id	sid	tid	token	lemma	pos
ijassa-1408	1	1	adv	adv	PROPN
ijassa-1408	1	2	syst	syst	PROPN
ijassa-1408	1	3	sci	sci	PROPN
ijassa-1408	1	4	appl	appl	PROPN
ijassa-1408	1	5	2023	2023	NUM
ijassa-1408	1	6	;	;	PUNCT
ijassa-1408	1	7	02:178–183	02:178–183	NUM
ijassa-1408	1	8	published	publish	VERB
ijassa-1408	1	9	online	online	ADV
ijassa-1408	1	10	at	at	ADP
ijassa-1408	1	11	https://ijassa.ipu.ru	https://ijassa.ipu.ru	ADV
ijassa-1408	1	12	.	.	PUNCT
ijassa-1408	2	1	a	a	DET
ijassa-1408	2	2	combinatorial	combinatorial	ADJ
ijassa-1408	2	3	view	view	NOUN
ijassa-1408	2	4	on	on	ADP
ijassa-1408	2	5	derivations	derivation	NOUN
ijassa-1408	2	6	in	in	ADP
ijassa-1408	2	7	bimodules	bimodule	NOUN
ijassa-1408	2	8	andronick	andronick	PROPN
ijassa-1408	2	9	a.	a.	PROPN
ijassa-1408	2	10	arutyunov	arutyunov	PROPN
ijassa-1408	2	11	*	*	PROPN
ijassa-1408	2	12	v.	v.	ADP
ijassa-1408	2	13	a.	a.	PROPN
ijassa-1408	2	14	trapeznikov	trapeznikov	PROPN
ijassa-1408	2	15	institute	institute	PROPN
ijassa-1408	2	16	of	of	ADP
ijassa-1408	2	17	control	control	PROPN
ijassa-1408	2	18	sciences	sciences	PROPN
ijassa-1408	2	19	of	of	ADP
ijassa-1408	2	20	russian	russian	ADJ
ijassa-1408	2	21	academy	academy	PROPN
ijassa-1408	2	22	of	of	ADP
ijassa-1408	2	23	sciences	sciences	PROPN
ijassa-1408	2	24	,	,	PUNCT
ijassa-1408	2	25	moscow	moscow	PROPN
ijassa-1408	2	26	,	,	PUNCT
ijassa-1408	2	27	russia	russia	PROPN
ijassa-1408	2	28	moscow	moscow	PROPN
ijassa-1408	2	29	institute	institute	PROPN
ijassa-1408	2	30	of	of	ADP
ijassa-1408	2	31	physics	physics	PROPN
ijassa-1408	2	32	and	and	CCONJ
ijassa-1408	2	33	technology	technology	NOUN
ijassa-1408	2	34	(	(	PUNCT
ijassa-1408	2	35	state	state	NOUN
ijassa-1408	2	36	university	university	NOUN
ijassa-1408	2	37	)	)	PUNCT
ijassa-1408	2	38	,	,	PUNCT
ijassa-1408	2	39	dolgoprudniy	dolgoprudniy	ADJ
ijassa-1408	2	40	,	,	PUNCT
ijassa-1408	2	41	russia	russia	PROPN
ijassa-1408	2	42	abstract	abstract	NOUN
ijassa-1408	2	43	:	:	PUNCT
ijassa-1408	2	44	this	this	DET
ijassa-1408	2	45	paper	paper	NOUN
ijassa-1408	2	46	is	be	AUX
ijassa-1408	2	47	devoted	devote	VERB
ijassa-1408	2	48	to	to	ADP
ijassa-1408	2	49	derivations	derivation	NOUN
ijassa-1408	2	50	in	in	ADP
ijassa-1408	2	51	bimodules	bimodule	NOUN
ijassa-1408	2	52	over	over	ADP
ijassa-1408	2	53	group	group	NOUN
ijassa-1408	2	54	rings	ring	NOUN
ijassa-1408	2	55	using	use	VERB
ijassa-1408	2	56	previously	previously	ADV
ijassa-1408	2	57	proposed	propose	VERB
ijassa-1408	2	58	methods	method	NOUN
ijassa-1408	2	59	which	which	PRON
ijassa-1408	2	60	are	be	AUX
ijassa-1408	2	61	related	relate	VERB
ijassa-1408	2	62	to	to	ADP
ijassa-1408	2	63	character	character	NOUN
ijassa-1408	2	64	spaces	space	NOUN
ijassa-1408	2	65	over	over	ADP
ijassa-1408	2	66	groupoids	groupoid	NOUN
ijassa-1408	2	67	.	.	PUNCT
ijassa-1408	3	1	we	we	PRON
ijassa-1408	3	2	consider	consider	VERB
ijassa-1408	3	3	bimodules	bimodule	NOUN
ijassa-1408	3	4	which	which	PRON
ijassa-1408	3	5	are	be	AUX
ijassa-1408	3	6	closures	closure	NOUN
ijassa-1408	3	7	of	of	ADP
ijassa-1408	3	8	a	a	DET
ijassa-1408	3	9	group	group	NOUN
ijassa-1408	3	10	algebra	algebra	NOUN
ijassa-1408	3	11	with	with	ADP
ijassa-1408	3	12	respect	respect	NOUN
ijassa-1408	3	13	to	to	ADP
ijassa-1408	3	14	norms	norm	NOUN
ijassa-1408	3	15	of	of	ADP
ijassa-1408	3	16	subordinate	subordinate	ADJ
ijassa-1408	3	17	supremum	supremum	PROPN
ijassa-1408	3	18	norma	norma	PROPN
ijassa-1408	3	19	.	.	PUNCT
ijassa-1408	4	1	the	the	DET
ijassa-1408	4	2	main	main	ADJ
ijassa-1408	4	3	theorem	theorem	NOUN
ijassa-1408	4	4	proves	prove	VERB
ijassa-1408	4	5	that	that	SCONJ
ijassa-1408	4	6	all	all	DET
ijassa-1408	4	7	derivations	derivation	NOUN
ijassa-1408	4	8	in	in	ADP
ijassa-1408	4	9	such	such	ADJ
ijassa-1408	4	10	bimodulues	bimodulue	NOUN
ijassa-1408	4	11	are	be	AUX
ijassa-1408	4	12	quasiinner	quasiinner	NOUN
ijassa-1408	4	13	.	.	PUNCT
ijassa-1408	5	1	we	we	PRON
ijassa-1408	5	2	also	also	ADV
ijassa-1408	5	3	consider	consider	VERB
ijassa-1408	5	4	some	some	DET
ijassa-1408	5	5	examples	example	NOUN
ijassa-1408	5	6	,	,	PUNCT
ijassa-1408	5	7	in	in	ADP
ijassa-1408	5	8	particular	particular	ADJ
ijassa-1408	5	9	the	the	DET
ijassa-1408	5	10	case	case	NOUN
ijassa-1408	5	11	of	of	ADP
ijassa-1408	5	12	(	(	PUNCT
ijassa-1408	5	13	σ	σ	NOUN
ijassa-1408	5	14	,	,	PUNCT
ijassa-1408	5	15	τ)-derivations	τ)-derivation	NOUN
ijassa-1408	5	16	.	.	PUNCT
ijassa-1408	6	1	keywords	keyword	NOUN
ijassa-1408	6	2	:	:	PUNCT
ijassa-1408	6	3	derivations	derivation	NOUN
ijassa-1408	6	4	,	,	PUNCT
ijassa-1408	6	5	bimodule	bimodule	NOUN
ijassa-1408	6	6	,	,	PUNCT
ijassa-1408	6	7	outer	outer	ADJ
ijassa-1408	6	8	derivations	derivation	NOUN
ijassa-1408	6	9	1	1	NUM
ijassa-1408	6	10	.	.	PUNCT
ijassa-1408	6	11	introduction	introduction	NOUN
ijassa-1408	6	12	derivations	derivation	NOUN
ijassa-1408	6	13	in	in	ADP
ijassa-1408	6	14	various	various	ADJ
ijassa-1408	6	15	associative	associative	ADJ
ijassa-1408	6	16	algebras	algebra	NOUN
ijassa-1408	6	17	have	have	AUX
ijassa-1408	6	18	been	be	AUX
ijassa-1408	6	19	actively	actively	ADV
ijassa-1408	6	20	studied	study	VERB
ijassa-1408	6	21	since	since	SCONJ
ijassa-1408	6	22	the	the	DET
ijassa-1408	6	23	middle	middle	NOUN
ijassa-1408	6	24	of	of	ADP
ijassa-1408	6	25	the	the	DET
ijassa-1408	6	26	last	last	ADJ
ijassa-1408	6	27	century	century	NOUN
ijassa-1408	6	28	.	.	PUNCT
ijassa-1408	7	1	in	in	ADP
ijassa-1408	7	2	particular	particular	ADJ
ijassa-1408	7	3	,	,	PUNCT
ijassa-1408	7	4	the	the	DET
ijassa-1408	7	5	following	follow	VERB
ijassa-1408	7	6	question	question	NOUN
ijassa-1408	7	7	,	,	PUNCT
ijassa-1408	7	8	known	know	VERB
ijassa-1408	7	9	as	as	ADP
ijassa-1408	7	10	the	the	DET
ijassa-1408	7	11	johnson	johnson	PROPN
ijassa-1408	7	12	problem	problem	NOUN
ijassa-1408	7	13	(	(	PUNCT
ijassa-1408	7	14	or	or	CCONJ
ijassa-1408	7	15	”	"	PUNCT
ijassa-1408	7	16	derivation	derivation	NOUN
ijassa-1408	7	17	problem	problem	NOUN
ijassa-1408	7	18	”	"	PUNCT
ijassa-1408	7	19	)	)	PUNCT
ijassa-1408	7	20	,	,	PUNCT
ijassa-1408	7	21	is	be	AUX
ijassa-1408	7	22	widely	widely	ADV
ijassa-1408	7	23	known	know	VERB
ijassa-1408	7	24	:	:	PUNCT
ijassa-1408	7	25	hypothesis	hypothesis	NOUN
ijassa-1408	7	26	(	(	PUNCT
ijassa-1408	7	27	[	[	X
ijassa-1408	7	28	1	1	NUM
ijassa-1408	7	29	]	]	PUNCT
ijassa-1408	7	30	,	,	PUNCT
ijassa-1408	7	31	question	question	NOUN
ijassa-1408	7	32	5.6.b	5.6.b	NUM
ijassa-1408	7	33	):	):	PUNCT
ijassa-1408	7	34	is	be	AUX
ijassa-1408	7	35	it	it	PRON
ijassa-1408	7	36	true	true	ADJ
ijassa-1408	7	37	that	that	SCONJ
ijassa-1408	7	38	all	all	DET
ijassa-1408	7	39	derivations	derivation	NOUN
ijassa-1408	7	40	in	in	ADP
ijassa-1408	7	41	l1(g	l1(g	PROPN
ijassa-1408	7	42	)	)	PUNCT
ijassa-1408	7	43	are	be	AUX
ijassa-1408	7	44	inner	inner	ADJ
ijassa-1408	7	45	?	?	PUNCT
ijassa-1408	8	1	here	here	ADV
ijassa-1408	8	2	and	and	CCONJ
ijassa-1408	8	3	hereafter	hereaft	ADJ
ijassa-1408	8	4	g	g	PROPN
ijassa-1408	8	5	is	be	AUX
ijassa-1408	8	6	a	a	DET
ijassa-1408	8	7	finitely	finitely	ADV
ijassa-1408	8	8	generated	generate	VERB
ijassa-1408	8	9	generally	generally	ADV
ijassa-1408	8	10	noncommutative	noncommutative	ADJ
ijassa-1408	8	11	group	group	NOUN
ijassa-1408	8	12	.	.	PUNCT
ijassa-1408	9	1	a	a	DET
ijassa-1408	9	2	partial	partial	ADJ
ijassa-1408	9	3	answer	answer	NOUN
ijassa-1408	9	4	to	to	ADP
ijassa-1408	9	5	this	this	DET
ijassa-1408	9	6	question	question	NOUN
ijassa-1408	9	7	was	be	AUX
ijassa-1408	9	8	given	give	VERB
ijassa-1408	9	9	by	by	ADP
ijassa-1408	9	10	b.	b.	PROPN
ijassa-1408	9	11	johnson	johnson	PROPN
ijassa-1408	9	12	himself	himself	PRON
ijassa-1408	9	13	in	in	ADP
ijassa-1408	9	14	[	[	X
ijassa-1408	9	15	2	2	NUM
ijassa-1408	9	16	]	]	PUNCT
ijassa-1408	9	17	,	,	PUNCT
ijassa-1408	9	18	and	and	CCONJ
ijassa-1408	9	19	the	the	DET
ijassa-1408	9	20	most	most	ADV
ijassa-1408	9	21	complete	complete	ADJ
ijassa-1408	9	22	answer	answer	NOUN
ijassa-1408	9	23	was	be	AUX
ijassa-1408	9	24	found	find	VERB
ijassa-1408	9	25	by	by	ADP
ijassa-1408	9	26	v.	v.	ADP
ijassa-1408	9	27	losert	losert	PROPN
ijassa-1408	9	28	in	in	ADP
ijassa-1408	9	29	[	[	X
ijassa-1408	9	30	3	3	NUM
ijassa-1408	9	31	]	]	PUNCT
ijassa-1408	9	32	.	.	PUNCT
ijassa-1408	10	1	a	a	DET
ijassa-1408	10	2	more	more	ADV
ijassa-1408	10	3	detailed	detailed	ADJ
ijassa-1408	10	4	description	description	NOUN
ijassa-1408	10	5	of	of	ADP
ijassa-1408	10	6	the	the	DET
ijassa-1408	10	7	history	history	NOUN
ijassa-1408	10	8	of	of	ADP
ijassa-1408	10	9	this	this	DET
ijassa-1408	10	10	problem	problem	NOUN
ijassa-1408	10	11	is	be	AUX
ijassa-1408	10	12	given	give	VERB
ijassa-1408	10	13	in	in	ADP
ijassa-1408	10	14	[	[	X
ijassa-1408	10	15	1	1	NUM
ijassa-1408	10	16	,	,	PUNCT
ijassa-1408	10	17	4	4	NUM
ijassa-1408	10	18	]	]	PUNCT
