13	:	:	PUNCT
ap-1187	130	14	k3	k3	VERB
ap-1187	130	15	+	+	PROPN
ap-1187	130	16	121	121	NUM
ap-1187	130	17	=	=	SYM
ap-1187	130	18	1	1	NUM
ap-1187	130	19	,	,	PUNCT
ap-1187	130	20	k3	k3	VERB
ap-1187	130	21	+	+	PROPN
ap-1187	130	22	112	112	NUM
ap-1187	130	23	=	=	SYM
ap-1187	130	24	j2	j2	PROPN
ap-1187	130	25	,	,	PUNCT
ap-1187	130	26	k3	k3	VERB
ap-1187	130	27	+	+	NOUN
ap-1187	130	28	211	211	NUM
ap-1187	130	29	=	=	SYM
ap-1187	130	30	j	j	NOUN
ap-1187	130	31	;	;	PUNCT
ap-1187	130	32	k3−212	k3−212	PROPN
ap-1187	130	33	=	=	NOUN
ap-1187	130	34	1	1	NUM
ap-1187	130	35	,	,	PUNCT
ap-1187	130	36	k3−221	k3−221	NOUN
ap-1187	130	37	=	=	SYM
ap-1187	130	38	j2	j2	PROPN
ap-1187	130	39	,	,	PUNCT
ap-1187	130	40	k3−122	k3−122	X
ap-1187	130	41	=	=	SYM
ap-1187	130	42	j	j	PROPN
ap-1187	130	43	;	;	PUNCT
ap-1187	130	44	k2	k2	PROPN
ap-1187	130	45	+	+	PROPN
ap-1187	130	46	313	313	NUM
ap-1187	130	47	=	=	SYM
ap-1187	130	48	1	1	NUM
ap-1187	130	49	,	,	PUNCT
ap-1187	130	50	k2	k2	X
ap-1187	130	51	+	+	PROPN
ap-1187	130	52	331	331	PROPN
ap-1187	130	53	=	=	SYM
ap-1187	130	54	j2	j2	PROPN
ap-1187	130	55	,	,	PUNCT
ap-1187	130	56	k2	k2	X
ap-1187	130	57	+	+	PROPN
ap-1187	130	58	133	133	NUM
ap-1187	130	59	=	=	SYM
ap-1187	130	60	j	j	PROPN
ap-1187	130	61	;	;	PUNCT
ap-1187	130	62	k2−131	k2−131	PROPN
ap-1187	131	1	=	=	SYM
ap-1187	131	2	1	1	NUM
ap-1187	131	3	,	,	PUNCT
ap-1187	131	4	k2−113	k2−113	NOUN
ap-1187	131	5	=	=	SYM
ap-1187	131	6	j2	j2	PROPN
ap-1187	131	7	,	,	PUNCT
ap-1187	131	8	k2−311	k2−311	NOUN
ap-1187	131	9	=	=	SYM
ap-1187	131	10	j	j	PROPN
ap-1187	131	11	;	;	PUNCT
ap-1187	131	12	k1	k1	X
ap-1187	131	13	+	+	PROPN
ap-1187	131	14	232	232	NUM
ap-1187	131	15	=	=	SYM
ap-1187	131	16	1	1	NUM
ap-1187	131	17	,	,	PUNCT
ap-1187	131	18	k1	k1	X
ap-1187	131	19	+	+	NOUN
ap-1187	131	20	223	223	NUM
ap-1187	131	21	=	=	SYM
ap-1187	131	22	j2	j2	PROPN
ap-1187	131	23	,	,	PUNCT
ap-1187	131	24	k1	k1	X
ap-1187	131	25	+	+	PROPN
ap-1187	131	26	322	322	NUM
ap-1187	131	27	=	=	SYM
ap-1187	131	28	j	j	PROPN
ap-1187	131	29	;	;	PUNCT
ap-1187	131	30	k1−323	k1−323	NOUN
ap-1187	131	31	=	=	SYM
ap-1187	131	32	1	1	NUM
ap-1187	131	33	,	,	PUNCT
ap-1187	131	34	k1−332	k1−332	NOUN
ap-1187	131	35	=	=	SYM
ap-1187	131	36	j2	j2	PROPN
ap-1187	131	37	,	,	PUNCT
ap-1187	131	38	k1−233	k1−233	NOUN
ap-1187	131	39	=	=	SYM
ap-1187	131	40	j	j	PROPN
ap-1187	131	41	;	;	PUNCT
ap-1187	131	42	k7123	k7123	NOUN
ap-1187	131	43	=	=	SYM
ap-1187	131	44	1	1	NUM
ap-1187	131	45	,	,	PUNCT
ap-1187	131	46	k7231	k7231	PROPN
ap-1187	131	47	=	=	SYM
ap-1187	131	48	j2	j2	PROPN
ap-1187	131	49	,	,	PUNCT
ap-1187	131	50	k7312	k7312	PROPN
ap-1187	131	51	=	=	SYM
ap-1187	131	52	j	j	PROPN
ap-1187	131	53	;	;	PUNCT
ap-1187	131	54	k8132	k8132	NOUN
ap-1187	131	55	=	=	SYM
ap-1187	131	56	1	1	NUM
ap-1187	131	57	,	,	PUNCT
ap-1187	131	58	k8321	k8321	PROPN
ap-1187	131	59	=	=	SYM
ap-1187	131	60	j2	j2	PROPN
ap-1187	131	61	,	,	PUNCT
ap-1187	131	62	k8213	k8213	PROPN
ap-1187	131	63	=	=	PUNCT
ap-1187	131	64	j.	j.	PROPN
ap-1187	131	65	all	all	DET
ap-1187	131	66	other	other	ADJ
ap-1187	131	67	components	component	NOUN
ap-1187	131	68	being	be	AUX
ap-1187	131	69	identically	identically	ADV
ap-1187	131	70	zero	zero	NUM
ap-1187	131	71	.	.	PUNCT
ap-1187	132	1	let	let	VERB
ap-1187	132	2	the	the	DET
ap-1187	132	3	capital	capital	NOUN
ap-1187	132	4	greek	greek	PROPN
ap-1187	132	5	indices	indice	VERB
ap-1187	132	6	φ	φ	PROPN
ap-1187	132	7	,	,	PUNCT
ap-1187	132	8	ω	ω	PROPN
ap-1187	132	9	take	take	VERB
ap-1187	132	10	on	on	ADP
ap-1187	132	11	the	the	DET
ap-1187	132	12	values	value	NOUN
ap-1187	132	13	from	from	ADP
ap-1187	132	14	1	1	NUM
ap-1187	132	15	to	to	PART
ap-1187	132	16	8	8	NUM
ap-1187	132	17	.	.	PUNCT
ap-1187	133	1	as	as	ADP
ap-1187	133	2	in	in	ADP
ap-1187	133	3	the	the	DET
ap-1187	133	4	case	case	NOUN
ap-1187	133	5	of	of	ADP
ap-1187	133	6	the	the	DET
ap-1187	133	7	ρα	ρα	PROPN
ap-1187	133	8	matrices	matrix	NOUN
ap-1187	133	9	,	,	PUNCT
ap-1187	133	10	we	we	PRON
ap-1187	133	11	define	define	VERB
ap-1187	133	12	the	the	DET
ap-1187	133	13	conjugate	conjugate	ADJ
ap-1187	133	14	matrices	matrix	NOUN
ap-1187	133	15	k̄ω̇	k̄ω̇	ADJ
ap-1187	133	16	,	,	PUNCT
ap-1187	133	17	by	by	ADP
ap-1187	133	18	replacing	replace	VERB
ap-1187	133	19	j	j	PROPN
ap-1187	133	20	by	by	ADP
ap-1187	133	21	j2	j2	PROPN
ap-1187	133	22	and	and	CCONJ
ap-1187	133	23	vice	vice	NOUN
ap-1187	133	24	versa	versa	NOUN
ap-1187	133	25	in	in	ADP
ap-1187	133	26	the	the	DET
ap-1187	133	27	matrices	matrix	NOUN
ap-1187	133	28	kω	kω	VERB
ap-1187	133	29	.	.	PUNCT
ap-1187	134	1	the	the	DET
ap-1187	134	2	ternary	ternary	ADJ
ap-1187	134	3	multiplication	multiplication	NOUN
ap-1187	134	4	table	table	NOUN
ap-1187	134	5	for	for	ADP
ap-1187	134	6	eight	eight	NUM
ap-1187	134	7	cubic	cubic	ADJ
ap-1187	134	8	matrices	matrix	NOUN
ap-1187	134	9	k	k	NOUN
ap-1187	134	10	,	,	PUNCT
ap-1187	134	11	with	with	ADP
ap-1187	134	12	the	the	DET
ap-1187	134	13	same	same	ADJ
ap-1187	134	14	definition	definition	NOUN
ap-1187	134	15	as	as	ADP
ap-1187	134	16	for	for	ADP
ap-1187	134	17	the	the	DET
ap-1187	134	18	ρmatrices	ρmatrice	NOUN
ap-1187	134	19	,	,	PUNCT
ap-1187	134	20	{	{	PUNCT
ap-1187	134	21	kγ	kγ	PROPN
ap-1187	134	22	,	,	PUNCT
ap-1187	134	23	kπ	kπ	PROPN
ap-1187	134	24	,	,	PUNCT
ap-1187	134	25	kλ}abc	kλ}abc	X
ap-1187	134	26	=	=	PUNCT
ap-1187	135	1	3∑	3∑	NUM
ap-1187	135	2	d	d	NOUN
ap-1187	135	3	,	,	PUNCT
ap-1187	135	4	e	e	NOUN
ap-1187	135	5	,	,	PUNCT
ap-1187	135	6	f=1	f=1	PRON
ap-1187	135	7	kγdaek	kγdaek	VERB
ap-1187	135	8	π	π	PROPN
ap-1187	135	9	ebfkλfcd	ebfkλfcd	PROPN
ap-1187	135	10	(	(	PUNCT
ap-1187	135	11	22	22	NUM
ap-1187	135	12	)	)	PUNCT
ap-1187	135	13	the	the	DET
ap-1187	135	14	z3	z3	PROPN
ap-1187	135	15	graded	grade	VERB
ap-1187	135	16	ternary	ternary	ADJ
ap-1187	135	17	commutator	commutator	NOUN
ap-1187	135	18	can	can	AUX
ap-1187	135	19	be	be	AUX
ap-1187	135	20	defined	define	VERB
ap-1187	135	21	as	as	SCONJ
ap-1187	135	22	follows	follow	VERB
ap-1187	135	23	:	:	PUNCT
ap-1187	135	24	{	{	PUNCT
ap-1187	135	25	kγ	kγ	PROPN
ap-1187	135	26	,	,	PUNCT
ap-1187	135	27	kπ	kπ	PROPN
ap-1187	135	28	,	,	PUNCT
ap-1187	135	29	kλ}z3	kλ}z3	PROPN
ap-1187	135	30	=	=	PUNCT
ap-1187	135	31	{	{	PUNCT
ap-1187	135	32	kπ	kπ	PROPN
ap-1187	135	33	,	,	PUNCT
ap-1187	135	34	kλ	kλ	PROPN
ap-1187	135	35	,	,	PUNCT
ap-1187	135	36	kγ}+	kγ}+	PROPN
ap-1187	135	37	j{kπ	j{kπ	PROPN
ap-1187	135	38	,	,	PUNCT
ap-1187	135	39	kλ	kλ	PROPN
ap-1187	135	40	,	,	PUNCT
ap-1187	135	41	kγ}+	kγ}+	PROPN
ap-1187	135	42	(	(	PUNCT
ap-1187	135	43	23	23	NUM
ap-1187	135	44	)	)	PUNCT
ap-1187	135	45	j2{kγ	j2{kγ	PROPN
ap-1187	135	46	,	,	PUNCT
ap-1187	135	47	kπ	kπ	PROPN
ap-1187	135	48	,	,	PUNCT
ap-1187	135	49	kλ	kλ	PROPN
ap-1187	135	50	}	}	PUNCT
ap-1187	135	51	the	the	DET
ap-1187	135	52	ternary	ternary	ADJ
ap-1187	135	53	multiplication	multiplication	NOUN
ap-1187	135	54	table	table	NOUN
ap-1187	135	55	for	for	ADP
ap-1187	135	56	these	these	DET
ap-1187	135	57	cubic	cubic	ADJ
ap-1187	135	58	matrices	matrix	NOUN
ap-1187	135	59	shall	shall	AUX
ap-1187	135	60	contain	contain	VERB
ap-1187	135	61	8	8	NUM
ap-1187	135	62	×	×	NOUN
ap-1187	135	63	8	8	NUM
ap-1187	135	64	×	×	NOUN
ap-1187	135	65	8	8	NUM
ap-1187	135	66	=	=	SYM
ap-1187	135	67	512	512	NUM
ap-1187	135	68	entries	entry	NOUN
ap-1187	135	69	,	,	PUNCT
ap-1187	135	70	and	and	CCONJ
ap-1187	135	71	we	we	PRON
ap-1187	135	72	can	can	AUX
ap-1187	135	73	not	not	PART
ap-1187	135	74	print	print	VERB
ap-1187	135	75	it	it	PRON
ap-1187	135	76	here	here	ADV
ap-1187	135	77	due	due	ADP
ap-1187	135	78	to	to	ADP
ap-1187	135	79	the	the	DET
ap-1187	135	80	lack	lack	NOUN
ap-1187	135	81	of	of	ADP
ap-1187	135	82	place	place	NOUN
ap-1187	135	83	.	.	PUNCT
ap-1187	136	1	nevertheless	nevertheless	ADV
ap-1187	136	2	,	,	PUNCT
ap-1187	136	3	there	there	PRON
ap-1187	136	4	are	be	VERB
ap-1187	136	5	some	some	DET
ap-1187	136	6	interesting	interesting	ADJ
ap-1187	136	7	properties	property	NOUN
ap-1187	136	8	that	that	PRON
ap-1187	136	9	can	can	AUX
ap-1187	136	10	be	be	AUX
ap-1187	136	11	noticed	notice	VERB
ap-1187	136	12	when	when	SCONJ
ap-1187	136	13	one	one	PRON
ap-1187	136	14	gets	get	VERB
ap-1187	136	15	a	a	DET
ap-1187	136	16	closer	close	ADJ
ap-1187	136	17	look	look	NOUN
ap-1187	136	18	at	at	ADP
ap-1187	136	19	the	the	DET
ap-1187	136	20	structure	structure	NOUN
ap-1187	136	21	of	of	ADP
ap-1187	136	22	the	the	DET
ap-1187	136	23	defining	define	VERB
ap-1187	136	24	table	table	NOUN
ap-1187	136	25	above	above	ADV
ap-1187	136	26	.	.	PUNCT
ap-1187	137	1	there	there	PRON
ap-1187	137	2	are	be	VERB
ap-1187	137	3	three	three	NUM
ap-1187	137	4	distinct	distinct	ADJ
ap-1187	137	5	groups	group	NOUN
ap-1187	137	6	of	of	ADP
ap-1187	137	7	two	two	NUM
ap-1187	137	8	generators	generator	NOUN