ijassa-1408	10	19	.	.	PUNCT
ijassa-1408	11	1	in	in	ADP
ijassa-1408	11	2	purely	purely	ADV
ijassa-1408	11	3	algebraic	algebraic	ADJ
ijassa-1408	11	4	form	form	NOUN
ijassa-1408	11	5	,	,	PUNCT
ijassa-1408	11	6	consider	consider	VERB
ijassa-1408	11	7	the	the	DET
ijassa-1408	11	8	group	group	NOUN
ijassa-1408	11	9	ring	ring	NOUN
ijassa-1408	11	10	c[g	c[g	PROPN
ijassa-1408	11	11	]	]	PUNCT
ijassa-1408	11	12	,	,	PUNCT
ijassa-1408	11	13	that	that	ADV
ijassa-1408	11	14	is	is	ADV
ijassa-1408	11	15	,	,	PUNCT
ijassa-1408	11	16	the	the	DET
ijassa-1408	11	17	space	space	NOUN
ijassa-1408	11	18	of	of	ADP
ijassa-1408	11	19	all	all	DET
ijassa-1408	11	20	linear	linear	ADJ
ijassa-1408	11	21	combinations	combination	NOUN
ijassa-1408	11	22	of	of	ADP
ijassa-1408	11	23	the	the	DET
ijassa-1408	11	24	form	form	NOUN
ijassa-1408	11	25	∑	∑	PUNCT
ijassa-1408	11	26	g∈g	g∈g	PROPN
ijassa-1408	11	27	x(g)g	x(g)g	PROPN
ijassa-1408	11	28	,	,	PUNCT
ijassa-1408	11	29	where	where	SCONJ
ijassa-1408	11	30	x	x	X
ijassa-1408	11	31	(	(	PUNCT
ijassa-1408	11	32	·	·	PUNCT
ijassa-1408	11	33	)	)	PUNCT
ijassa-1408	11	34	is	be	AUX
ijassa-1408	11	35	a	a	DET
ijassa-1408	11	36	finite	finite	ADJ
ijassa-1408	11	37	function	function	NOUN
ijassa-1408	11	38	–	–	PUNCT
ijassa-1408	11	39	a	a	DET
ijassa-1408	11	40	function	function	NOUN
ijassa-1408	11	41	with	with	ADP
ijassa-1408	11	42	a	a	DET
ijassa-1408	11	43	finite	finite	ADJ
ijassa-1408	11	44	support	support	NOUN
ijassa-1408	11	45	.	.	PUNCT
ijassa-1408	12	1	the	the	DET
ijassa-1408	12	2	derivation	derivation	NOUN
ijassa-1408	12	3	in	in	ADP
ijassa-1408	12	4	this	this	DET
ijassa-1408	12	5	case	case	NOUN
ijassa-1408	12	6	is	be	AUX
ijassa-1408	12	7	a	a	DET
ijassa-1408	12	8	linear	linear	ADJ
ijassa-1408	12	9	operator	operator	NOUN
ijassa-1408	12	10	d	d	NOUN
ijassa-1408	12	11	:	:	PUNCT
ijassa-1408	12	12	c[g	c[g	X
ijassa-1408	12	13	]	]	PUNCT
ijassa-1408	12	14	→	→	SYM
ijassa-1408	12	15	c[g	c[g	X
ijassa-1408	12	16	]	]	PUNCT
ijassa-1408	12	17	satisfying	satisfy	VERB
ijassa-1408	12	18	the	the	DET
ijassa-1408	12	19	leibniz	leibniz	PROPN
ijassa-1408	12	20	rule	rule	PROPN
ijassa-1408	12	21	d(uv	d(uv	NOUN
ijassa-1408	12	22	)	)	PUNCT
ijassa-1408	12	23	=	=	SYM
ijassa-1408	13	1	d(u)v	d(u)v	PROPN
ijassa-1408	14	1	+	+	CCONJ
ijassa-1408	14	2	ud(v	ud(v	NUM
ijassa-1408	14	3	)	)	PUNCT
ijassa-1408	14	4	,	,	PUNCT
ijassa-1408	14	5	∀u	∀u	NOUN
ijassa-1408	14	6	,	,	PUNCT
ijassa-1408	14	7	v	v	NOUN
ijassa-1408	14	8	∈	∈	PROPN
ijassa-1408	14	9	c[g	c[g	NOUN
ijassa-1408	14	10	]	]	PUNCT
ijassa-1408	14	11	.	.	PUNCT
ijassa-1408	15	1	the	the	DET
ijassa-1408	15	2	johnson	johnson	PROPN
ijassa-1408	15	3	’s	’s	PART
ijassa-1408	15	4	problem	problem	NOUN
ijassa-1408	15	5	is	be	AUX
ijassa-1408	15	6	whether	whether	SCONJ
ijassa-1408	15	7	there	there	PRON
ijassa-1408	15	8	are	be	VERB
ijassa-1408	15	9	derivation	derivation	NOUN
ijassa-1408	15	10	other	other	ADJ
ijassa-1408	15	11	than	than	ADP
ijassa-1408	15	12	inner	inner	ADJ
ijassa-1408	15	13	,	,	PUNCT
ijassa-1408	15	14	i.e.	i.e.	X
ijassa-1408	15	15	,	,	PUNCT
ijassa-1408	15	16	having	have	VERB
ijassa-1408	15	17	the	the	DET
ijassa-1408	15	18	form	form	NOUN
ijassa-1408	15	19	da	da	NOUN
ijassa-1408	15	20	:	:	PUNCT
ijassa-1408	15	21	x→	x→	PUNCT
ijassa-1408	16	1	[	[	X
ijassa-1408	16	2	a	a	X
ijassa-1408	16	3	,	,	PUNCT
ijassa-1408	16	4	x	x	X
ijassa-1408	16	5	]	]	X
ijassa-1408	16	6	,	,	PUNCT
ijassa-1408	16	7	a	a	DET
ijassa-1408	16	8	∈	∈	PROPN
ijassa-1408	16	9	c[g	c[g	NOUN
ijassa-1408	16	10	]	]	PUNCT
ijassa-1408	16	11	.	.	PUNCT
ijassa-1408	17	1	in	in	ADP
ijassa-1408	17	2	this	this	DET
ijassa-1408	17	3	formulation	formulation	NOUN
ijassa-1408	17	4	of	of	ADP
ijassa-1408	17	5	the	the	DET
ijassa-1408	17	6	problem	problem	NOUN
ijassa-1408	17	7	,	,	PUNCT
ijassa-1408	17	8	the	the	DET
ijassa-1408	17	9	algebra	algebra	NOUN
ijassa-1408	17	10	of	of	ADP
ijassa-1408	17	11	outer	outer	ADJ
ijassa-1408	17	12	derivations	derivation	NOUN
ijassa-1408	17	13	will	will	AUX
ijassa-1408	17	14	be	be	AUX
ijassa-1408	17	15	nontrivial	nontrivial	ADJ
ijassa-1408	17	16	(	(	PUNCT
ijassa-1408	17	17	see	see	VERB
ijassa-1408	17	18	central	central	ADJ
ijassa-1408	17	19	derivations	derivation	NOUN
ijassa-1408	17	20	from	from	ADP
ijassa-1408	17	21	[	[	X
ijassa-1408	17	22	5	5	NUM
ijassa-1408	17	23	]	]	PUNCT
ijassa-1408	17	24	as	as	ADV
ijassa-1408	17	25	well	well	ADV
ijassa-1408	17	26	as	as	ADP
ijassa-1408	17	27	more	more	ADJ
ijassa-1408	17	28	general	general	ADJ
ijassa-1408	17	29	results	result	NOUN
ijassa-1408	17	30	from	from	ADP
ijassa-1408	17	31	[	[	X
ijassa-1408	17	32	4	4	NUM
ijassa-1408	17	33	]	]	NUM
ijassa-1408	17	34	)	)	PUNCT
ijassa-1408	17	35	.	.	PUNCT
ijassa-1408	18	1	in	in	ADP
ijassa-1408	18	2	the	the	DET
ijassa-1408	18	3	present	present	ADJ
ijassa-1408	18	4	paper	paper	NOUN
ijassa-1408	18	5	we	we	PRON
ijassa-1408	18	6	focus	focus	VERB
ijassa-1408	18	7	on	on	ADP
ijassa-1408	18	8	the	the	DET
ijassa-1408	18	9	study	study	NOUN
ijassa-1408	18	10	of	of	ADP
ijassa-1408	18	11	banach	banach	NOUN
ijassa-1408	18	12	spaces	space	NOUN
ijassa-1408	18	13	equipped	equip	VERB
ijassa-1408	18	14	with	with	ADP
ijassa-1408	18	15	a	a	DET
ijassa-1408	18	16	bimodule	bimodule	ADJ
ijassa-1408	18	17	structure	structure	NOUN
ijassa-1408	18	18	over	over	ADP
ijassa-1408	18	19	a	a	DET
ijassa-1408	18	20	group	group	NOUN
ijassa-1408	18	21	ring	ring	NOUN
ijassa-1408	18	22	c[g	c[g	NOUN
ijassa-1408	18	23	]	]	PUNCT
ijassa-1408	18	24	of	of	ADP
ijassa-1408	18	25	the	the	DET
ijassa-1408	18	26	following	follow	VERB
ijassa-1408	18	27	form	form	NOUN
ijassa-1408	18	28	.	.	PUNCT
ijassa-1408	19	1	let	let	VERB
ijassa-1408	19	2	us	we	PRON
ijassa-1408	19	3	fix	fix	VERB
ijassa-1408	19	4	a	a	DET
ijassa-1408	19	5	norm	norm	NOUN
ijassa-1408	19	6	∥	∥	X
ijassa-1408	19	7	·	·	PUNCT
ijassa-1408	19	8	∥	∥	NUM
ijassa-1408	19	9	in	in	ADP
ijassa-1408	19	10	c[g	c[g	NOUN
ijassa-1408	19	11	]	]	PUNCT
ijassa-1408	19	12	and	and	CCONJ
ijassa-1408	19	13	let	let	VERB
ijassa-1408	19	14	a	a	PRON
ijassa-1408	19	15	be	be	AUX
ijassa-1408	19	16	the	the	DET
ijassa-1408	19	17	closure	closure	NOUN
ijassa-1408	19	18	of	of	ADP
ijassa-1408	19	19	the	the	DET
ijassa-1408	19	20	group	group	NOUN
ijassa-1408	19	21	ring	ring	NOUN
ijassa-1408	19	22	by	by	ADP
ijassa-1408	19	23	this	this	DET
ijassa-1408	19	24	norm	norm	NOUN
ijassa-1408	19	25	.	.	PUNCT
ijassa-1408	20	1	a	a	PRON
ijassa-1408	20	2	is	be	AUX
ijassa-1408	20	3	not	not	PART
ijassa-1408	20	4	an	an	DET
ijassa-1408	20	5	algebra	algebra	NOUN
ijassa-1408	20	6	,	,	PUNCT
ijassa-1408	20	7	but	but	CCONJ
ijassa-1408	20	8	it	it	PRON
ijassa-1408	20	9	is	be	AUX
ijassa-1408	20	10	naturally	naturally	ADV
ijassa-1408	20	11	understood	understand	VERB
ijassa-1408	20	12	as	as	ADP
ijassa-1408	20	13	a	a	DET
ijassa-1408	20	14	free	free	ADJ
ijassa-1408	20	15	bimodule	bimodule	NOUN
ijassa-1408	20	16	over	over	ADP
ijassa-1408	20	17	the	the	DET
ijassa-1408	20	18	ring	ring	NOUN
ijassa-1408	20	19	c[g	c[g	NOUN
ijassa-1408	20	20	]	]	PUNCT
ijassa-1408	20	21	.	.	PUNCT
ijassa-1408	21	1	∗corresponding	∗corresponde	VERB
ijassa-1408	21	2	author	author	NOUN
ijassa-1408	21	3	:	:	PUNCT
ijassa-1408	21	4	andronick.arutyunov@gmail.com	andronick.arutyunov@gmail.com	X
ijassa-1408	21	5	a	a	DET
ijassa-1408	21	6	combinatorial	combinatorial	ADJ
ijassa-1408	21	7	view	view	NOUN
ijassa-1408	21	8	on	on	ADP
ijassa-1408	21	9	derivations	derivation	NOUN
ijassa-1408	21	10	in	in	ADP
ijassa-1408	21	11	bimodules	bimodule	NOUN
ijassa-1408	21	12	179	179	NUM
ijassa-1408	21	13	the	the	DET
ijassa-1408	21	14	ring	ring	NOUN
ijassa-1408	21	15	c[g	c[g	NOUN
ijassa-1408	21	16	]	]	PUNCT
ijassa-1408	21	17	will	will	AUX
ijassa-1408	21	18	be	be	AUX
ijassa-1408	21	19	defined	define	VERB
ijassa-1408	21	20	as	as	ADP
ijassa-1408	21	21	a	a	DET
ijassa-1408	21	22	space	space	NOUN
ijassa-1408	21	23	with	with	ADP
ijassa-1408	21	24	the	the	DET
ijassa-1408	21	25	supremum	supremum	ADJ
ijassa-1408	21	26	norm	norm	NOUN
ijassa-1408	21	27	∥	∥	X
ijassa-1408	21	28	·	·	PUNCT
ijassa-1408	21	29	∥|s	∥|	NOUN
ijassa-1408	21	30	,	,	PUNCT
ijassa-1408	21	31	i.e.	i.e.	X
ijassa-1408	21	32	for	for	ADP
ijassa-1408	21	33	ω	ω	NUM
ijassa-1408	21	34	=	=	SYM
ijassa-1408	21	35	∑	∑	PUNCT
ijassa-1408	21	36	g∈g	g∈g	PROPN
ijassa-1408	21	37	x(g)g	x(g)g	PROPN
ijassa-1408	21	38	we	we	PRON
ijassa-1408	21	39	put	put	VERB
ijassa-1408	21	40	∥ω∥s	∥ω∥s	NOUN
ijassa-1408	22	1	:	:	PUNCT
ijassa-1408	22	2	=	=	SYM
ijassa-1408	22	3	sup	sup	NUM
ijassa-1408	22	4	g∈g	g∈g	PROPN
ijassa-1408	22	5	|x(g)|	|x(g)|	PROPN
ijassa-1408	22	6	.	.	PUNCT
ijassa-1408	23	1	the	the	DET
ijassa-1408	23	2	boundedness	boundedness	NOUN
ijassa-1408	23	3	of	of	ADP
ijassa-1408	23	4	operators	operator	NOUN
ijassa-1408	23	5	will	will	AUX