ap-1187	137	9	,	,	PUNCT
ap-1187	137	10	each	each	PRON
ap-1187	137	11	of	of	ADP
ap-1187	137	12	them	they	PRON
ap-1187	137	13	reproducing	reproduce	VERB
ap-1187	137	14	the	the	DET
ap-1187	137	15	structure	structure	NOUN
ap-1187	137	16	of	of	ADP
ap-1187	137	17	ρ	ρ	NOUN
ap-1187	137	18	-	-	NOUN
ap-1187	137	19	matrices	matrix	NOUN
ap-1187	137	20	,	,	PUNCT
ap-1187	137	21	only	only	ADV
ap-1187	137	22	with	with	ADP
ap-1187	137	23	a	a	DET
ap-1187	137	24	different	different	ADJ
ap-1187	137	25	choice	choice	NOUN
ap-1187	137	26	of	of	ADP
ap-1187	137	27	two	two	NUM
ap-1187	137	28	indices	index	NOUN
ap-1187	137	29	:	:	PUNCT
ap-1187	137	30	(	(	PUNCT
ap-1187	137	31	1	1	NUM
ap-1187	137	32	,	,	PUNCT
ap-1187	137	33	2	2	NUM
ap-1187	137	34	)	)	PUNCT
ap-1187	137	35	,	,	PUNCT
ap-1187	137	36	2	2	NUM
ap-1187	137	37	,	,	PUNCT
ap-1187	137	38	3	3	NUM
ap-1187	137	39	nd	nd	SYM
ap-1187	137	40	3	3	NUM
ap-1187	137	41	,	,	PUNCT
ap-1187	137	42	1	1	NUM
ap-1187	137	43	.	.	PUNCT
ap-1187	138	1	they	they	PRON
ap-1187	138	2	obviously	obviously	ADV
ap-1187	138	3	reproduce	reproduce	VERB
ap-1187	138	4	the	the	DET
ap-1187	138	5	multiplication	multiplication	NOUN
ap-1187	138	6	rules	rule	NOUN
ap-1187	138	7	of	of	ADP
ap-1187	138	8	the	the	DET
ap-1187	138	9	ρ	ρ	NOUN
ap-1187	138	10	-	-	PUNCT
ap-1187	138	11	matrices	matrix	NOUN
ap-1187	138	12	.	.	PUNCT
ap-1187	139	1	the	the	DET
ap-1187	139	2	last	last	ADJ
ap-1187	139	3	two	two	NUM
ap-1187	139	4	generators	generator	NOUN
ap-1187	139	5	are	be	AUX
ap-1187	139	6	new	new	ADJ
ap-1187	139	7	in	in	ADP
ap-1187	139	8	the	the	DET
ap-1187	139	9	sense	sense	NOUN
ap-1187	139	10	that	that	SCONJ
ap-1187	139	11	the	the	DET
ap-1187	139	12	combinations	combination	NOUN
ap-1187	139	13	with	with	ADP
ap-1187	139	14	three	three	NUM
ap-1187	139	15	different	different	ADJ
ap-1187	139	16	indices	index	NOUN
ap-1187	139	17	did	do	AUX
ap-1187	139	18	not	not	PART
ap-1187	139	19	exist	exist	VERB
ap-1187	139	20	in	in	ADP
ap-1187	139	21	the	the	DET
ap-1187	139	22	previous	previous	ADJ
ap-1187	139	23	twodimensional	twodimensional	ADJ
ap-1187	139	24	case	case	NOUN
ap-1187	139	25	.	.	PUNCT
ap-1187	140	1	their	their	PRON
ap-1187	140	2	z3	z3	NOUN
ap-1187	140	3	-	-	PUNCT
ap-1187	140	4	graded	grade	VERB
ap-1187	140	5	ternary	ternary	ADJ
ap-1187	140	6	commutators	commutator	NOUN
ap-1187	140	7	vanish	vanish	VERB
ap-1187	140	8	,	,	PUNCT
ap-1187	140	9	which	which	PRON
ap-1187	140	10	reproduces	reproduce	VERB
ap-1187	140	11	the	the	DET
ap-1187	140	12	behavior	behavior	NOUN
ap-1187	140	13	of	of	ADP
ap-1187	140	14	two	two	NUM
ap-1187	140	15	generators	generator	NOUN
ap-1187	140	16	of	of	ADP
ap-1187	140	17	the	the	DET
ap-1187	140	18	cartan	cartan	ADJ
ap-1187	140	19	subalgebra	subalgebra	NOUN
ap-1187	140	20	of	of	ADP
ap-1187	140	21	su(3	su(3	PROPN
ap-1187	140	22	)	)	PUNCT
ap-1187	140	23	.	.	PUNCT
ap-1187	141	1	there	there	PRON
ap-1187	141	2	is	be	VERB
ap-1187	141	3	one	one	NUM
ap-1187	141	4	drawback	drawback	NOUN
ap-1187	141	5	here	here	ADV
ap-1187	141	6	,	,	PUNCT
ap-1187	141	7	namely	namely	ADV
ap-1187	141	8	,	,	PUNCT
ap-1187	141	9	the	the	DET
ap-1187	141	10	multiplication	multiplication	NOUN
ap-1187	141	11	does	do	AUX
ap-1187	141	12	not	not	PART
ap-1187	141	13	close	close	VERB
ap-1187	141	14	under	under	ADP
ap-1187	141	15	the	the	DET
ap-1187	141	16	z3	z3	NOUN
ap-1187	141	17	-	-	PUNCT
ap-1187	141	18	graded	grade	VERB
ap-1187	141	19	ternary	ternary	ADJ
ap-1187	141	20	commutator	commutator	NOUN
ap-1187	141	21	:	:	PUNCT
ap-1187	141	22	one	one	NUM
ap-1187	141	23	needs	need	VERB
ap-1187	141	24	to	to	PART
ap-1187	141	25	form	form	VERB
ap-1187	141	26	real	real	ADJ
ap-1187	141	27	and	and	CCONJ
ap-1187	141	28	imaginary	imaginary	ADJ
ap-1187	141	29	combinations	combination	NOUN
ap-1187	141	30	of	of	ADP
ap-1187	141	31	k	k	PROPN
ap-1187	141	32	and	and	CCONJ
ap-1187	141	33	k̄	k̄	ADV
ap-1187	141	34	cubic	cubic	ADJ
ap-1187	141	35	matrices	matrix	NOUN
ap-1187	141	36	in	in	ADP
ap-1187	141	37	order	order	NOUN
ap-1187	141	38	to	to	PART
ap-1187	141	39	make	make	VERB
ap-1187	141	40	the	the	DET
ap-1187	141	41	corresponding	corresponding	ADJ
ap-1187	141	42	ternary	ternary	ADJ
ap-1187	141	43	algebra	algebra	NOUN
ap-1187	141	44	complete	complete	ADJ
ap-1187	141	45	.	.	PUNCT
ap-1187	142	1	the	the	DET
ap-1187	142	2	covariance	covariance	NOUN
ap-1187	142	3	principle	principle	NOUN
ap-1187	142	4	applied	apply	VERB
ap-1187	142	5	to	to	ADP
ap-1187	142	6	the	the	DET
ap-1187	142	7	cubic	cubic	ADJ
ap-1187	142	8	matrices	matrix	NOUN
ap-1187	142	9	kφabc	kφabc	PROPN
ap-1187	142	10	underlinear	underlinear	ADJ
ap-1187	142	11	change	change	NOUN
ap-1187	142	12	of	of	ADP
ap-1187	142	13	the	the	DET
ap-1187	142	14	basis	basis	NOUN
ap-1187	142	15	from	from	ADP
ap-1187	142	16	θa	θa	PRON
ap-1187	142	17	to	to	ADP
ap-1187	142	18	θa′	θa′	NOUN
ap-1187	142	19	=	=	SYM
ap-1187	142	20	ua′	ua′	PROPN
ap-1187	143	1	b	b	PROPN
ap-1187	143	2	θb	θb	PROPN
ap-1187	143	3	means	mean	VERB
ap-1187	143	4	that	that	SCONJ
ap-1187	143	5	we	we	PRON
ap-1187	143	6	want	want	VERB
ap-1187	143	7	to	to	PART
ap-1187	143	8	solve	solve	VERB
ap-1187	143	9	the	the	DET
ap-1187	143	10	following	following	ADJ
ap-1187	143	11	equations	equation	NOUN
ap-1187	143	12	:	:	PUNCT
ap-1187	143	13	sφ	sφ	PROPN
ap-1187	143	14	′	′	NUM
ap-1187	143	15	ω	ω	NUM
ap-1187	143	16	kωdef	kωdef	NOUN
ap-1187	143	17	=	=	PUNCT
ap-1187	143	18	kφ	kφ	PROPN
ap-1187	143	19	′	′	NUM
ap-1187	143	20	a′b′c′u	a′b′c′u	NOUN
ap-1187	143	21	a′	a′	PROPN
ap-1187	143	22	d	d	SYM
ap-1187	143	23	u	u	X
ap-1187	143	24	b′	b′	NUM
ap-1187	143	25	e	e	NOUN
ap-1187	143	26	u	u	NOUN
ap-1187	143	27	c′	c′	PROPN
ap-1187	143	28	f	f	PROPN
ap-1187	143	29	,	,	PUNCT
ap-1187	143	30	(	(	PUNCT
ap-1187	143	31	24	24	NUM
ap-1187	143	32	)	)	PUNCT
ap-1187	143	33	40	40	NUM
ap-1187	143	34	acta	acta	PROPN
ap-1187	143	35	polytechnica	polytechnica	PROPN
ap-1187	143	36	vol	vol	NOUN
ap-1187	143	37	.	.	PROPN
ap-1187	144	1	50	50	NUM
ap-1187	144	2	no	no	NOUN
ap-1187	144	3	.	.	PUNCT
ap-1187	145	1	3/2010	3/2010	NUM
ap-1187	145	2	it	it	PRON
ap-1187	145	3	takes	take	VERB
ap-1187	145	4	more	more	ADJ
ap-1187	145	5	time	time	NOUN
ap-1187	145	6	to	to	PART
ap-1187	145	7	prove	prove	VERB
ap-1187	145	8	,	,	PUNCT
ap-1187	145	9	but	but	CCONJ
ap-1187	145	10	the	the	DET
ap-1187	145	11	result	result	NOUN
ap-1187	145	12	is	be	AUX
ap-1187	145	13	that	that	SCONJ
ap-1187	145	14	the	the	DET
ap-1187	145	15	8×8	8×8	NUM
ap-1187	145	16	matrices	matrix	NOUN
ap-1187	145	17	sφ	sφ	ADP
ap-1187	145	18	′	′	NUM
ap-1187	145	19	ω	ω	NUM
ap-1187	145	20	are	be	AUX
ap-1187	145	21	the	the	DET
ap-1187	145	22	adjoint	adjoint	PROPN
ap-1187	145	23	representation	representation	NOUN
ap-1187	145	24	of	of	ADP
ap-1187	145	25	the	the	DET
ap-1187	145	26	su(3	su(3	PROPN
ap-1187	145	27	)	)	PUNCT
ap-1187	145	28	group	group	NOUN
ap-1187	145	29	,	,	PUNCT
ap-1187	145	30	whereas	whereas	SCONJ
ap-1187	145	31	the	the	DET
ap-1187	145	32	3	3	NUM
ap-1187	145	33	×	×	NOUN
ap-1187	145	34	3	3	NUM
ap-1187	145	35	matrices	matrix	NOUN
ap-1187	146	1	ua′	ua′	INTJ
ap-1187	147	1	d	d	NOUN
ap-1187	147	2	are	be	AUX
ap-1187	147	3	the	the	DET
ap-1187	147	4	fundamental	fundamental	ADJ
ap-1187	147	5	representation	representation	NOUN
ap-1187	147	6	of	of	ADP
ap-1187	147	7	the	the	DET
ap-1187	147	8	same	same	ADJ
ap-1187	147	9	group	group	NOUN
ap-1187	147	10	,	,	PUNCT
ap-1187	147	11	up	up	ADP
ap-1187	147	12	to	to	ADP
ap-1187	147	13	the	the	DET
ap-1187	147	14	phase	phase	NOUN
ap-1187	147	15	factor	factor	NOUN
ap-1187	147	16	that	that	PRON
ap-1187	147	17	can	can	AUX
ap-1187	147	18	take	take	VERB
ap-1187	147	19	on	on	ADP
ap-1187	147	20	the	the	DET
ap-1187	147	21	values	value	NOUN
ap-1187	147	22	1	1	NUM
ap-1187	147	23	,	,	PUNCT
ap-1187	147	24	j	j	PROPN
ap-1187	147	25	or	or	CCONJ
ap-1187	147	26	j2	j2	PROPN
ap-1187	147	27	.	.	PUNCT
ap-1187	148	1	the	the	DET
ap-1187	148	2	nine	nine	NUM
ap-1187	148	3	independent	independent	ADJ
ap-1187	148	4	two	two	NUM
ap-1187	148	5	-	-	PUNCT
ap-1187	148	6	forms	form	NOUN
ap-1187	148	7	p	p	X
ap-1187	148	8	i	i	PRON
ap-1187	148	9	aḃ	aḃ	PRON
ap-1187	149	1	=	=	PUNCT
ap-1187	150	1	−j2	−j2	INTJ
ap-1187	150	2	p̄	p̄	INTJ
ap-1187	150	3	i	i	PRON
ap-1187	150	4	ḃa	ḃa	VERB
ap-1187	150	5	transform	transform	VERB
ap-1187	150	6	as	as	ADP
ap-1187	150	7	the	the	DET
ap-1187	150	8	3⊗	3⊗	NUM
ap-1187	150	9	3̄	3̄	NUM
ap-1187	150	10	representation	representation	NOUN
ap-1187	150	11	of	of	ADP
ap-1187	150	12	su(3	su(3	PROPN
ap-1187	150	13	)	)	PUNCT
ap-1187	150	14	finally	finally	ADV
ap-1187	150	15	,	,	PUNCT
ap-1187	150	16	the	the	DET
ap-1187	150	17	elements	element	NOUN
ap-1187	150	18	of	of	ADP
ap-1187	150	19	the	the	DET
ap-1187	150	20	tensor	tensor	NOUN