ijassa-1408	23	6	be	be	AUX
ijassa-1408	23	7	defined	define	VERB
ijassa-1408	23	8	as	as	SCONJ
ijassa-1408	23	9	follows	follow	VERB
ijassa-1408	23	10	.	.	PUNCT
ijassa-1408	24	1	let	let	VERB
ijassa-1408	24	2	us	we	PRON
ijassa-1408	24	3	define	define	VERB
ijassa-1408	24	4	the	the	DET
ijassa-1408	24	5	norm	norm	NOUN
ijassa-1408	24	6	of	of	ADP
ijassa-1408	24	7	the	the	DET
ijassa-1408	24	8	operator	operator	NOUN
ijassa-1408	24	9	d	d	NOUN
ijassa-1408	24	10	as	as	ADP
ijassa-1408	24	11	∥d∥	∥d∥	NOUN
ijassa-1408	24	12	=	=	NOUN
ijassa-1408	24	13	sup	sup	NOUN
ijassa-1408	24	14	0̸=ω∈c[g	0̸=ω∈c[g	NOUN
ijassa-1408	24	15	]	]	X
ijassa-1408	24	16	∥d(ω)∥	∥d(ω)∥	PROPN
ijassa-1408	24	17	∥ω∥s	∥ω∥s	NOUN
ijassa-1408	24	18	.	.	PUNCT
ijassa-1408	25	1	(	(	PUNCT
ijassa-1408	25	2	1.1	1.1	NUM
ijassa-1408	25	3	)	)	PUNCT
ijassa-1408	25	4	definition	definition	NOUN
ijassa-1408	25	5	1.1	1.1	NUM
ijassa-1408	25	6	:	:	PUNCT
ijassa-1408	25	7	by	by	ADP
ijassa-1408	25	8	the	the	DET
ijassa-1408	25	9	derivation	derivation	NOUN
ijassa-1408	25	10	over	over	ADP
ijassa-1408	25	11	c[g	c[g	NOUN
ijassa-1408	25	12	]	]	PUNCT
ijassa-1408	25	13	with	with	ADP
ijassa-1408	25	14	values	value	NOUN
ijassa-1408	25	15	in	in	ADP
ijassa-1408	25	16	bimodule	bimodule	NOUN
ijassa-1408	25	17	a	a	PRON
ijassa-1408	25	18	we	we	PRON
ijassa-1408	25	19	will	will	AUX
ijassa-1408	25	20	call	call	VERB
ijassa-1408	25	21	a	a	DET
ijassa-1408	25	22	linear	linear	ADJ
ijassa-1408	25	23	bounded	bound	VERB
ijassa-1408	25	24	operator	operator	NOUN
ijassa-1408	26	1	d	d	NOUN
ijassa-1408	26	2	:	:	PUNCT
ijassa-1408	26	3	c[g	c[g	X
ijassa-1408	26	4	]	]	X
ijassa-1408	26	5	→	→	PUNCT
ijassa-1408	26	6	a	a	DET
ijassa-1408	26	7	such	such	ADJ
ijassa-1408	26	8	that	that	DET
ijassa-1408	26	9	d(uv	d(uv	NOUN
ijassa-1408	26	10	)	)	PUNCT
ijassa-1408	26	11	=	=	SYM
ijassa-1408	27	1	d(u)v	d(u)v	PROPN
ijassa-1408	28	1	+	+	CCONJ
ijassa-1408	28	2	ud(v	ud(v	NUM
ijassa-1408	28	3	)	)	PUNCT
ijassa-1408	28	4	,	,	PUNCT
ijassa-1408	28	5	∀u	∀u	NOUN
ijassa-1408	28	6	,	,	PUNCT
ijassa-1408	28	7	v	v	NOUN
ijassa-1408	28	8	∈	∈	PROPN
ijassa-1408	28	9	c[g	c[g	NOUN
ijassa-1408	28	10	]	]	PUNCT
ijassa-1408	28	11	.	.	PUNCT
ijassa-1408	29	1	(	(	PUNCT
ijassa-1408	29	2	1.2	1.2	NUM
ijassa-1408	29	3	)	)	PUNCT
ijassa-1408	29	4	the	the	DET
ijassa-1408	29	5	space	space	NOUN
ijassa-1408	29	6	of	of	ADP
ijassa-1408	29	7	such	such	ADJ
ijassa-1408	29	8	operators	operator	NOUN
ijassa-1408	29	9	we	we	PRON
ijassa-1408	29	10	will	will	AUX
ijassa-1408	29	11	denote	denote	VERB
ijassa-1408	29	12	by	by	ADP
ijassa-1408	29	13	der(a	der(a	PROPN
ijassa-1408	29	14	)	)	PUNCT
ijassa-1408	29	15	.	.	PUNCT
ijassa-1408	30	1	for	for	ADP
ijassa-1408	30	2	a	a	DET
ijassa-1408	30	3	wide	wide	ADJ
ijassa-1408	30	4	class	class	NOUN
ijassa-1408	30	5	of	of	ADP
ijassa-1408	30	6	norms	norm	NOUN
ijassa-1408	30	7	(	(	PUNCT
ijassa-1408	30	8	including	include	VERB
ijassa-1408	30	9	natural	natural	ADJ
ijassa-1408	30	10	class	class	NOUN
ijassa-1408	30	11	of	of	ADP
ijassa-1408	30	12	ℓp	ℓp	NOUN
ijassa-1408	30	13	-	-	PUNCT
ijassa-1408	30	14	norms	norm	NOUN
ijassa-1408	30	15	)	)	PUNCT
ijassa-1408	30	16	the	the	DET
ijassa-1408	30	17	following	follow	VERB
ijassa-1408	30	18	statement	statement	NOUN
ijassa-1408	30	19	will	will	AUX
ijassa-1408	30	20	be	be	AUX
ijassa-1408	30	21	proved	prove	VERB
ijassa-1408	30	22	.	.	PUNCT
ijassa-1408	31	1	theorem	theorem	VERB
ijassa-1408	31	2	1.1	1.1	NUM
ijassa-1408	31	3	:	:	PUNCT
ijassa-1408	31	4	if	if	SCONJ
ijassa-1408	31	5	the	the	DET
ijassa-1408	31	6	norm	norm	NOUN
ijassa-1408	31	7	∥	∥	X
ijassa-1408	31	8	·	·	PUNCT
ijassa-1408	31	9	∥	∥	PRON
ijassa-1408	31	10	is	be	AUX
ijassa-1408	31	11	subordinate	subordinate	ADJ
ijassa-1408	31	12	to	to	ADP
ijassa-1408	31	13	the	the	DET
ijassa-1408	31	14	supremum	supremum	ADJ
ijassa-1408	31	15	norm	norm	NOUN
ijassa-1408	31	16	,	,	PUNCT
ijassa-1408	31	17	then	then	ADV
ijassa-1408	31	18	all	all	DET
ijassa-1408	31	19	derivations	derivation	NOUN
ijassa-1408	31	20	in	in	ADP
ijassa-1408	31	21	the	the	DET
ijassa-1408	31	22	bimodule	bimodule	NOUN
ijassa-1408	31	23	a	a	PRON
ijassa-1408	31	24	are	be	AUX
ijassa-1408	31	25	quasi	quasi	ADJ
ijassa-1408	31	26	-	-	ADJ
ijassa-1408	31	27	inner	inner	ADJ
ijassa-1408	31	28	.	.	PUNCT
ijassa-1408	32	1	let	let	VERB
ijassa-1408	32	2	us	we	PRON
ijassa-1408	32	3	explain	explain	VERB
ijassa-1408	32	4	about	about	ADP
ijassa-1408	32	5	which	which	DET
ijassa-1408	32	6	norms	norm	VERB
ijassa-1408	32	7	we	we	PRON
ijassa-1408	32	8	are	be	AUX
ijassa-1408	32	9	talking	talk	VERB
ijassa-1408	32	10	about	about	ADP
ijassa-1408	32	11	.	.	PUNCT
ijassa-1408	33	1	definition	definition	NOUN
ijassa-1408	33	2	1.2	1.2	NUM
ijassa-1408	33	3	:	:	PUNCT
ijassa-1408	33	4	we	we	PRON
ijassa-1408	33	5	will	will	AUX
ijassa-1408	33	6	say	say	VERB
ijassa-1408	33	7	that	that	SCONJ
ijassa-1408	33	8	the	the	DET
ijassa-1408	33	9	norm	norm	NOUN
ijassa-1408	33	10	∥	∥	X
ijassa-1408	33	11	·	·	PUNCT
ijassa-1408	33	12	∥	∥	PUNCT
ijassa-1408	33	13	is	be	AUX
ijassa-1408	33	14	subordinated	subordinate	VERB
ijassa-1408	33	15	to	to	ADP
ijassa-1408	33	16	the	the	DET
ijassa-1408	33	17	norm	norm	NOUN
ijassa-1408	33	18	∥	∥	X
ijassa-1408	33	19	·	·	PUNCT
ijassa-1408	34	1	∥s	∥s	PROPN
ijassa-1408	34	2	iff	iff	PROPN
ijassa-1408	34	3	∥ω∥	∥ω∥	NUM
ijassa-1408	34	4	<	<	X
ijassa-1408	34	5	∞	∞	PROPN
ijassa-1408	34	6	=	=	NOUN
ijassa-1408	34	7	⇒	⇒	NOUN
ijassa-1408	34	8	∥ω∥s	∥ω∥s	VERB
ijassa-1408	35	1	<	<	X
ijassa-1408	35	2	∞	∞	NUM
ijassa-1408	35	3	a	a	DET
ijassa-1408	35	4	rigorous	rigorous	ADJ
ijassa-1408	35	5	definition	definition	NOUN
ijassa-1408	35	6	of	of	ADP
ijassa-1408	35	7	quasi	quasi	ADJ
ijassa-1408	35	8	-	-	ADJ
ijassa-1408	35	9	inner	inner	ADJ
ijassa-1408	35	10	derivations	derivation	NOUN
ijassa-1408	35	11	is	be	AUX
ijassa-1408	35	12	given	give	VERB
ijassa-1408	35	13	below	below	ADV
ijassa-1408	35	14	(	(	PUNCT
ijassa-1408	35	15	see	see	VERB
ijassa-1408	35	16	definition	definition	NOUN
ijassa-1408	35	17	2.1	2.1	NUM
ijassa-1408	35	18	)	)	PUNCT
ijassa-1408	35	19	.	.	PUNCT
ijassa-1408	36	1	informally	informally	ADV
ijassa-1408	36	2	speaking	speak	VERB
ijassa-1408	36	3	,	,	PUNCT
ijassa-1408	36	4	quasi	quasi	ADJ
ijassa-1408	36	5	-	-	ADJ
ijassa-1408	36	6	inner	inner	ADJ
ijassa-1408	36	7	derivations	derivation	NOUN
ijassa-1408	36	8	are	be	AUX
ijassa-1408	36	9	such	such	ADJ
ijassa-1408	36	10	operators	operator	NOUN
ijassa-1408	36	11	that	that	PRON
ijassa-1408	36	12	can	can	AUX
ijassa-1408	36	13	be	be	AUX
ijassa-1408	36	14	represented	represent	VERB
ijassa-1408	36	15	as	as	ADP
ijassa-1408	36	16	a	a	DET
ijassa-1408	36	17	formal	formal	ADJ
ijassa-1408	36	18	infinite	infinite	ADJ
ijassa-1408	36	19	sum	sum	NOUN
ijassa-1408	36	20	of	of	ADP
ijassa-1408	36	21	inner	inner	ADJ
ijassa-1408	36	22	derivations	derivation	NOUN
ijassa-1408	36	23	,	,	PUNCT
ijassa-1408	36	24	i.e.	i.e.	X
ijassa-1408	36	25	the	the	DET
ijassa-1408	36	26	commutator	commutator	NOUN
ijassa-1408	36	27	x→	x→	PUNCT
ijassa-1408	37	1	[	[	X
ijassa-1408	37	2	a	a	X
ijassa-1408	37	3	,	,	PUNCT
ijassa-1408	37	4	x	x	X
ijassa-1408	37	5	]	]	X
ijassa-1408	37	6	,	,	PUNCT
ijassa-1408	37	7	for	for	ADP
ijassa-1408	37	8	the	the	DET
ijassa-1408	37	9	element	element	NOUN
ijassa-1408	37	10	a	a	PRON
ijassa-1408	37	11	not	not	PART
ijassa-1408	37	12	lying	lie	VERB
ijassa-1408	37	13	in	in	ADP
ijassa-1408	37	14	a	a	PRON
ijassa-1408	37	15	in	in	ADP
ijassa-1408	37	16	general	general	NOUN
ijassa-1408	37	17	.	.	PUNCT
ijassa-1408	38	1	2	2	X
ijassa-1408	38	2	.	.	NUM
ijassa-1408	38	3	preliminaries	preliminary	NOUN
ijassa-1408	38	4	the	the	DET
ijassa-1408	38	5	following	follow	VERB
ijassa-1408	38	6	definitions	definition	NOUN
ijassa-1408	38	7	and	and	CCONJ
ijassa-1408	38	8	results	result	NOUN
ijassa-1408	38	9	are	be	AUX
ijassa-1408	38	10	based	base	VERB
ijassa-1408	38	11	on	on	ADP
ijassa-1408	38	12	[	[	X
ijassa-1408	38	13	4	4	NUM
ijassa-1408	38	14	,	,	PUNCT
ijassa-1408	38	15	6	6	NUM
ijassa-1408	38	16	]	]	PUNCT
ijassa-1408	38	17	.	.	PUNCT
ijassa-1408	39	1	let	let	VERB
ijassa-1408	39	2	γ	γ	X
ijassa-1408	39	3	be	be	AUX
ijassa-1408	39	4	a	a	DET
ijassa-1408	39	5	groupoid	groupoid	NOUN
ijassa-1408	39	6	of	of	ADP
ijassa-1408	39	7	connected	connected	ADJ
ijassa-1408	39	8	action	action	NOUN
ijassa-1408	39	9	in	in	ADP
ijassa-1408	39	10	which	which	PRON
ijassa-1408	39	11	objects	object	VERB
ijassa-1408	39	12	coincide	coincide	NOUN
ijassa-1408	39	13	with	with	ADP
ijassa-1408	39	14	elements	element	NOUN
ijassa-1408	39	15	of	of	ADP
ijassa-1408	39	16	the	the	DET
ijassa-1408	39	17	group	group	NOUN
ijassa-1408	39	18	obj(γ	obj(γ	NOUN
ijassa-1408	39	19	)	)	PUNCT
ijassa-1408	39	20	=	=	SYM
ijassa-1408	39	21	g	g	NOUN
ijassa-1408	39	22	,	,	PUNCT