ap-1187	150	21	product	product	NOUN
ap-1187	150	22	of	of	ADP
ap-1187	150	23	both	both	DET
ap-1187	150	24	types	type	NOUN
ap-1187	150	25	of	of	ADP
ap-1187	150	26	j	j	NOUN
ap-1187	150	27	-	-	PUNCT
ap-1187	150	28	anti	anti	ADJ
ap-1187	150	29	-	-	ADJ
ap-1187	150	30	commuting	commuting	ADJ
ap-1187	150	31	entities	entity	NOUN
ap-1187	150	32	,	,	PUNCT
ap-1187	150	33	θa	θa	PRON
ap-1187	150	34	and	and	CCONJ
ap-1187	150	35	qb	qb	PROPN
ap-1187	150	36	can	can	AUX
ap-1187	150	37	be	be	AUX
ap-1187	150	38	formed	form	VERB
ap-1187	150	39	,	,	PUNCT
ap-1187	150	40	giving	give	VERB
ap-1187	150	41	six	six	NUM
ap-1187	150	42	quarks	quark	NOUN
ap-1187	150	43	,	,	PUNCT
ap-1187	150	44	qb	qb	PROPN
ap-1187	150	45	a	a	PRON
ap-1187	150	46	,	,	PUNCT
ap-1187	150	47	transforming	transform	VERB
ap-1187	150	48	via	via	ADP
ap-1187	150	49	z3	z3	PROPN
ap-1187	150	50	coverings	covering	NOUN
ap-1187	150	51	of	of	ADP
ap-1187	150	52	sl(2,c	sl(2,c	NOUN
ap-1187	150	53	)	)	PUNCT
ap-1187	150	54	and	and	CCONJ
ap-1187	150	55	su(3	su(3	PROPN
ap-1187	150	56	)	)	PUNCT
ap-1187	150	57	,	,	PUNCT
ap-1187	150	58	which	which	PRON
ap-1187	150	59	looks	look	VERB
ap-1187	150	60	very	very	ADV
ap-1187	150	61	much	much	ADV
ap-1187	150	62	like	like	ADP
ap-1187	150	63	the	the	DET
ap-1187	150	64	three	three	NUM
ap-1187	150	65	flavors	flavor	NOUN
ap-1187	150	66	.	.	PUNCT
ap-1187	151	1	5	5	X
ap-1187	151	2	.	.	X
ap-1187	151	3	we	we	PRON
ap-1187	151	4	have	have	AUX
ap-1187	151	5	shown	show	VERB
ap-1187	151	6	how	how	SCONJ
ap-1187	151	7	the	the	DET
ap-1187	151	8	requirement	requirement	NOUN
ap-1187	151	9	of	of	ADP
ap-1187	151	10	covariance	covariance	NOUN
ap-1187	151	11	of	of	ADP
ap-1187	151	12	z3	z3	NOUN
ap-1187	151	13	-	-	PUNCT
ap-1187	151	14	graded	grade	VERB
ap-1187	151	15	cubic	cubic	ADJ
ap-1187	151	16	generalization	generalization	NOUN
ap-1187	151	17	of	of	ADP
ap-1187	151	18	anticommutation	anticommutation	NOUN
ap-1187	151	19	relations	relation	NOUN
ap-1187	151	20	leads	lead	VERB
ap-1187	151	21	to	to	ADP
ap-1187	151	22	spinor	spinor	NOUN
ap-1187	151	23	and	and	CCONJ
ap-1187	151	24	vector	vector	NOUN
ap-1187	151	25	representations	representation	NOUN
ap-1187	151	26	of	of	ADP
ap-1187	151	27	the	the	DET
ap-1187	151	28	lorentz	lorentz	PROPN
ap-1187	151	29	group	group	NOUN
ap-1187	151	30	and	and	CCONJ
ap-1187	151	31	the	the	DET
ap-1187	151	32	fundamental	fundamental	ADJ
ap-1187	151	33	and	and	CCONJ
ap-1187	151	34	adjoint	adjoint	NOUN
ap-1187	151	35	representations	representation	NOUN
ap-1187	151	36	of	of	ADP
ap-1187	151	37	the	the	DET
ap-1187	151	38	su(3	su(3	PROPN
ap-1187	151	39	)	)	PUNCT
ap-1187	151	40	group	group	NOUN
ap-1187	151	41	,	,	PUNCT
ap-1187	151	42	thus	thus	ADV
ap-1187	151	43	giving	give	VERB
ap-1187	151	44	the	the	DET
ap-1187	151	45	cubic	cubic	ADJ
ap-1187	151	46	z3	z3	NOUN
ap-1187	151	47	-	-	PUNCT
ap-1187	151	48	graded	grade	VERB
ap-1187	151	49	quark	quark	NOUN
ap-1187	151	50	algebra	algebra	NOUN
ap-1187	151	51	the	the	DET
ap-1187	151	52	primary	primary	ADJ
ap-1187	151	53	role	role	NOUN
ap-1187	151	54	in	in	ADP
ap-1187	151	55	determining	determine	VERB
ap-1187	151	56	the	the	DET
ap-1187	151	57	lorentz	lorentz	PROPN
ap-1187	151	58	and	and	CCONJ
ap-1187	151	59	su(3	su(3	PROPN
ap-1187	151	60	)	)	PUNCT
ap-1187	151	61	symmetries	symmetry	NOUN
ap-1187	151	62	.	.	PUNCT
ap-1187	152	1	however	however	ADV
ap-1187	152	2	,	,	PUNCT
ap-1187	152	3	these	these	DET
ap-1187	152	4	representations	representation	NOUN
ap-1187	152	5	coincide	coincide	VERB
ap-1187	152	6	with	with	ADP
ap-1187	152	7	the	the	DET
ap-1187	152	8	usual	usual	ADJ
ap-1187	152	9	ones	one	NOUN
ap-1187	152	10	only	only	ADV
ap-1187	152	11	when	when	SCONJ
ap-1187	152	12	applied	apply	VERB
ap-1187	152	13	to	to	ADP
ap-1187	152	14	special	special	ADJ
ap-1187	152	15	combinations	combination	NOUN
ap-1187	152	16	of	of	ADP
ap-1187	152	17	quark	quark	NOUN
ap-1187	152	18	variables	variable	NOUN
ap-1187	152	19	,	,	PUNCT
ap-1187	152	20	cubic	cubic	ADJ
ap-1187	152	21	(	(	PUNCT
ap-1187	152	22	spinor	spinor	NOUN
ap-1187	152	23	)	)	PUNCT
ap-1187	152	24	or	or	CCONJ
ap-1187	152	25	quadratic	quadratic	ADJ
ap-1187	152	26	(	(	PUNCT
ap-1187	152	27	vector	vector	NOUN
ap-1187	152	28	)	)	PUNCT
ap-1187	152	29	representations	representation	NOUN
ap-1187	152	30	of	of	ADP
ap-1187	152	31	the	the	DET
ap-1187	152	32	lorentz	lorentz	PROPN
ap-1187	152	33	group	group	NOUN
ap-1187	152	34	.	.	PUNCT
ap-1187	153	1	while	while	SCONJ
ap-1187	153	2	acting	act	VERB
ap-1187	153	3	on	on	ADP
ap-1187	153	4	quark	quark	PROPN
ap-1187	153	5	variables	variable	NOUN
ap-1187	153	6	,	,	PUNCT
ap-1187	153	7	the	the	DET
ap-1187	153	8	representations	representation	NOUN
ap-1187	153	9	correspond	correspond	VERB
ap-1187	153	10	to	to	ADP
ap-1187	153	11	the	the	DET
ap-1187	153	12	z3	z3	NOUN
ap-1187	153	13	-	-	PUNCT
ap-1187	153	14	covering	covering	NOUN
ap-1187	153	15	of	of	ADP
ap-1187	153	16	groups	group	NOUN
ap-1187	153	17	.	.	PUNCT
ap-1187	154	1	in	in	ADP
ap-1187	154	2	this	this	DET
ap-1187	154	3	sense	sense	NOUN
ap-1187	154	4	quarks	quark	NOUN
ap-1187	154	5	are	be	AUX
ap-1187	154	6	not	not	PART
ap-1187	154	7	like	like	ADP
ap-1187	154	8	ordinary	ordinary	ADJ
ap-1187	154	9	spinors	spinor	NOUN
ap-1187	154	10	or	or	CCONJ
ap-1187	154	11	fermions	fermion	NOUN
ap-1187	154	12	,	,	PUNCT
ap-1187	154	13	and	and	CCONJ
ap-1187	154	14	as	as	ADP
ap-1187	154	15	such	such	ADJ
ap-1187	154	16	,	,	PUNCT
ap-1187	154	17	do	do	AUX
ap-1187	154	18	not	not	PART
ap-1187	154	19	obey	obey	VERB
ap-1187	154	20	the	the	DET
ap-1187	154	21	usual	usual	ADJ
ap-1187	154	22	dirac	dirac	NOUN
ap-1187	154	23	equation	equation	NOUN
ap-1187	154	24	.	.	PUNCT
ap-1187	155	1	if	if	SCONJ
ap-1187	155	2	the	the	DET
ap-1187	155	3	sigma	sigma	NOUN
ap-1187	155	4	-	-	PUNCT
ap-1187	155	5	matrices	matrix	NOUN
ap-1187	155	6	are	be	AUX
ap-1187	155	7	to	to	PART
ap-1187	155	8	be	be	AUX
ap-1187	155	9	replaced	replace	VERB
ap-1187	155	10	by	by	ADP
ap-1187	155	11	the	the	DET
ap-1187	155	12	nonhermitian	nonhermitian	ADJ
ap-1187	155	13	matrices	matrix	NOUN
ap-1187	155	14	πμ	πμ	VERB
ap-1187	155	15	aḃ	aḃ	PRON
ap-1187	155	16	,	,	PUNCT
ap-1187	155	17	instead	instead	ADV
ap-1187	155	18	of	of	ADP
ap-1187	155	19	the	the	DET
ap-1187	155	20	usual	usual	ADJ
ap-1187	155	21	wave	wave	NOUN
ap-1187	155	22	-	-	PUNCT
ap-1187	155	23	like	like	ADJ
ap-1187	155	24	solutions	solution	NOUN
ap-1187	155	25	of	of	ADP
ap-1187	155	26	dirac	dirac	NOUN
ap-1187	155	27	’s	’s	PART
ap-1187	155	28	equation	equation	NOUN
ap-1187	155	29	we	we	PRON
ap-1187	155	30	shall	shall	AUX
ap-1187	155	31	get	get	VERB
ap-1187	155	32	the	the	DET
ap-1187	155	33	exponentials	exponential	NOUN
ap-1187	155	34	of	of	ADP
ap-1187	155	35	complex	complex	ADJ
ap-1187	155	36	wave	wave	NOUN
ap-1187	155	37	vectors	vector	NOUN
ap-1187	155	38	,	,	PUNCT
ap-1187	155	39	and	and	CCONJ
ap-1187	155	40	such	such	ADJ
ap-1187	155	41	solutions	solution	NOUN
ap-1187	155	42	can	can	AUX
ap-1187	155	43	not	not	PART
ap-1187	155	44	propagate	propagate	VERB
ap-1187	155	45	.	.	PUNCT
ap-1187	156	1	nevertheless	nevertheless	ADV
ap-1187	156	2	,	,	PUNCT
ap-1187	156	3	as	as	SCONJ
ap-1187	156	4	argued	argue	VERB
ap-1187	156	5	in	in	ADP
ap-1187	156	6	[	[	PUNCT
ap-1187	156	7	9	9	NUM
ap-1187	156	8	]	]	PUNCT
ap-1187	156	9	,	,	PUNCT
ap-1187	156	10	certain	certain	ADJ
ap-1187	156	11	tri	tri	ADJ
ap-1187	156	12	-	-	ADJ
ap-1187	156	13	linear	linear	ADJ
ap-1187	156	14	and	and	CCONJ
ap-1187	156	15	bi	bi	ADJ
ap-1187	156	16	-	-	ADJ
ap-1187	156	17	linear	linear	ADJ
ap-1187	156	18	combinations	combination	NOUN
ap-1187	156	19	of	of	ADP
ap-1187	156	20	such	such	ADJ
ap-1187	156	21	solutions	solution	NOUN
ap-1187	156	22	behave	behave	VERB
ap-1187	156	23	as	as	ADP
ap-1187	156	24	usual	usual	ADJ
ap-1187	156	25	plane	plane	NOUN
ap-1187	156	26	waves	wave	NOUN
ap-1187	156	27	,	,	PUNCT
ap-1187	156	28	with	with	ADP
ap-1187	156	29	real	real	ADJ
ap-1187	156	30	wave	wave	NOUN
ap-1187	156	31	vectors	vector	NOUN
ap-1187	156	32	and	and	CCONJ
ap-1187	156	33	frequencies	frequency	NOUN
ap-1187	156	34	,	,	PUNCT
ap-1187	156	35	if	if	SCONJ
ap-1187	156	36	there	there	PRON
ap-1187	156	37	is	be	VERB
ap-1187	156	38	a	a	DET
ap-1187	156	39	convenient	convenient	ADJ
ap-1187	156	40	coupling	coupling	NOUN
ap-1187	156	41	of	of	ADP
ap-1187	156	42	non	non	ADJ
ap-1187	156	43	-	-	ADJ
ap-1187	156	44	propagating	propagating	ADJ
ap-1187	156	45	solutions	solution	NOUN
ap-1187	156	46	in	in	ADP
ap-1187	156	47	the	the	DET
ap-1187	156	48	k	k	NOUN
ap-1187	156	49	-	-	NOUN
ap-1187	156	50	space	space	NOUN
ap-1187	156	51	.	.	PUNCT
ap-1187	157	1	acknowledgement	acknowledgement	NOUN
ap-1187	157	2	we	we	PRON
ap-1187	157	3	are	be	AUX
ap-1187	157	4	greatly	greatly	ADV