ijassa-1408	39	23	and	and	CCONJ
ijassa-1408	39	24	morphisms	morphism	NOUN
ijassa-1408	39	25	are	be	AUX
ijassa-1408	39	26	pairs	pair	NOUN
ijassa-1408	39	27	of	of	ADP
ijassa-1408	39	28	elements	element	NOUN
ijassa-1408	39	29	of	of	ADP
ijassa-1408	39	30	the	the	DET
ijassa-1408	39	31	group	group	NOUN
ijassa-1408	39	32	,	,	PUNCT
ijassa-1408	39	33	i.e.	i.e.	X
ijassa-1408	39	34	hom	hom	X
ijassa-1408	39	35	(	(	PUNCT
ijassa-1408	39	36	γ	γ	NOUN
ijassa-1408	39	37	)	)	PUNCT
ijassa-1408	39	38	=	=	SYM
ijassa-1408	39	39	g×g	g×g	PROPN
ijassa-1408	39	40	.	.	PUNCT
ijassa-1408	40	1	moreover	moreover	ADV
ijassa-1408	40	2	,	,	PUNCT
ijassa-1408	40	3	the	the	DET
ijassa-1408	40	4	morphism	morphism	NOUN
ijassa-1408	40	5	ϕ	ϕ	PROPN
ijassa-1408	40	6	:	:	PUNCT
ijassa-1408	40	7	=	=	SYM
ijassa-1408	40	8	(	(	PUNCT
ijassa-1408	40	9	u	u	NOUN
ijassa-1408	40	10	,	,	PUNCT
ijassa-1408	40	11	v	v	NOUN
ijassa-1408	40	12	)	)	PUNCT
ijassa-1408	40	13	has	have	VERB
ijassa-1408	40	14	the	the	DET
ijassa-1408	40	15	source	source	NOUN
ijassa-1408	40	16	s(ϕ	s(ϕ	PROPN
ijassa-1408	40	17	)	)	PUNCT
ijassa-1408	41	1	=	=	SYM
ijassa-1408	41	2	v−1u	v−1u	NOUN
ijassa-1408	41	3	and	and	CCONJ
ijassa-1408	41	4	the	the	DET
ijassa-1408	41	5	target	target	NOUN
ijassa-1408	41	6	t(ϕ	t(ϕ	ADP
ijassa-1408	41	7	)	)	PUNCT
ijassa-1408	41	8	=	=	SYM
ijassa-1408	41	9	uv−1	uv−1	PROPN
ijassa-1408	41	10	.	.	PUNCT
ijassa-1408	42	1	we	we	PRON
ijassa-1408	42	2	will	will	AUX
ijassa-1408	42	3	call	call	VERB
ijassa-1408	42	4	endomorphisms	endomorphism	NOUN
ijassa-1408	42	5	(	(	PUNCT
ijassa-1408	42	6	i.e.	i.e.	X
ijassa-1408	42	7	morphisms	morphism	NOUN
ijassa-1408	42	8	whose	whose	DET
ijassa-1408	42	9	source	source	NOUN
ijassa-1408	42	10	and	and	CCONJ
ijassa-1408	42	11	target	target	NOUN
ijassa-1408	42	12	coincide	coincide	NOUN
ijassa-1408	42	13	)	)	PUNCT
ijassa-1408	42	14	ϕ	ϕ	NOUN
ijassa-1408	42	15	as	as	ADP
ijassa-1408	42	16	loops	loop	NOUN
ijassa-1408	42	17	for	for	ADP
ijassa-1408	42	18	clarity	clarity	NOUN
ijassa-1408	42	19	.	.	PUNCT
ijassa-1408	43	1	then	then	ADV
ijassa-1408	43	2	we	we	PRON
ijassa-1408	43	3	define	define	VERB
ijassa-1408	43	4	a	a	DET
ijassa-1408	43	5	character	character	NOUN
ijassa-1408	43	6	as	as	ADP
ijassa-1408	43	7	a	a	DET
ijassa-1408	43	8	complex	complex	ADV
ijassa-1408	43	9	-	-	PUNCT
ijassa-1408	43	10	valued	value	VERB
ijassa-1408	43	11	function	function	NOUN
ijassa-1408	43	12	χ	χ	X
ijassa-1408	43	13	:	:	PUNCT
ijassa-1408	43	14	hom	hom	X
ijassa-1408	43	15	(	(	PUNCT
ijassa-1408	43	16	γ	γ	X
ijassa-1408	43	17	)	)	PUNCT
ijassa-1408	43	18	→	→	PUNCT
ijassa-1408	43	19	c	c	NOUN
ijassa-1408	43	20	such	such	ADJ
ijassa-1408	43	21	that	that	PRON
ijassa-1408	43	22	χ(ψ	χ(ψ	NOUN
ijassa-1408	43	23	◦	◦	PROPN
ijassa-1408	43	24	ϕ	ϕ	NOUN
ijassa-1408	43	25	)	)	PUNCT
ijassa-1408	43	26	=	=	SYM
ijassa-1408	43	27	χ(ψ	χ(ψ	NOUN
ijassa-1408	43	28	)	)	PUNCT
ijassa-1408	44	1	+	+	CCONJ
ijassa-1408	44	2	χ(ϕ	χ(ϕ	NOUN
ijassa-1408	44	3	)	)	PUNCT
ijassa-1408	44	4	,	,	PUNCT
ijassa-1408	44	5	(	(	PUNCT
ijassa-1408	44	6	2.3	2.3	NUM
ijassa-1408	44	7	)	)	PUNCT
ijassa-1408	44	8	for	for	ADP
ijassa-1408	44	9	all	all	DET
ijassa-1408	44	10	pairs	pair	NOUN
ijassa-1408	44	11	of	of	ADP
ijassa-1408	44	12	linkable	linkable	ADJ
ijassa-1408	44	13	morphisms	morphisms	PROPN
ijassa-1408	44	14	ϕ	ϕ	PROPN
ijassa-1408	44	15	,	,	PUNCT
ijassa-1408	44	16	ψ	ψ	NOUN
ijassa-1408	44	17	.	.	PUNCT
ijassa-1408	45	1	the	the	DET
ijassa-1408	45	2	groupoid	groupoid	PROPN
ijassa-1408	45	3	γ	γ	PROPN
ijassa-1408	45	4	will	will	AUX
ijassa-1408	45	5	be	be	AUX
ijassa-1408	45	6	represented	represent	VERB
ijassa-1408	45	7	as	as	ADP
ijassa-1408	45	8	an	an	DET
ijassa-1408	45	9	uncoupled	uncoupled	ADJ
ijassa-1408	45	10	union	union	NOUN
ijassa-1408	45	11	of	of	ADP
ijassa-1408	45	12	subgroupoids	subgroupoids	PROPN
ijassa-1408	45	13	γ[u	γ[u	PROPN
ijassa-1408	45	14	]	]	PUNCT
ijassa-1408	45	15	,	,	PUNCT
ijassa-1408	45	16	where	where	SCONJ
ijassa-1408	45	17	[	[	X
ijassa-1408	45	18	u	u	X
ijassa-1408	45	19	]	]	X
ijassa-1408	45	20	is	be	AUX
ijassa-1408	45	21	a	a	DET
ijassa-1408	45	22	class	class	NOUN
ijassa-1408	45	23	of	of	ADP
ijassa-1408	45	24	conjugate	conjugate	ADJ
ijassa-1408	45	25	elements	element	NOUN
ijassa-1408	45	26	.	.	PUNCT
ijassa-1408	46	1	[	[	X
ijassa-1408	46	2	u	u	X
ijassa-1408	46	3	]	]	X
ijassa-1408	46	4	=	=	SYM
ijassa-1408	46	5	{	{	PUNCT
ijassa-1408	46	6	tut−1|t	tut−1|t	NOUN
ijassa-1408	46	7	∈	∈	PROPN
ijassa-1408	46	8	g	g	NOUN
ijassa-1408	46	9	}	}	PUNCT
ijassa-1408	46	10	.	.	PUNCT
ijassa-1408	47	1	objects	object	NOUN
ijassa-1408	47	2	of	of	ADP
ijassa-1408	47	3	the	the	DET
ijassa-1408	47	4	subgroupoid	subgroupoid	NOUN
ijassa-1408	47	5	γ[u	γ[u	PROPN
ijassa-1408	47	6	]	]	PUNCT
ijassa-1408	47	7	coincide	coincide	NOUN
ijassa-1408	47	8	with	with	ADP
ijassa-1408	47	9	the	the	DET
ijassa-1408	47	10	class	class	NOUN
ijassa-1408	47	11	[	[	X
ijassa-1408	47	12	u	u	X
ijassa-1408	47	13	]	]	X
ijassa-1408	47	14	.	.	PUNCT
ijassa-1408	48	1	copyright	copyright	NOUN
ijassa-1408	48	2	©	©	PROPN
ijassa-1408	48	3	2023	2023	NUM
ijassa-1408	48	4	assa	assa	NOUN
ijassa-1408	48	5	.	.	PUNCT
ijassa-1408	49	1	adv	adv	PROPN
ijassa-1408	49	2	syst	syst	PROPN
ijassa-1408	49	3	sci	sci	PROPN
ijassa-1408	49	4	appl	appl	PROPN
ijassa-1408	49	5	(	(	PUNCT
ijassa-1408	49	6	2023	2023	NUM
ijassa-1408	49	7	)	)	PUNCT
ijassa-1408	49	8	180	180	NUM
ijassa-1408	49	9	a.	a.	NOUN
ijassa-1408	49	10	aurutyunov	aurutyunov	NOUN
ijassa-1408	49	11	lemma	lemma	PROPN
ijassa-1408	49	12	2.1	2.1	NUM
ijassa-1408	49	13	:	:	PUNCT
ijassa-1408	49	14	for	for	ADP
ijassa-1408	49	15	every	every	DET
ijassa-1408	49	16	derivation	derivation	NOUN
ijassa-1408	49	17	d	d	PROPN
ijassa-1408	49	18	∈	∈	NOUN
ijassa-1408	49	19	der(as	der(a	NOUN
ijassa-1408	49	20	)	)	PUNCT
ijassa-1408	49	21	there	there	PRON
ijassa-1408	49	22	exists	exist	VERB
ijassa-1408	49	23	a	a	DET
ijassa-1408	49	24	character	character	NOUN
ijassa-1408	49	25	χ	χ	PROPN
ijassa-1408	49	26	∈	∈	PROPN
ijassa-1408	49	27	x(γ	x(γ	PROPN
ijassa-1408	49	28	)	)	PUNCT
ijassa-1408	49	29	such	such	ADJ
ijassa-1408	49	30	that	that	SCONJ
ijassa-1408	49	31	the	the	DET
ijassa-1408	49	32	following	follow	VERB
ijassa-1408	49	33	formula	formula	NOUN
ijassa-1408	49	34	holds	hold	VERB
ijassa-1408	49	35	d(g	d(g	PROPN
ijassa-1408	49	36	)	)	PUNCT
ijassa-1408	49	37	=	=	SYM
ijassa-1408	49	38	g	g	PROPN
ijassa-1408	49	39	(	(	PUNCT
ijassa-1408	49	40	∑	∑	PROPN
ijassa-1408	49	41	t∈g	t∈g	NOUN
ijassa-1408	49	42	χ(gt	χ(gt	NOUN
ijassa-1408	49	43	,	,	PUNCT
ijassa-1408	49	44	g)t	g)t	X
ijassa-1408	49	45	)	)	PUNCT
ijassa-1408	49	46	,	,	PUNCT
ijassa-1408	49	47	∀g	∀g	X
ijassa-1408	49	48	∈	∈	PROPN
ijassa-1408	49	49	g.	g.	NOUN
ijassa-1408	49	50	(	(	PUNCT
ijassa-1408	49	51	2.4	2.4	NUM
ijassa-1408	49	52	)	)	PUNCT
ijassa-1408	49	53	proof	proof	NOUN
ijassa-1408	49	54	the	the	DET
ijassa-1408	49	55	proof	proof	NOUN
ijassa-1408	49	56	literally	literally	ADV
ijassa-1408	49	57	repeats	repeat	VERB
ijassa-1408	49	58	the	the	DET
ijassa-1408	49	59	proof	proof	NOUN
ijassa-1408	49	60	of	of	ADP
ijassa-1408	49	61	theorem	theorem	NOUN
ijassa-1408	49	62	1	1	NUM
ijassa-1408	49	63	of	of	ADP
ijassa-1408	49	64	[	[	X
ijassa-1408	49	65	5	5	NUM
ijassa-1408	49	66	]	]	PUNCT
ijassa-1408	49	67	except	except	SCONJ
ijassa-1408	49	68	for	for	ADP
ijassa-1408	49	69	the	the	DET
ijassa-1408	49	70	property	property	NOUN
ijassa-1408	49	71	of	of	ADP
ijassa-1408	49	72	local	local	ADJ
ijassa-1408	49	73	finiteness	finiteness	NOUN
ijassa-1408	49	74	,	,	PUNCT
ijassa-1408	49	75	which	which	PRON
ijassa-1408	49	76	was	be	AUX
ijassa-1408	49	77	a	a	DET
ijassa-1408	49	78	consequence	consequence	NOUN
ijassa-1408	49	79	of	of	ADP
ijassa-1408	49	80	the	the	DET
ijassa-1408	49	81	finiteness	finiteness	NOUN
ijassa-1408	49	82	of	of	ADP
ijassa-1408	49	83	nonzero	nonzero	PROPN
ijassa-1408	49	84	terms	term	NOUN
ijassa-1408	49	85	in	in	ADP
ijassa-1408	49	86	elements	element	NOUN
ijassa-1408	49	87	of	of	ADP
ijassa-1408	49	88	group	group	NOUN
ijassa-1408	49	89	algebras	algebra	NOUN
ijassa-1408	49	90	.	.	PUNCT
ijassa-1408	50	1	let	let	VERB
ijassa-1408	50	2	us	we	PRON
ijassa-1408	50	3	make	make	VERB
ijassa-1408	50	4	it	it	PRON
ijassa-1408	50	5	clear	clear	ADJ
ijassa-1408	50	6	that	that	SCONJ
ijassa-1408	50	7	character	character	NOUN
ijassa-1408	50	8	values	value	NOUN
ijassa-1408	50	9	are	be	AUX
ijassa-1408	50	10	coefficients	coefficient	NOUN
ijassa-1408	50	11	of	of	ADP
ijassa-1408	50	12	the	the	DET
ijassa-1408	50	13	expansion	expansion	NOUN
ijassa-1408	50	14	of	of	ADP
ijassa-1408	50	15	a	a	DET
ijassa-1408	50	16	linear	linear	ADJ
ijassa-1408	50	17	operator	operator	NOUN
ijassa-1408	50	18	by	by	ADP
ijassa-1408	50	19	standard	standard	ADJ
ijassa-1408	50	20	basis	basis	NOUN
ijassa-1408	50	21	of	of	ADP
ijassa-1408	50	22	the	the	DET
ijassa-1408	50	23	ring	ring	NOUN
ijassa-1408	50	24	c[g	c[g	NOUN
ijassa-1408	50	25	]	]	PUNCT
ijassa-1408	50	26	.	.	PUNCT
ijassa-1408	51	1	due	due	ADP
ijassa-1408	51	2	to	to	ADP
ijassa-1408	51	3	the	the	DET
ijassa-1408	51	4	implementation	implementation	NOUN
ijassa-1408	51	5	of	of	ADP
ijassa-1408	51	6	the	the	DET
ijassa-1408	51	7	leibniz	leibniz	PROPN
ijassa-1408	51	8	rule	rule	NOUN
ijassa-1408	51	9	,	,	PUNCT
ijassa-1408	51	10	the	the	DET
ijassa-1408	51	11	calculation	calculation	NOUN
ijassa-1408	51	12	shows	show	VERB
ijassa-1408	51	13	that	that	SCONJ
ijassa-1408	51	14	the	the	DET
ijassa-1408	51	15	property	property	NOUN
ijassa-1408	51	16	(	(	PUNCT
ijassa-1408	51	17	2.3	2.3	NUM
ijassa-1408	51	18	)	)	PUNCT
ijassa-1408	51	19	is	be	AUX
ijassa-1408	51	20	fulfilled	fulfil	VERB
ijassa-1408	51	21	.	.	PUNCT
ijassa-1408	52	1	the	the	DET
ijassa-1408	52	2	space	space	NOUN
ijassa-1408	52	3	of	of	ADP
ijassa-1408	52	4	quasi	quasi	ADJ
ijassa-1408	52	5	-	-	ADJ
ijassa-1408	52	6	inner	inner	ADJ
ijassa-1408	52	7	derivations	derivation	NOUN
ijassa-1408	52	8	was	be	AUX
ijassa-1408	52	9	introduced	introduce	VERB
ijassa-1408	52	10	earlier	early	ADV
ijassa-1408	52	11	in	in	ADP
ijassa-1408	52	12	[	[	X
ijassa-1408	52	13	6	6	NUM
ijassa-1408	52	14	]	]	PUNCT
ijassa-1408	52	15	.	.	PUNCT
ijassa-1408	53	1	it	it	PRON
ijassa-1408	53	2	will	will	AUX
ijassa-1408	53	3	play	play	VERB
ijassa-1408	53	4	an	an	DET
ijassa-1408	53	5	important	important	ADJ
ijassa-1408	53	6	role	role	NOUN
ijassa-1408	53	7	below	below	ADV
ijassa-1408	53	8	.	.	PUNCT
ijassa-1408	54	1	definition	definition	NOUN
ijassa-1408	54	2	2.1	2.1	NUM
ijassa-1408	54	3	:	:	PUNCT
ijassa-1408	54	4	we	we	PRON
ijassa-1408	54	5	call	call	VERB
ijassa-1408	54	6	the	the	DET
ijassa-1408	54	7	derivation	derivation	NOUN
ijassa-1408	54	8	d	d	PROPN
ijassa-1408	54	9	∈	∈	PROPN
ijassa-1408	54	10	der(a(g	der(a(g	NOUN
ijassa-1408	54	11	)	)	PUNCT
ijassa-1408	54	12	)	)	PUNCT
ijassa-1408	54	13	quasi	quasi	NOUN
ijassa-1408	54	14	-	-	ADJ
ijassa-1408	54	15	inner	inner	ADJ
ijassa-1408	54	16	if	if	SCONJ
ijassa-1408	54	17	the	the	DET
ijassa-1408	54	18	character	character	NOUN
ijassa-1408	54	19	χ	χ	NOUN
ijassa-1408	54	20	in	in	ADP
ijassa-1408	54	21	the	the	DET
ijassa-1408	54	22	formula	formula	NOUN
ijassa-1408	54	23	(	(	PUNCT
ijassa-1408	54	24	2.4	2.4	NUM
ijassa-1408	54	25	)	)	PUNCT
ijassa-1408	54	26	is	be	AUX
ijassa-1408	54	27	zero	zero	NUM
ijassa-1408	54	28	on	on	ADP
ijassa-1408	54	29	all	all	DET
ijassa-1408	54	30	loops	loop	NOUN
ijassa-1408	54	31	.	.	PUNCT
ijassa-1408	55	1	it	it	PRON
ijassa-1408	55	2	is	be	AUX
ijassa-1408	55	3	easy	easy	ADJ
ijassa-1408	55	4	to	to	PART
ijassa-1408	55	5	see	see	VERB
ijassa-1408	55	6	that	that	SCONJ
ijassa-1408	55	7	the	the	DET
ijassa-1408	55	8	inner	inner	ADJ
ijassa-1408	55	9	derivations	derivation	NOUN
ijassa-1408	55	10	are	be	AUX
ijassa-1408	55	11	quasi	quasi	ADJ
ijassa-1408	55	12	-	-	ADJ
ijassa-1408	55	13	inner	inner	ADJ
ijassa-1408	55	14	.	.	PUNCT
ijassa-1408	56	1	indeed	indeed	ADV
ijassa-1408	56	2	,	,	PUNCT
ijassa-1408	56	3	let	let	VERB
ijassa-1408	56	4	a	a	DET
ijassa-1408	56	5	∈	∈	NOUN
ijassa-1408	56	6	g	g	NOUN
ijassa-1408	56	7	be	be	AUX
ijassa-1408	56	8	a	a	DET
ijassa-1408	56	9	basis	basis	NOUN
ijassa-1408	56	10	element	element	NOUN
ijassa-1408	56	11	,	,	PUNCT
ijassa-1408	56	12	then	then	ADV
ijassa-1408	56	13	the	the	DET
ijassa-1408	56	14	character	character	NOUN
ijassa-1408	56	15	χa	χa	AUX
ijassa-1408	56	16	corresponding	correspond	VERB
ijassa-1408	56	17	to	to	ADP
ijassa-1408	56	18	the	the	DET
ijassa-1408	56	19	inner	inner	ADJ
ijassa-1408	56	20	derivation	derivation	NOUN
ijassa-1408	56	21	da	da	NOUN
ijassa-1408	56	22	:	:	PUNCT
ijassa-1408	56	23	x→	x→	PUNCT
ijassa-1408	57	1	[	[	X
ijassa-1408	57	2	x	x	X
ijassa-1408	57	3	,	,	PUNCT
ijassa-1408	57	4	a	a	PRON
ijassa-1408	57	5	]	]	X
ijassa-1408	57	6	has	have	VERB
ijassa-1408	57	7	the	the	DET
ijassa-1408	57	8	form	form	NOUN
ijassa-1408	57	9	(	(	PUNCT
ijassa-1408	57	10	see	see	VERB
ijassa-1408	57	11	section	section	NOUN
ijassa-1408	57	12	2.2	2.2	NUM
ijassa-1408	57	13	in	in	ADP
ijassa-1408	57	14	[	[	X
ijassa-1408	57	15	5	5	NUM
ijassa-1408	57	16	]	]	PUNCT
ijassa-1408	57	17	for	for	ADP
ijassa-1408	57	18	details	detail	NOUN
ijassa-1408	57	19	)	)	PUNCT
ijassa-1408	57	20	χa(ϕ	χa(ϕ	NUM
ijassa-1408	57	21	)	)	PUNCT
ijassa-1408	57	22	=	=	PUNCT
ijassa-1408	57	23	1	1	PROPN
ijassa-1408	57	24	,	,	PUNCT
ijassa-1408	57	25	ϕ	ϕ	PROPN
ijassa-1408	57	26	∈	∈	PROPN
ijassa-1408	58	1	hom	hom	X
ijassa-1408	59	1	(	(	PUNCT
ijassa-1408	59	2	a	a	DET
ijassa-1408	59	3	,	,	PUNCT
ijassa-1408	59	4	b	b	NOUN
ijassa-1408	59	5	)	)	PUNCT
ijassa-1408	59	6	,	,	PUNCT
ijassa-1408	60	1	b	b	X
ijassa-1408	60	2	̸=	̸=	PROPN
ijassa-1408	60	3	a	a	X
ijassa-1408	60	4	,	,	PUNCT
ijassa-1408	60	5	−1	−1	NOUN
ijassa-1408	60	6	ϕ	ϕ	PROPN
ijassa-1408	60	7	∈	∈	PROPN
ijassa-1408	60	8	hom	hom	X
ijassa-1408	60	9	(	(	PUNCT
ijassa-1408	60	10	b	b	NOUN
ijassa-1408	60	11	,	,	PUNCT
ijassa-1408	60	12	a	a	NOUN
ijassa-1408	60	13	)	)	PUNCT
ijassa-1408	60	14	,	,	PUNCT
ijassa-1408	60	15	b	b	X
ijassa-1408	60	16	̸=	̸=	PROPN
ijassa-1408	60	17	a	a	PRON
ijassa-1408	60	18	,	,	PUNCT
ijassa-1408	60	19	0	0	NUM
ijassa-1408	60	20	otherwise	otherwise	ADV
ijassa-1408	60	21	.	.	PUNCT
ijassa-1408	61	1	the	the	DET
ijassa-1408	61	2	character	character	NOUN
ijassa-1408	61	3	χa	χa	PROPN
ijassa-1408	61	4	is	be	AUX
ijassa-1408	61	5	zero	zero	NUM
ijassa-1408	61	6	on	on	ADP
ijassa-1408	61	7	all	all	DET
ijassa-1408	61	8	loops	loop	NOUN
ijassa-1408	61	9	.	.	PUNCT
ijassa-1408	62	1	the	the	DET
ijassa-1408	62	2	inner	inner	ADJ
ijassa-1408	62	3	derivation	derivation	NOUN
ijassa-1408	62	4	is	be	AUX
ijassa-1408	62	5	a	a	DET
ijassa-1408	62	6	sum	sum	NOUN
ijassa-1408	62	7	of	of	ADP
ijassa-1408	62	8	(	(	PUNCT
ijassa-1408	62	9	possibly	possibly	ADV
ijassa-1408	62	10	infinite	infinite	VERB
ijassa-1408	62	11	)	)	PUNCT
ijassa-1408	62	12	characters	character	NOUN
ijassa-1408	62	13	χa	χa	VERB
ijassa-1408	62	14	,	,	PUNCT
ijassa-1408	62	15	and	and	CCONJ
ijassa-1408	62	16	hence	hence	ADV
ijassa-1408	62	17	is	be	AUX
ijassa-1408	62	18	itself	itself	PRON
ijassa-1408	62	19	trivial	trivial	ADJ
ijassa-1408	62	20	on	on	ADP
ijassa-1408	62	21	loops	loop	NOUN
ijassa-1408	62	22	.	.	PUNCT
ijassa-1408	63	1	the	the	DET
ijassa-1408	63	2	role	role	NOUN
ijassa-1408	63	3	of	of	ADP
ijassa-1408	63	4	quasi	quasi	ADJ
ijassa-1408	63	5	-	-	ADJ
ijassa-1408	63	6	inner	inner	ADJ
ijassa-1408	63	7	derivations	derivation	NOUN
ijassa-1408	63	8	for	for	ADP
ijassa-1408	63	9	group	group	NOUN
ijassa-1408	63	10	rings	ring	NOUN
ijassa-1408	63	11	is	be	AUX
ijassa-1408	63	12	that	that	SCONJ
ijassa-1408	63	13	they	they	PRON
ijassa-1408	63	14	form	form	VERB
ijassa-1408	63	15	an	an	DET
ijassa-1408	63	16	ideal	ideal	NOUN
ijassa-1408	63	17	containing	contain	VERB
ijassa-1408	63	18	the	the	DET
ijassa-1408	63	19	ideal	ideal	NOUN
ijassa-1408	63	20	of	of	ADP
ijassa-1408	63	21	inner	inner	ADJ
ijassa-1408	63	22	derivations	derivation	NOUN
ijassa-1408	63	23	(	(	PUNCT
ijassa-1408	63	24	theorem	theorem	VERB
ijassa-1408	63	25	4.1	4.1	NUM
ijassa-1408	63	26	,	,	PUNCT
ijassa-1408	63	27	[	[	X
ijassa-1408	63	28	6	6	NUM
ijassa-1408	63	29	]	]	NUM
ijassa-1408	63	30	)	)	PUNCT
ijassa-1408	63	31	,	,	PUNCT
ijassa-1408	63	32	with	with	ADP
ijassa-1408	63	33	examples	example	NOUN
ijassa-1408	63	34	of	of	ADP
ijassa-1408	63	35	quasi	quasi	ADJ
ijassa-1408	63	36	-	-	ADJ
ijassa-1408	63	37	inner	inner	ADJ
ijassa-1408	63	38	derivations	derivation	NOUN
ijassa-1408	63	39	that	that	PRON
ijassa-1408	63	40	are	be	AUX
ijassa-1408	63	41	not	not	PART
ijassa-1408	63	42	inner	inner	ADJ
ijassa-1408	63	43	in	in	ADP
ijassa-1408	63	44	the	the	DET
ijassa-1408	63	45	group	group	NOUN
ijassa-1408	63	46	ring	ring	NOUN
ijassa-1408	63	47	(	(	PUNCT
ijassa-1408	63	48	section	section	NOUN
ijassa-1408	63	49	3.3	3.3	NUM
ijassa-1408	63	50	of	of	ADP
ijassa-1408	63	51	[	[	X
ijassa-1408	63	52	5	5	NUM
ijassa-1408	63	53	]	]	PUNCT
ijassa-1408	63	54	–	–	PUNCT
ijassa-1408	63	55	the	the	DET
ijassa-1408	63	56	case	case	NOUN
ijassa-1408	63	57	of	of	ADP
ijassa-1408	63	58	heisenberg	heisenberg	PROPN
ijassa-1408	63	59	group	group	PROPN
ijassa-1408	63	60	)	)	PUNCT
ijassa-1408	63	61	.	.	PUNCT
ijassa-1408	64	1	the	the	DET
ijassa-1408	64	2	coincidence	coincidence	NOUN
ijassa-1408	64	3	of	of	ADP
ijassa-1408	64	4	spaces	space	NOUN
ijassa-1408	64	5	of	of	ADP
ijassa-1408	64	6	inner	inner	ADJ
ijassa-1408	64	7	and	and	CCONJ
ijassa-1408	64	8	quasi	quasi	ADJ
ijassa-1408	64	9	-	-	ADJ
ijassa-1408	64	10	inner	inner	ADJ
ijassa-1408	64	11	derivations	derivation	NOUN
ijassa-1408	64	12	in	in	ADP
ijassa-1408	64	13	a	a	DET