ap-1187	157	5	indebted	indebted	ADJ
ap-1187	157	6	to	to	ADP
ap-1187	157	7	michel	michel	PROPN
ap-1187	157	8	dubois	dubois	PROPN
ap-1187	157	9	-	-	PUNCT
ap-1187	157	10	violette	violette	PROPN
ap-1187	157	11	for	for	ADP
ap-1187	157	12	numerous	numerous	ADJ
ap-1187	157	13	discussions	discussion	NOUN
ap-1187	157	14	and	and	CCONJ
ap-1187	157	15	enlightening	enlightening	ADJ
ap-1187	157	16	remarks	remark	NOUN
ap-1187	157	17	.	.	PUNCT
ap-1187	158	1	references	reference	NOUN
ap-1187	158	2	[	[	X
ap-1187	158	3	1	1	NUM
ap-1187	158	4	]	]	PUNCT
ap-1187	158	5	born	bear	VERB
ap-1187	158	6	,	,	PUNCT
ap-1187	158	7	m.	m.	NOUN
ap-1187	158	8	,	,	PUNCT
ap-1187	158	9	jordan	jordan	PROPN
ap-1187	158	10	,	,	PUNCT
ap-1187	158	11	p.	p.	NOUN
ap-1187	158	12	:	:	PUNCT
ap-1187	158	13	zeitschrift	zeitschrift	ADJ
ap-1187	158	14	fur	fur	NOUN
ap-1187	158	15	physik	physik	NOUN
ap-1187	158	16	34	34	NUM
ap-1187	158	17	858–878	858–878	NUM
ap-1187	158	18	(	(	PUNCT
ap-1187	158	19	1925	1925	NUM
ap-1187	158	20	)	)	PUNCT
ap-1187	158	21	;	;	PUNCT
ap-1187	158	22	ibid	ibid	PROPN
ap-1187	158	23	heisenberg	heisenberg	PROPN
ap-1187	158	24	,	,	PUNCT
ap-1187	158	25	w.	w.	PROPN
ap-1187	158	26	,	,	PUNCT
ap-1187	158	27	879–890	879–890	NUM
ap-1187	158	28	(	(	PUNCT
ap-1187	158	29	1925	1925	NUM
ap-1187	158	30	)	)	PUNCT
ap-1187	158	31	.	.	PUNCT
ap-1187	159	1	[	[	X
ap-1187	159	2	2	2	NUM
ap-1187	159	3	]	]	X
ap-1187	159	4	von	von	PROPN
ap-1187	159	5	neumann	neumann	PROPN
ap-1187	159	6	,	,	PUNCT
ap-1187	159	7	j.	j.	PROPN
ap-1187	159	8	:	:	PROPN
ap-1187	159	9	mathematical	mathematical	ADJ
ap-1187	159	10	foundations	foundation	NOUN
ap-1187	159	11	of	of	ADP
ap-1187	159	12	quantum	quantum	ADJ
ap-1187	159	13	mechanics	mechanic	NOUN
ap-1187	159	14	,	,	PUNCT
ap-1187	159	15	princeton	princeton	PROPN
ap-1187	159	16	univ	univ	PROPN
ap-1187	159	17	.	.	PUNCT
ap-1187	160	1	press	press	PROPN
ap-1187	160	2	(	(	PUNCT
ap-1187	160	3	1996	1996	NUM
ap-1187	160	4	)	)	PUNCT
ap-1187	160	5	.	.	PUNCT
ap-1187	161	1	[	[	X
ap-1187	161	2	3	3	NUM
ap-1187	161	3	]	]	X
ap-1187	161	4	einstein	einstein	NOUN
ap-1187	161	5	,	,	PUNCT
ap-1187	161	6	a.	a.	NOUN
ap-1187	161	7	,	,	PUNCT
ap-1187	161	8	infeld	infeld	NOUN
ap-1187	161	9	,	,	PUNCT
ap-1187	161	10	l.	l.	PROPN
ap-1187	161	11	:	:	PUNCT
ap-1187	161	12	the	the	DET
ap-1187	161	13	evolution	evolution	NOUN
ap-1187	161	14	of	of	ADP
ap-1187	161	15	physics	physics	PROPN
ap-1187	161	16	,	,	PUNCT
ap-1187	161	17	simon	simon	PROPN
ap-1187	161	18	and	and	CCONJ
ap-1187	161	19	schuster	schuster	PROPN
ap-1187	161	20	,	,	PUNCT
ap-1187	161	21	n.y	n.y	PROPN
ap-1187	161	22	.	.	PROPN
ap-1187	161	23	(	(	PUNCT
ap-1187	161	24	1967	1967	NUM
ap-1187	161	25	)	)	PUNCT
ap-1187	161	26	.	.	PUNCT
ap-1187	162	1	[	[	X
ap-1187	162	2	4	4	NUM
ap-1187	162	3	]	]	X
ap-1187	162	4	dubois	dubois	PROPN
ap-1187	162	5	-	-	PUNCT
ap-1187	162	6	violette	violette	NOUN
ap-1187	162	7	,	,	PUNCT
ap-1187	162	8	m.	m.	NOUN
ap-1187	162	9	,	,	PUNCT
ap-1187	162	10	kerner	kerner	PROPN
ap-1187	162	11	,	,	PUNCT
ap-1187	162	12	r.	r.	PROPN
ap-1187	162	13	,	,	PUNCT
ap-1187	162	14	madore	madore	PROPN
ap-1187	162	15	,	,	PUNCT
ap-1187	162	16	j.	j.	PROPN
ap-1187	162	17	:	:	PUNCT
ap-1187	162	18	journ	journ	PROPN
ap-1187	162	19	.	.	PUNCT
ap-1187	163	1	math	math	NOUN
ap-1187	163	2	.	.	PUNCT
ap-1187	164	1	phys	phy	NOUN
ap-1187	164	2	.	.	PUNCT
ap-1187	165	1	31	31	NUM
ap-1187	165	2	,	,	PUNCT
ap-1187	165	3	316–322	316–322	NUM
ap-1187	165	4	(	(	PUNCT
ap-1187	165	5	1990	1990	NUM
ap-1187	165	6	)	)	PUNCT
ap-1187	165	7	;	;	PUNCT
ap-1187	165	8	ibid	ibid	NOUN
ap-1187	165	9	,	,	PUNCT
ap-1187	165	10	31	31	NUM
ap-1187	165	11	,	,	PUNCT
ap-1187	165	12	323–331	323–331	NUM
ap-1187	165	13	(	(	PUNCT
ap-1187	165	14	1990	1990	NUM
ap-1187	165	15	)	)	PUNCT
ap-1187	165	16	.	.	PUNCT
ap-1187	166	1	[	[	X
ap-1187	166	2	5	5	NUM
ap-1187	166	3	]	]	SYM
ap-1187	166	4	kerner	kerner	PROPN
ap-1187	166	5	,	,	PUNCT
ap-1187	166	6	r.	r.	PROPN
ap-1187	166	7	:	:	PUNCT
ap-1187	166	8	journ	journ	PROPN
ap-1187	166	9	.	.	PUNCT
ap-1187	167	1	math	math	NOUN
ap-1187	167	2	.	.	PUNCT
ap-1187	168	1	phys	phy	NOUN
ap-1187	168	2	.	.	PUNCT
ap-1187	168	3	,	,	PUNCT
ap-1187	168	4	33	33	NUM
ap-1187	168	5	,	,	PUNCT
ap-1187	168	6	403–411	403–411	NUM
ap-1187	168	7	(	(	PUNCT
ap-1187	168	8	1992	1992	NUM
ap-1187	168	9	)	)	PUNCT
ap-1187	168	10	.	.	PUNCT
ap-1187	169	1	[	[	X