ijassa-1408	64	14	bimodule	bimodule	NOUN
ijassa-1408	64	15	a	a	PRON
ijassa-1408	64	16	is	be	AUX
ijassa-1408	64	17	equivalent	equivalent	ADJ
ijassa-1408	64	18	to	to	ADP
ijassa-1408	64	19	the	the	DET
ijassa-1408	64	20	fact	fact	NOUN
ijassa-1408	64	21	that	that	SCONJ
ijassa-1408	64	22	inner	inner	ADJ
ijassa-1408	64	23	derivations	derivation	NOUN
ijassa-1408	64	24	are	be	AUX
ijassa-1408	64	25	dense	dense	ADJ
ijassa-1408	64	26	in	in	ADP
ijassa-1408	64	27	the	the	DET
ijassa-1408	64	28	space	space	NOUN
ijassa-1408	64	29	of	of	ADP
ijassa-1408	64	30	quasi	quasi	ADJ
ijassa-1408	64	31	-	-	ADJ
ijassa-1408	64	32	inner	inner	ADJ
ijassa-1408	64	33	derivations	derivation	NOUN
ijassa-1408	64	34	.	.	PUNCT
ijassa-1408	65	1	3	3	X
ijassa-1408	65	2	.	.	X
ijassa-1408	65	3	derivations	derivation	NOUN
ijassa-1408	65	4	in	in	ADP
ijassa-1408	65	5	bimodules	bimodule	NOUN
ijassa-1408	65	6	recall	recall	VERB
ijassa-1408	65	7	that	that	SCONJ
ijassa-1408	65	8	in	in	ADP
ijassa-1408	65	9	the	the	DET
ijassa-1408	65	10	group	group	NOUN
ijassa-1408	65	11	ring	ring	NOUN
ijassa-1408	65	12	c[g	c[g	PROPN
ijassa-1408	65	13	]	]	PUNCT
ijassa-1408	65	14	we	we	PRON
ijassa-1408	65	15	have	have	VERB
ijassa-1408	65	16	a	a	DET
ijassa-1408	65	17	”	"	PUNCT
ijassa-1408	65	18	supremum	supremum	ADJ
ijassa-1408	65	19	norm	norm	NOUN
ijassa-1408	65	20	”	"	PUNCT
ijassa-1408	65	21	.	.	PUNCT
ijassa-1408	66	1	for	for	ADP
ijassa-1408	66	2	x	x	SYM
ijassa-1408	66	3	=	=	SYM
ijassa-1408	66	4	∑	∑	PUNCT
ijassa-1408	66	5	g∈g	g∈g	PROPN
ijassa-1408	66	6	x(g)g	x(g)g	PROPN
ijassa-1408	66	7	∈	∈	PROPN
ijassa-1408	66	8	c[g	c[g	NOUN
ijassa-1408	66	9	]	]	X
ijassa-1408	66	10	,	,	PUNCT
ijassa-1408	66	11	where	where	SCONJ
ijassa-1408	66	12	x	x	X
ijassa-1408	66	13	(	(	PUNCT
ijassa-1408	66	14	·	·	PUNCT
ijassa-1408	66	15	)	)	PUNCT
ijassa-1408	66	16	is	be	AUX
ijassa-1408	66	17	a	a	DET
ijassa-1408	66	18	finite	finite	ADJ
ijassa-1408	66	19	function	function	NOUN
ijassa-1408	66	20	,	,	PUNCT
ijassa-1408	66	21	the	the	DET
ijassa-1408	66	22	norm	norm	NOUN
ijassa-1408	66	23	is	be	AUX
ijassa-1408	66	24	∥x∥s	∥x∥s	NOUN
ijassa-1408	66	25	:	:	PUNCT
ijassa-1408	67	1	=	=	SYM
ijassa-1408	67	2	sup	sup	NUM
ijassa-1408	67	3	g∈g	g∈g	PROPN
ijassa-1408	67	4	|x(g)|	|x(g)|	PROPN
ijassa-1408	67	5	.	.	PUNCT
ijassa-1408	68	1	(	(	PUNCT
ijassa-1408	68	2	3.5	3.5	NUM
ijassa-1408	68	3	)	)	PUNCT
ijassa-1408	68	4	the	the	DET
ijassa-1408	68	5	banach	banach	NOUN
ijassa-1408	68	6	bimodule	bimodule	NOUN
ijassa-1408	68	7	that	that	PRON
ijassa-1408	68	8	is	be	AUX
ijassa-1408	68	9	the	the	DET
ijassa-1408	68	10	closure	closure	NOUN
ijassa-1408	68	11	of	of	ADP
ijassa-1408	68	12	c[g	c[g	NOUN
ijassa-1408	68	13	]	]	PUNCT
ijassa-1408	68	14	by	by	ADP
ijassa-1408	68	15	the	the	DET
ijassa-1408	68	16	supremum	supremum	ADJ
ijassa-1408	68	17	norm	norm	NOUN
ijassa-1408	68	18	is	be	AUX
ijassa-1408	68	19	denoted	denote	VERB
ijassa-1408	68	20	by	by	ADP
ijassa-1408	68	21	as(g	as(g	NOUN
ijassa-1408	68	22	)	)	PUNCT
ijassa-1408	68	23	.	.	PUNCT
ijassa-1408	69	1	the	the	DET
ijassa-1408	69	2	bimodule	bimodule	NOUN
ijassa-1408	69	3	as(g	as(g	PRON
ijassa-1408	69	4	)	)	PUNCT
ijassa-1408	69	5	can	can	AUX
ijassa-1408	69	6	be	be	AUX
ijassa-1408	69	7	understood	understand	VERB
ijassa-1408	69	8	as	as	ADP
ijassa-1408	69	9	the	the	DET
ijassa-1408	69	10	space	space	NOUN
ijassa-1408	69	11	of	of	ADP
ijassa-1408	69	12	elements	element	NOUN
ijassa-1408	69	13	of	of	ADP
ijassa-1408	69	14	the	the	DET
ijassa-1408	69	15	form∑	form∑	PROPN
ijassa-1408	69	16	g∈g	g∈g	PROPN
ijassa-1408	69	17	x(g)g	x(g)g	PROPN
ijassa-1408	69	18	,	,	PUNCT
ijassa-1408	69	19	where	where	SCONJ
ijassa-1408	69	20	the	the	DET
ijassa-1408	69	21	function	function	NOUN
ijassa-1408	69	22	x(g	x(g	PROPN
ijassa-1408	69	23	)	)	PUNCT
ijassa-1408	69	24	is	be	AUX
ijassa-1408	69	25	bounded	bound	VERB
ijassa-1408	69	26	.	.	PUNCT
ijassa-1408	70	1	this	this	DET
ijassa-1408	70	2	a	a	DET
ijassa-1408	70	3	sort	sort	NOUN
ijassa-1408	70	4	of	of	ADP
ijassa-1408	70	5	free	free	ADJ
ijassa-1408	70	6	bimodule	bimodule	NOUN
ijassa-1408	70	7	over	over	ADP
ijassa-1408	70	8	c[g	c[g	NOUN
ijassa-1408	70	9	]	]	PUNCT
ijassa-1408	70	10	.	.	PUNCT
ijassa-1408	71	1	lemma	lemma	PROPN
ijassa-1408	71	2	3.1	3.1	NUM
ijassa-1408	71	3	:	:	PUNCT
ijassa-1408	71	4	all	all	DET
ijassa-1408	71	5	derivations	derivation	NOUN
ijassa-1408	71	6	with	with	ADP
ijassa-1408	71	7	values	value	NOUN
ijassa-1408	71	8	in	in	ADP
ijassa-1408	71	9	the	the	DET
ijassa-1408	71	10	banach	banach	NOUN
ijassa-1408	71	11	bimodule	bimodule	NOUN
ijassa-1408	71	12	as	as	SCONJ
ijassa-1408	71	13	are	be	AUX
ijassa-1408	71	14	quasi	quasi	ADJ
ijassa-1408	71	15	-	-	ADJ
ijassa-1408	71	16	inner	inner	ADJ
ijassa-1408	71	17	.	.	PUNCT
ijassa-1408	72	1	copyright	copyright	NOUN
ijassa-1408	72	2	©	©	ADP
ijassa-1408	72	3	2023	2023	NUM
ijassa-1408	72	4	assa	assa	NOUN
ijassa-1408	72	5	.	.	PUNCT
ijassa-1408	73	1	adv	adv	PROPN
ijassa-1408	73	2	syst	syst	PROPN
ijassa-1408	73	3	sci	sci	PROPN
ijassa-1408	73	4	appl	appl	PROPN
ijassa-1408	73	5	(	(	PUNCT
ijassa-1408	73	6	2023	2023	NUM
ijassa-1408	73	7	)	)	PUNCT
ijassa-1408	73	8	a	a	DET
ijassa-1408	73	9	combinatorial	combinatorial	ADJ
ijassa-1408	73	10	view	view	NOUN
ijassa-1408	73	11	on	on	ADP
ijassa-1408	73	12	derivations	derivation	NOUN
ijassa-1408	73	13	in	in	ADP
ijassa-1408	73	14	bimodules	bimodule	NOUN
ijassa-1408	73	15	181	181	NUM
ijassa-1408	73	16	proof	proof	NOUN
ijassa-1408	73	17	let	let	VERB
ijassa-1408	73	18	χ	χ	PRON
ijassa-1408	73	19	be	be	AUX
ijassa-1408	73	20	the	the	DET
ijassa-1408	73	21	character	character	NOUN
ijassa-1408	73	22	corresponding	correspond	VERB
ijassa-1408	73	23	in	in	ADP
ijassa-1408	73	24	the	the	DET
ijassa-1408	73	25	sense	sense	NOUN
ijassa-1408	73	26	of	of	ADP
ijassa-1408	73	27	lemma	lemma	PROPN
ijassa-1408	73	28	2.1	2.1	NUM
ijassa-1408	73	29	to	to	ADP
ijassa-1408	73	30	a	a	DET
ijassa-1408	73	31	nontrivial	nontrivial	ADJ
ijassa-1408	73	32	derivation	derivation	NOUN
ijassa-1408	73	33	d.	d.	PROPN
ijassa-1408	73	34	let	let	VERB
ijassa-1408	73	35	us	we	PRON
ijassa-1408	73	36	show	show	VERB
ijassa-1408	73	37	that	that	SCONJ
ijassa-1408	73	38	if	if	SCONJ
ijassa-1408	73	39	the	the	DET
ijassa-1408	73	40	character	character	NOUN
ijassa-1408	73	41	χ	χ	NOUN
ijassa-1408	73	42	takes	take	VERB
ijassa-1408	73	43	a	a	DET
ijassa-1408	73	44	nonzero	nonzero	NOUN
ijassa-1408	73	45	value	value	NOUN
ijassa-1408	73	46	on	on	ADP
ijassa-1408	73	47	some	some	DET
ijassa-1408	73	48	loop	loop	NOUN
ijassa-1408	73	49	,	,	PUNCT
ijassa-1408	73	50	then	then	ADV
ijassa-1408	73	51	the	the	DET
ijassa-1408	73	52	operator	operator	NOUN
ijassa-1408	73	53	d	d	NOUN
ijassa-1408	73	54	is	be	AUX
ijassa-1408	73	55	unbounded	unbounded	ADJ
ijassa-1408	73	56	.	.	PUNCT
ijassa-1408	74	1	consider	consider	VERB
ijassa-1408	74	2	the	the	DET
ijassa-1408	74	3	loop	loop	NOUN
ijassa-1408	74	4	ϕ	ϕ	PROPN
ijassa-1408	74	5	∈	∈	PROPN
ijassa-1408	74	6	hom	hom	X
ijassa-1408	75	1	(	(	PUNCT
ijassa-1408	75	2	g	g	NOUN
ijassa-1408	75	3	,	,	PUNCT
ijassa-1408	75	4	g	g	NOUN
ijassa-1408	75	5	)	)	PUNCT
ijassa-1408	75	6	.	.	PUNCT
ijassa-1408	76	1	as	as	SCONJ
ijassa-1408	76	2	it	it	PRON
ijassa-1408	76	3	can	can	AUX
ijassa-1408	76	4	be	be	AUX
ijassa-1408	76	5	seen	see	VERB
ijassa-1408	76	6	from	from	ADP
ijassa-1408	76	7	the	the	DET
ijassa-1408	76	8	definition	definition	NOUN
ijassa-1408	76	9	,	,	PUNCT
ijassa-1408	76	10	for	for	ADP
ijassa-1408	76	11	some	some	DET
ijassa-1408	76	12	t	t	NOUN
ijassa-1408	76	13	∈	∈	PROPN
ijassa-1408	76	14	z(g	z(g	NOUN
ijassa-1408	76	15	)	)	PUNCT
ijassa-1408	76	16	,	,	PUNCT
ijassa-1408	76	17	the	the	DET
ijassa-1408	76	18	notation	notation	NOUN
ijassa-1408	76	19	ϕ	ϕ	PROPN
ijassa-1408	76	20	=	=	SYM
ijassa-1408	76	21	(	(	PUNCT
ijassa-1408	76	22	gt	gt	PROPN
ijassa-1408	76	23	,	,	PUNCT
ijassa-1408	76	24	t	t	PROPN
ijassa-1408	76	25	)	)	PUNCT
ijassa-1408	76	26	is	be	AUX
ijassa-1408	76	27	valid	valid	ADJ
ijassa-1408	76	28	.	.	PUNCT
ijassa-1408	77	1	let	let	VERB
ijassa-1408	77	2	χ(ϕ	χ(ϕ	VERB
ijassa-1408	77	3	)	)	PUNCT
ijassa-1408	77	4	̸=	̸=	PROPN
ijassa-1408	77	5	0	0	NUM
ijassa-1408	77	6	.	.	PUNCT
ijassa-1408	78	1	without	without	ADP
ijassa-1408	78	2	loss	loss	NOUN
ijassa-1408	78	3	of	of	ADP
ijassa-1408	78	4	generality	generality	NOUN
ijassa-1408	78	5	,	,	PUNCT
ijassa-1408	78	6	we	we	PRON
ijassa-1408	78	7	may	may	AUX
ijassa-1408	78	8	assume	assume	VERB
ijassa-1408	78	9	that	that	SCONJ
ijassa-1408	78	10	χ(ϕ	χ(ϕ	NOUN
ijassa-1408	78	11	)	)	PUNCT
ijassa-1408	79	1	=	=	SYM
ijassa-1408	79	2	1	1	X
ijassa-1408	79	3	.	.	X
ijassa-1408	79	4	note	note	VERB
ijassa-1408	79	5	that	that	SCONJ
ijassa-1408	79	6	the	the	DET
ijassa-1408	79	7	element	element	NOUN
ijassa-1408	79	8	t	t	PROPN
ijassa-1408	79	9	can	can	AUX
ijassa-1408	79	10	not	not	PART
ijassa-1408	79	11	be	be	AUX
ijassa-1408	79	12	of	of	ADP
ijassa-1408	79	13	finite	finite	ADJ
ijassa-1408	79	14	order	order	NOUN
ijassa-1408	79	15	in	in	ADP
ijassa-1408	79	16	the	the	DET
ijassa-1408	79	17	group	group	NOUN
ijassa-1408	79	18	g	g	NOUN
ijassa-1408	79	19	,	,	PUNCT
ijassa-1408	79	20	otherwise	otherwise	ADV
ijassa-1408	79	21	we	we	PRON
ijassa-1408	79	22	would	would	AUX
ijassa-1408	79	23	get	get	VERB
ijassa-1408	79	24	that	that	DET
ijassa-1408	79	25	χ((g	χ((g	ADJ
ijassa-1408	79	26	,	,	PUNCT
ijassa-1408	79	27	e	e	NOUN
ijassa-1408	79	28	)	)	PUNCT
ijassa-1408	79	29	)	)	PUNCT
ijassa-1408	80	1	=	=	PUNCT
ijassa-1408	80	2	ord(t	ord(t	PROPN
ijassa-1408	80	3	)	)	PUNCT
ijassa-1408	80	4	,	,	PUNCT
ijassa-1408	80	5	which	which	PRON
ijassa-1408	80	6	is	be	AUX
ijassa-1408	80	7	impossible	impossible	ADJ
ijassa-1408	80	8	since	since	SCONJ
ijassa-1408	80	9	(	(	PUNCT
ijassa-1408	80	10	g	g	NOUN
ijassa-1408	80	11	,	,	PUNCT
ijassa-1408	80	12	e	e	NOUN
ijassa-1408	80	13	)	)	PUNCT
ijassa-1408	80	14	is	be	AUX
ijassa-1408	80	15	a	a	DET
ijassa-1408	80	16	neutral	neutral	ADJ
ijassa-1408	80	17	morphism	morphism	NOUN
ijassa-1408	80	18	.	.	PUNCT
ijassa-1408	81	1	given	give	VERB
ijassa-1408	81	2	that	that	PRON
ijassa-1408	81	3	t	t	PROPN
ijassa-1408	81	4	is	be	AUX
ijassa-1408	81	5	of	of	ADP
ijassa-1408	81	6	infinite	infinite	ADJ
ijassa-1408	81	7	order	order	NOUN
ijassa-1408	81	8	and	and	CCONJ
ijassa-1408	81	9	using	use	VERB
ijassa-1408	81	10	the	the	DET
ijassa-1408	81	11	property	property	NOUN
ijassa-1408	81	12	(	(	PUNCT
ijassa-1408	81	13	2.3	2.3	NUM
ijassa-1408	81	14	)	)	PUNCT
ijassa-1408	81	15	,	,	PUNCT
ijassa-1408	81	16	we	we	PRON
ijassa-1408	81	17	get	get	VERB
ijassa-1408	81	18	the	the	DET
ijassa-1408	81	19	following	follow	VERB
ijassa-1408	81	20	χ((gtn	χ((gtn	PROPN
ijassa-1408	81	21	,	,	PUNCT
ijassa-1408	81	22	tn	tn	PROPN
ijassa-1408	81	23	)	)	PUNCT
ijassa-1408	81	24	)	)	PUNCT
ijassa-1408	82	1	=	=	SYM
ijassa-1408	82	2	χ(ϕn	χ(ϕn	NOUN
ijassa-1408	82	3	)	)	PUNCT
ijassa-1408	82	4	=	=	VERB
ijassa-1408	83	1	n.	n.	NOUN
ijassa-1408	83	2	with	with	ADP
ijassa-1408	83	3	the	the	DET
ijassa-1408	83	4	formula	formula	NOUN
ijassa-1408	83	5	(	(	PUNCT
ijassa-1408	83	6	2.4	2.4	NUM
ijassa-1408	83	7	)	)	PUNCT
ijassa-1408	83	8	we	we	PRON
ijassa-1408	83	9	get	get	VERB
ijassa-1408	83	10	that	that	PRON
ijassa-1408	83	11	∥d(tn)∥s	∥d(tn)∥	NOUN
ijassa-1408	83	12	≥	≥	PRON
ijassa-1408	83	13	n.	n.	NOUN
ijassa-1408	83	14	so	so	ADV
ijassa-1408	83	15	∥d(tn)∥s	∥d(tn)∥	NOUN
ijassa-1408	83	16	→	→	SYM
ijassa-1408	83	17	∞	∞	NUM
ijassa-1408	83	18	at	at	ADP
ijassa-1408	83	19	n→	n→	PROPN
ijassa-1408	83	20	∞.	∞.	PROPN
ijassa-1408	83	21	at	at	ADP
ijassa-1408	83	22	the	the	DET
ijassa-1408	83	23	same	same	ADJ
ijassa-1408	83	24	time	time	NOUN
ijassa-1408	84	1	∥gtn∥s	∥gtn∥s	NOUN
ijassa-1408	84	2	=	=	SYM
ijassa-1408	84	3	1	1	X
ijassa-1408	84	4	.	.	PUNCT
ijassa-1408	85	1	in	in	ADP
ijassa-1408	85	2	this	this	DET
ijassa-1408	85	3	case	case	NOUN
ijassa-1408	85	4	the	the	DET
ijassa-1408	85	5	operator	operator	NOUN
ijassa-1408	85	6	d	d	PROPN
ijassa-1408	85	7	–	–	PUNCT
ijassa-1408	85	8	converts	convert	VERB
ijassa-1408	85	9	a	a	DET
ijassa-1408	85	10	bounded	bounded	ADJ
ijassa-1408	85	11	sequence	sequence	NOUN
ijassa-1408	85	12	into	into	ADP
ijassa-1408	85	13	an	an	DET
ijassa-1408	85	14	unbounded	unbounded	ADJ
ijassa-1408	85	15	one	one	NOUN
ijassa-1408	85	16	,	,	PUNCT
ijassa-1408	85	17	and	and	CCONJ
ijassa-1408	85	18	hence	hence	ADV
ijassa-1408	85	19	is	be	AUX
ijassa-1408	85	20	not	not	PART
ijassa-1408	85	21	bounded	bound	VERB
ijassa-1408	85	22	itself	itself	PRON
ijassa-1408	85	23	.	.	PUNCT
ijassa-1408	86	1	proposition	proposition	NOUN
ijassa-1408	86	2	3.1	3.1	NUM
ijassa-1408	86	3	:	:	PUNCT
ijassa-1408	86	4	if	if	SCONJ
ijassa-1408	86	5	the	the	DET
ijassa-1408	86	6	character	character	NOUN
ijassa-1408	86	7	χ	χ	NOUN
ijassa-1408	86	8	defines	define	VERB
ijassa-1408	86	9	the	the	DET
ijassa-1408	86	10	derivation	derivation	NOUN
ijassa-1408	86	11	d	d	X
ijassa-1408	86	12	∈	∈	NOUN
ijassa-1408	86	13	der(as	der(a	NOUN
ijassa-1408	86	14	)	)	PUNCT
ijassa-1408	86	15	then	then	ADV
ijassa-1408	86	16	for	for	ADP
ijassa-1408	86	17	any	any	DET
ijassa-1408	86	18	two	two	NUM
ijassa-1408	86	19	morphisms	morphism	NOUN
ijassa-1408	86	20	ϕ	ϕ	NOUN
ijassa-1408	86	21	,	,	PUNCT
ijassa-1408	86	22	ψ	ψ	X
ijassa-1408	86	23	∈	∈	PROPN
ijassa-1408	86	24	hom	hom	X
ijassa-1408	86	25	(	(	PUNCT
ijassa-1408	86	26	a	a	DET
ijassa-1408	86	27	,	,	PUNCT
ijassa-1408	86	28	b	b	X
ijassa-1408	86	29	)	)	PUNCT
ijassa-1408	86	30	we	we	PRON
ijassa-1408	86	31	have	have	VERB
ijassa-1408	86	32	that	that	DET
ijassa-1408	86	33	χ(ϕ	χ(ϕ	NOUN
ijassa-1408	86	34	)	)	PUNCT
ijassa-1408	86	35	=	=	SYM
ijassa-1408	86	36	χ(ψ	χ(ψ	NOUN
ijassa-1408	86	37	)	)	PUNCT
ijassa-1408	86	38	.	.	PUNCT
ijassa-1408	87	1	proof	proof	NOUN
ijassa-1408	87	2	by	by	ADP
ijassa-1408	87	3	the	the	DET
ijassa-1408	87	4	lemma	lemma	PROPN
ijassa-1408	87	5	3.1	3.1	NUM
ijassa-1408	87	6	for	for	ADP
ijassa-1408	87	7	each	each	DET
ijassa-1408	87	8	derivation	derivation	NOUN
ijassa-1408	87	9	d	d	X
ijassa-1408	87	10	∈	∈	NOUN
ijassa-1408	87	11	der(as	der(a	NOUN
ijassa-1408	87	12	)	)	PUNCT
ijassa-1408	88	1	,	,	PUNCT
ijassa-1408	88	2	the	the	DET
ijassa-1408	88	3	corresponding	correspond	VERB
ijassa-1408	88	4	character	character	NOUN
ijassa-1408	88	5	χ	χ	NOUN
ijassa-1408	88	6	,	,	PUNCT
ijassa-1408	88	7	in	in	ADP
ijassa-1408	88	8	the	the	DET
ijassa-1408	88	9	sense	sense	NOUN
ijassa-1408	88	10	of	of	ADP
ijassa-1408	88	11	the	the	DET
ijassa-1408	88	12	lemma	lemma	PROPN
ijassa-1408	88	13	2.1	2.1	NUM
ijassa-1408	88	14	,	,	PUNCT
ijassa-1408	88	15	is	be	AUX
ijassa-1408	88	16	zero	zero	NUM
ijassa-1408	88	17	on	on	ADP
ijassa-1408	88	18	loops	loop	NOUN
ijassa-1408	88	19	.	.	PUNCT
ijassa-1408	89	1	for	for	ADP
ijassa-1408	89	2	two	two	NUM
ijassa-1408	89	3	different	different	ADJ
ijassa-1408	89	4	objects	object	NOUN
ijassa-1408	89	5	a	a	DET
ijassa-1408	89	6	̸=	̸=	PROPN
ijassa-1408	89	7	b	b	NUM
ijassa-1408	89	8	,	,	PUNCT
ijassa-1408	89	9	and	and	CCONJ
ijassa-1408	89	10	two	two	NUM
ijassa-1408	89	11	morphisms	morphism	NOUN
ijassa-1408	89	12	ϕ	ϕ	NOUN
ijassa-1408	89	13	,	,	PUNCT
ijassa-1408	89	14	ψ	ψ	X
ijassa-1408	89	15	∈	∈	PROPN
ijassa-1408	89	16	hom	hom	X
ijassa-1408	89	17	(	(	PUNCT
ijassa-1408	89	18	a	a	DET
ijassa-1408	89	19	,	,	PUNCT
ijassa-1408	89	20	b	b	NOUN
ijassa-1408	89	21	)	)	PUNCT
ijassa-1408	89	22	(	(	PUNCT
ijassa-1408	89	23	if	if	SCONJ
ijassa-1408	89	24	they	they	PRON
ijassa-1408	89	25	exist	exist	VERB
ijassa-1408	89	26	,	,	PUNCT
ijassa-1408	89	27	of	of	ADP
ijassa-1408	89	28	course	course	NOUN
ijassa-1408	89	29	)	)	PUNCT
ijassa-1408	89	30	there	there	PRON
ijassa-1408	89	31	exists	exist	VERB
ijassa-1408	89	32	a	a	DET
ijassa-1408	89	33	loop	loop	NOUN
ijassa-1408	89	34	ζ	ζ	NOUN
ijassa-1408	89	35	∈	∈	NOUN
ijassa-1408	89	36	hom	hom	X
ijassa-1408	89	37	(	(	PUNCT
ijassa-1408	89	38	a	a	PRON
ijassa-1408	89	39	,	,	PUNCT
ijassa-1408	89	40	a	a	NOUN
ijassa-1408	89	41	)	)	PUNCT
ijassa-1408	89	42	such	such	ADJ
ijassa-1408	89	43	that	that	SCONJ
ijassa-1408	89	44	ϕ	ϕ	NOUN
ijassa-1408	89	45	◦	◦	NOUN
ijassa-1408	89	46	ζ	ζ	NOUN
ijassa-1408	89	47	=	=	SYM
ijassa-1408	89	48	ψ	ψ	NOUN
ijassa-1408	89	49	.	.	PUNCT
ijassa-1408	90	1	so	so	ADV
ijassa-1408	90	2	,	,	PUNCT
ijassa-1408	90	3	since	since	SCONJ
ijassa-1408	90	4	χ(ζ	χ(ζ	NOUN
ijassa-1408	90	5	)	)	PUNCT
ijassa-1408	90	6	=	=	SYM
ijassa-1408	90	7	0	0	NUM
ijassa-1408	90	8	,	,	PUNCT
ijassa-1408	90	9	by	by	ADP
ijassa-1408	90	10	the	the	DET
ijassa-1408	90	11	formula	formula	NOUN
ijassa-1408	90	12	(	(	PUNCT
ijassa-1408	90	13	2.3	2.3	NUM
ijassa-1408	90	14	)	)	PUNCT
ijassa-1408	90	15	we	we	PRON
ijassa-1408	90	16	have	have	VERB
ijassa-1408	90	17	that	that	DET
ijassa-1408	90	18	χ(ϕ	χ(ϕ	NOUN
ijassa-1408	90	19	)	)	PUNCT
ijassa-1408	90	20	=	=	SYM
ijassa-1408	90	21	χ(ψ	χ(ψ	NOUN
ijassa-1408	90	22	)	)	PUNCT
ijassa-1408	90	23	.	.	PUNCT
ijassa-1408	91	1	let	let	VERB
ijassa-1408	91	2	us	we	PRON
ijassa-1408	91	3	proceed	proceed	VERB
ijassa-1408	91	4	to	to	ADP
ijassa-1408	91	5	the	the	DET
ijassa-1408	91	6	proof	proof	NOUN
ijassa-1408	91	7	of	of	ADP
ijassa-1408	91	8	the	the	DET
ijassa-1408	91	9	1.1	1.1	NUM
ijassa-1408	91	10	theorem	theorem	ADJ
ijassa-1408	91	11	,	,	PUNCT
ijassa-1408	91	12	i.e.	i.e.	X
ijassa-1408	91	13	we	we	PRON
ijassa-1408	91	14	show	show	VERB
ijassa-1408	91	15	that	that	SCONJ
ijassa-1408	91	16	if	if	SCONJ
ijassa-1408	91	17	norm	norm	NOUN
ijassa-1408	91	18	∥	∥	X
ijassa-1408	91	19	·	·	PUNCT
ijassa-1408	91	20	∥	∥	PUNCT
ijassa-1408	91	21	is	be	AUX
ijassa-1408	91	22	subject	subject	ADJ
ijassa-1408	91	23	to	to	ADP
ijassa-1408	91	24	the	the	DET