ap-1187	169	2	6	6	NUM
ap-1187	169	3	]	]	X
ap-1187	169	4	abramov	abramov	NOUN
ap-1187	169	5	,	,	PUNCT
ap-1187	169	6	v.	v.	PROPN
ap-1187	169	7	,	,	PUNCT
ap-1187	169	8	kerner	kerner	PROPN
ap-1187	169	9	,	,	PUNCT
ap-1187	169	10	r.	r.	PROPN
ap-1187	169	11	,	,	PUNCT
ap-1187	169	12	le	le	PROPN
ap-1187	169	13	roy	roy	PROPN
ap-1187	169	14	,	,	PUNCT
ap-1187	169	15	b.	b.	PROPN
ap-1187	169	16	:	:	PUNCT
ap-1187	169	17	journ	journ	PROPN
ap-1187	169	18	.	.	PUNCT
ap-1187	170	1	math	math	NOUN
ap-1187	170	2	.	.	PUNCT
ap-1187	171	1	phys	phy	NOUN
ap-1187	171	2	.	.	PUNCT
ap-1187	171	3	,	,	PUNCT
ap-1187	171	4	38	38	NUM
ap-1187	171	5	,	,	PUNCT
ap-1187	171	6	1	1	NUM
ap-1187	171	7	650–1	650–1	NUM
ap-1187	171	8	669	669	NUM
ap-1187	171	9	(	(	PUNCT
ap-1187	171	10	1997	1997	NUM
ap-1187	171	11	)	)	PUNCT
ap-1187	171	12	.	.	PUNCT
ap-1187	172	1	[	[	X
ap-1187	172	2	7	7	NUM
ap-1187	172	3	]	]	X
ap-1187	172	4	lipatov	lipatov	NOUN
ap-1187	172	5	,	,	PUNCT
ap-1187	172	6	l.	l.	PROPN
ap-1187	172	7	n.	n.	PROPN
ap-1187	172	8	,	,	PUNCT
ap-1187	172	9	rausch	rausch	PROPN
ap-1187	172	10	de	de	PROPN
ap-1187	172	11	traubenberg	traubenberg	PROPN
ap-1187	172	12	,	,	PUNCT
ap-1187	172	13	m.	m.	NOUN
ap-1187	172	14	,	,	PUNCT
ap-1187	172	15	volkov	volkov	PROPN
ap-1187	172	16	,	,	PUNCT
ap-1187	172	17	g.	g.	PROPN
ap-1187	172	18	g.	g.	PROPN
ap-1187	172	19	:	:	PUNCT
ap-1187	172	20	journ	journ	PROPN
ap-1187	172	21	.	.	PUNCT
ap-1187	173	1	of	of	ADP
ap-1187	173	2	math	math	NOUN
ap-1187	173	3	.	.	PUNCT
ap-1187	174	1	phys	phy	NOUN
ap-1187	174	2	.	.	PUNCT
ap-1187	175	1	49	49	NUM
ap-1187	175	2	013502	013502	NUM
ap-1187	175	3	(	(	PUNCT
ap-1187	175	4	2008	2008	NUM
ap-1187	175	5	)	)	PUNCT
ap-1187	175	6	.	.	PUNCT
ap-1187	176	1	[	[	X
ap-1187	176	2	8	8	NUM
ap-1187	176	3	]	]	PUNCT
ap-1187	176	4	campoamor	campoamor	NOUN
ap-1187	176	5	-	-	PUNCT
ap-1187	176	6	stursberg	stursberg	PROPN
ap-1187	176	7	,	,	PUNCT
ap-1187	176	8	r.	r.	PROPN
ap-1187	176	9	,	,	PUNCT
ap-1187	176	10	rausch	rausch	PROPN
ap-1187	176	11	de	de	PROPN
ap-1187	176	12	traubenberg	traubenberg	PROPN
ap-1187	176	13	,	,	PUNCT
ap-1187	176	14	m.	m.	NOUN
ap-1187	176	15	:	:	PUNCT
ap-1187	176	16	journ	journ	NOUN
ap-1187	176	17	.	.	PUNCT
ap-1187	177	1	of	of	ADP
ap-1187	177	2	math	math	NOUN
ap-1187	177	3	.	.	PUNCT
ap-1187	178	1	phys	phy	NOUN
ap-1187	178	2	.	.	PUNCT
ap-1187	179	1	49	49	NUM
ap-1187	179	2	063506	063506	NUM
ap-1187	179	3	(	(	PUNCT
ap-1187	179	4	2008	2008	NUM
ap-1187	179	5	)	)	PUNCT
ap-1187	179	6	.	.	PUNCT
ap-1187	180	1	[	[	X
ap-1187	180	2	9	9	NUM
ap-1187	180	3	]	]	SYM
ap-1187	180	4	kerner	kerner	PROPN
ap-1187	180	5	,	,	PUNCT
ap-1187	180	6	r.	r.	PROPN
ap-1187	180	7	:	:	PUNCT
ap-1187	180	8	class	class	NOUN
ap-1187	180	9	.	.	PUNCT
ap-1187	181	1	and	and	CCONJ
ap-1187	181	2	quantum	quantum	NOUN
ap-1187	181	3	gravity	gravity	NOUN
ap-1187	181	4	,	,	PUNCT
ap-1187	181	5	14	14	NUM
ap-1187	181	6	,	,	PUNCT
ap-1187	181	7	a203	a203	PROPN
ap-1187	181	8	-	-	PUNCT
ap-1187	181	9	a225	a225	PROPN
ap-1187	181	10	(	(	PUNCT
ap-1187	181	11	1997	1997	NUM
ap-1187	181	12	)	)	PUNCT
ap-1187	181	13	.	.	PUNCT
ap-1187	182	1	richard	richard	PROPN
ap-1187	182	2	kerner	kerner	PROPN
ap-1187	182	3	laboratoire	laboratoire	PROPN
ap-1187	182	4	de	de	PROPN
ap-1187	182	5	physique	physique	PROPN
ap-1187	182	6	théorique	théorique	PROPN
ap-1187	182	7	de	de	X
ap-1187	182	8	la	la	X
ap-1187	182	9	matière	matière	PROPN
ap-1187	182	10	condensée	condensée	PROPN
ap-1187	182	11	université	université	ADJ
ap-1187	182	12	pierre	pierre	PROPN
ap-1187	182	13	-	-	PUNCT
ap-1187	182	14	et	et	PROPN
ap-1187	182	15	-	-	PUNCT
ap-1187	182	16	marie	marie	PROPN
ap-1187	182	17	-	-	PUNCT
ap-1187	182	18	curie	curie	PROPN
ap-1187	182	19	–	–	PUNCT
ap-1187	182	20	cnrs	cnrs	NOUN
ap-1187	182	21	umr	umr	ADJ
ap-1187	182	22	7600	7600	NUM
ap-1187	182	23	tour	tour	NOUN
ap-1187	182	24	22	22	NUM
ap-1187	182	25	,	,	PUNCT
ap-1187	182	26	4	4	NUM
ap-1187	182	27	-	-	PUNCT
ap-1187	182	28	ème	ème	NOUN
ap-1187	182	29	étage	étage	NOUN
ap-1187	182	30	,	,	PUNCT
ap-1187	182	31	bôite	bôite	VERB
ap-1187	182	32	121	121	NUM
ap-1187	182	33	4	4	NUM
ap-1187	182	34	,	,	PUNCT
ap-1187	182	35	place	place	NOUN
ap-1187	182	36	jussieu	jussieu	PROPN
ap-1187	182	37	,	,	PUNCT
ap-1187	182	38	75005	75005	NUM
ap-1187	182	39	paris	paris	PROPN
ap-1187	182	40	,	,	PUNCT
ap-1187	182	41	france	france	PROPN
ap-1187	182	42	41	41	NUM