ijassa-1408	91	25	supremum	supremum	ADJ
ijassa-1408	91	26	norm	norm	NOUN
ijassa-1408	91	27	∥	∥	X
ijassa-1408	91	28	·	·	PUNCT
ijassa-1408	91	29	∥s	∥s	NOUN
ijassa-1408	91	30	,	,	PUNCT
ijassa-1408	91	31	then	then	ADV
ijassa-1408	91	32	all	all	DET
ijassa-1408	91	33	derivations	derivation	NOUN
ijassa-1408	91	34	with	with	ADP
ijassa-1408	91	35	values	value	NOUN
ijassa-1408	91	36	in	in	ADP
ijassa-1408	91	37	the	the	DET
ijassa-1408	91	38	bimodule	bimodule	NOUN
ijassa-1408	91	39	a	a	PRON
ijassa-1408	91	40	are	be	AUX
ijassa-1408	91	41	quasi	quasi	ADJ
ijassa-1408	91	42	-	-	ADJ
ijassa-1408	91	43	inner	inner	ADJ
ijassa-1408	91	44	.	.	PUNCT
ijassa-1408	92	1	proof	proof	NOUN
ijassa-1408	92	2	of	of	ADP
ijassa-1408	92	3	theorem	theorem	ADJ
ijassa-1408	92	4	1.1	1.1	NUM
ijassa-1408	92	5	consider	consider	VERB
ijassa-1408	92	6	a	a	DET
ijassa-1408	92	7	bounded	bounded	ADJ
ijassa-1408	92	8	operator	operator	NOUN
ijassa-1408	92	9	d	d	NOUN
ijassa-1408	92	10	over	over	ADP
ijassa-1408	92	11	a.	a.	NOUN
ijassa-1408	92	12	from	from	ADP
ijassa-1408	92	13	boundedness	boundedness	NOUN
ijassa-1408	92	14	we	we	PRON
ijassa-1408	92	15	obtain	obtain	VERB
ijassa-1408	92	16	that	that	PRON
ijassa-1408	92	17	for	for	ADP
ijassa-1408	92	18	some	some	DET
ijassa-1408	92	19	constant	constant	ADJ
ijassa-1408	92	20	a	a	DET
ijassa-1408	92	21	holds	hold	VERB
ijassa-1408	92	22	an	an	DET
ijassa-1408	92	23	inequaluty	inequaluty	ADJ
ijassa-1408	92	24	∥d(g)∥	∥d(g)∥	NOUN
ijassa-1408	92	25	<	<	X
ijassa-1408	92	26	a	a	PRON
ijassa-1408	92	27	for	for	ADP
ijassa-1408	92	28	all	all	DET
ijassa-1408	92	29	basis	basis	NOUN
ijassa-1408	92	30	elements	element	NOUN
ijassa-1408	92	31	g	g	PROPN
ijassa-1408	92	32	∈	∈	PROPN
ijassa-1408	92	33	g.	g.	NOUN
ijassa-1408	92	34	from	from	ADP
ijassa-1408	92	35	the	the	DET
ijassa-1408	92	36	norm	norm	NOUN
ijassa-1408	92	37	subordination	subordination	NOUN
ijassa-1408	92	38	we	we	PRON
ijassa-1408	92	39	have	have	VERB
ijassa-1408	92	40	that	that	DET
ijassa-1408	92	41	∥d(g)∥s	∥d(g)∥	NOUN
ijassa-1408	92	42	<	<	X
ijassa-1408	92	43	ca	ca	NOUN
ijassa-1408	92	44	.	.	PUNCT
ijassa-1408	93	1	so	so	ADV
ijassa-1408	93	2	the	the	DET
ijassa-1408	93	3	character	character	NOUN
ijassa-1408	93	4	χ	χ	PRON
ijassa-1408	93	5	corresponding	correspond	VERB
ijassa-1408	93	6	to	to	ADP
ijassa-1408	93	7	the	the	DET
ijassa-1408	93	8	derivation	derivation	NOUN
ijassa-1408	93	9	d	d	NOUN
ijassa-1408	93	10	is	be	AUX
ijassa-1408	93	11	trivial	trivial	ADJ
ijassa-1408	93	12	on	on	ADP
ijassa-1408	93	13	loops	loop	NOUN
ijassa-1408	93	14	by	by	ADP
ijassa-1408	93	15	the	the	DET
ijassa-1408	93	16	lemma	lemma	PROPN
ijassa-1408	93	17	3.1	3.1	NUM
ijassa-1408	93	18	,	,	PUNCT
ijassa-1408	93	19	and	and	CCONJ
ijassa-1408	93	20	so	so	ADV
ijassa-1408	93	21	the	the	DET
ijassa-1408	93	22	derivation	derivation	NOUN
ijassa-1408	93	23	d	d	NOUN
ijassa-1408	93	24	is	be	AUX
ijassa-1408	93	25	quasi	quasi	ADJ
ijassa-1408	93	26	-	-	ADJ
ijassa-1408	93	27	inner	inner	ADJ
ijassa-1408	93	28	.	.	PUNCT
ijassa-1408	94	1	4	4	X
ijassa-1408	94	2	.	.	X
ijassa-1408	94	3	examples	example	NOUN
ijassa-1408	94	4	and	and	CCONJ
ijassa-1408	94	5	applications	application	NOUN
ijassa-1408	94	6	consider	consider	VERB
ijassa-1408	94	7	the	the	DET
ijassa-1408	94	8	space	space	NOUN
ijassa-1408	94	9	ℓp(g	ℓp(g	NOUN
ijassa-1408	94	10	)	)	PUNCT
ijassa-1408	94	11	,	,	PUNCT
ijassa-1408	94	12	i.e.	i.e.	X
ijassa-1408	94	13	,	,	PUNCT
ijassa-1408	94	14	all	all	DET
ijassa-1408	94	15	elements	element	NOUN
ijassa-1408	94	16	of	of	ADP
ijassa-1408	94	17	the	the	DET
ijassa-1408	94	18	form	form	NOUN
ijassa-1408	94	19	ω	ω	NOUN
ijassa-1408	94	20	=	=	SYM
ijassa-1408	94	21	∑	∑	PROPN
ijassa-1408	94	22	g∈g	g∈g	PROPN
ijassa-1408	94	23	x(g)g	x(g)g	PROPN
ijassa-1408	94	24	,	,	PUNCT
ijassa-1408	94	25	bounded	bound	VERB
ijassa-1408	94	26	by	by	ADP
ijassa-1408	94	27	the	the	DET
ijassa-1408	94	28	ℓp	ℓp	ADJ
ijassa-1408	94	29	-	-	PUNCT
ijassa-1408	94	30	norm	norm	NOUN
ijassa-1408	94	31	∥ω∥p	∥ω∥p	NOUN
ijassa-1408	94	32	:	:	PUNCT
ijassa-1408	95	1	=	=	SYM
ijassa-1408	95	2	p	p	ADP
ijassa-1408	95	3	√∑	√∑	PROPN
ijassa-1408	95	4	g∈g	g∈g	PROPN
ijassa-1408	95	5	|x(g)|p	|x(g)|p	NOUN
ijassa-1408	95	6	.	.	PUNCT
ijassa-1408	96	1	(	(	PUNCT
ijassa-1408	96	2	4.6	4.6	NUM
ijassa-1408	96	3	)	)	PUNCT
ijassa-1408	96	4	it	it	PRON
ijassa-1408	96	5	is	be	AUX
ijassa-1408	96	6	clear	clear	ADJ
ijassa-1408	96	7	that	that	SCONJ
ijassa-1408	96	8	such	such	ADJ
ijassa-1408	96	9	norm	norm	NOUN
ijassa-1408	96	10	is	be	AUX
ijassa-1408	96	11	subordinate	subordinate	ADJ
ijassa-1408	96	12	to	to	ADP
ijassa-1408	96	13	the	the	DET
ijassa-1408	96	14	supremum	supremum	NOUN
ijassa-1408	96	15	for	for	ADP
ijassa-1408	96	16	p	p	PRON
ijassa-1408	96	17	≥	≥	NOUN
ijassa-1408	96	18	1	1	NUM
ijassa-1408	96	19	:	:	PUNCT
ijassa-1408	97	1	∥ω∥p	∥ω∥p	VERB
ijassa-1408	97	2	≤	≤	NUM
ijassa-1408	98	1	sup	sup	NOUN
ijassa-1408	98	2	g∈g	g∈g	PROPN
ijassa-1408	98	3	|x(g)|	|x(g)|	PROPN
ijassa-1408	98	4	.	.	PUNCT
ijassa-1408	98	5	example	example	NOUN
ijassa-1408	98	6	4.1	4.1	NUM
ijassa-1408	98	7	:	:	PUNCT
ijassa-1408	98	8	all	all	DET
ijassa-1408	98	9	derivations	derivation	NOUN
ijassa-1408	98	10	in	in	ADP
ijassa-1408	98	11	der(ℓp(g	der(ℓp(g	PROPN
ijassa-1408	98	12	)	)	PUNCT
ijassa-1408	98	13	)	)	PUNCT
ijassa-1408	99	1	,	,	PUNCT
ijassa-1408	99	2	p	p	NOUN
ijassa-1408	99	3	≥	≥	NUM
ijassa-1408	99	4	1	1	NUM
ijassa-1408	99	5	are	be	AUX
ijassa-1408	99	6	quasi	quasi	ADJ
ijassa-1408	99	7	-	-	ADJ
ijassa-1408	99	8	inner	inner	ADJ
ijassa-1408	99	9	.	.	PUNCT
ijassa-1408	100	1	in	in	ADP
ijassa-1408	100	2	[	[	X
ijassa-1408	100	3	8	8	NUM
ijassa-1408	100	4	]	]	PUNCT
ijassa-1408	100	5	was	be	AUX
ijassa-1408	100	6	shown	show	VERB
ijassa-1408	100	7	that	that	SCONJ
ijassa-1408	100	8	for	for	ADP
ijassa-1408	100	9	p	p	NOUN
ijassa-1408	100	10	=	=	SYM
ijassa-1408	100	11	1	1	NUM
ijassa-1408	100	12	all	all	DET
ijassa-1408	100	13	derivations	derivation	NOUN
ijassa-1408	100	14	are	be	AUX
ijassa-1408	100	15	inner	inner	ADJ
ijassa-1408	100	16	.	.	PUNCT
ijassa-1408	101	1	the	the	DET
ijassa-1408	101	2	case	case	NOUN
ijassa-1408	101	3	p	p	X
ijassa-1408	101	4	>	>	X
ijassa-1408	101	5	1	1	NUM
ijassa-1408	101	6	is	be	AUX
ijassa-1408	101	7	new	new	ADJ
ijassa-1408	101	8	.	.	PUNCT
ijassa-1408	102	1	the	the	DET
ijassa-1408	102	2	natural	natural	ADJ
ijassa-1408	102	3	question	question	NOUN
ijassa-1408	102	4	remains	remain	VERB
ijassa-1408	102	5	as	as	ADP
ijassa-1408	102	6	to	to	ADP
ijassa-1408	102	7	whether	whether	SCONJ
ijassa-1408	102	8	inner	inner	ADJ
ijassa-1408	102	9	and	and	CCONJ
ijassa-1408	102	10	quasi	quasi	ADJ
ijassa-1408	102	11	-	-	ADJ
ijassa-1408	102	12	inner	inner	ADJ
ijassa-1408	102	13	derivations	derivation	NOUN
ijassa-1408	102	14	coincide	coincide	NOUN
ijassa-1408	102	15	.	.	PUNCT
ijassa-1408	103	1	this	this	DET
ijassa-1408	103	2	question	question	NOUN
ijassa-1408	103	3	look	look	VERB
ijassa-1408	103	4	not	not	PART
ijassa-1408	103	5	obviouse	obviouse	ADJ
ijassa-1408	103	6	.	.	PUNCT
ijassa-1408	104	1	but	but	CCONJ
ijassa-1408	104	2	note	note	VERB
ijassa-1408	104	3	that	that	SCONJ
ijassa-1408	104	4	qasi	qasi	ADJ
ijassa-1408	104	5	-	-	PUNCT
ijassa-1408	104	6	inner	inner	ADJ
ijassa-1408	104	7	derivations	derivation	NOUN
ijassa-1408	104	8	can	can	AUX
ijassa-1408	104	9	be	be	AUX
ijassa-1408	104	10	understood	understand	VERB
ijassa-1408	104	11	as	as	ADP
ijassa-1408	104	12	formal	formal	ADJ
ijassa-1408	104	13	sums	sum	NOUN
ijassa-1408	104	14	of	of	ADP
ijassa-1408	104	15	inner	inner	ADJ
ijassa-1408	104	16	one	one	NUM
ijassa-1408	104	17	.	.	PUNCT
ijassa-1408	105	1	therefore	therefore	ADV
ijassa-1408	105	2	,	,	PUNCT
ijassa-1408	105	3	in	in	ADP
ijassa-1408	105	4	terms	term	NOUN
ijassa-1408	105	5	of	of	ADP
ijassa-1408	105	6	analysis	analysis	NOUN
ijassa-1408	105	7	difference	difference	NOUN
ijassa-1408	105	8	between	between	ADP
ijassa-1408	105	9	inner	inner	ADJ
ijassa-1408	105	10	and	and	CCONJ
ijassa-1408	105	11	quasi	quasi	ADJ
ijassa-1408	105	12	-	-	ADJ
ijassa-1408	105	13	inner	inner	ADJ
ijassa-1408	105	14	derivations	derivation	NOUN
ijassa-1408	105	15	is	be	AUX
ijassa-1408	105	16	minor	minor	ADJ
ijassa-1408	105	17	.	.	PUNCT
ijassa-1408	106	1	copyright	copyright	NOUN
ijassa-1408	106	2	©	©	ADP
ijassa-1408	106	3	2023	2023	NUM
ijassa-1408	106	4	assa	assa	NOUN
ijassa-1408	106	5	.	.	PUNCT
ijassa-1408	107	1	adv	adv	PROPN
ijassa-1408	107	2	syst	syst	PROPN
ijassa-1408	107	3	sci	sci	PROPN
ijassa-1408	107	4	appl	appl	PROPN
ijassa-1408	107	5	(	(	PUNCT
ijassa-1408	107	6	2023	2023	NUM
ijassa-1408	107	7	)	)	PUNCT
ijassa-1408	107	8	182	182	NUM
ijassa-1408	107	9	a.	a.	NOUN
ijassa-1408	107	10	aurutyunov	aurutyunov	NOUN
ijassa-1408	107	11	the	the	DET
ijassa-1408	107	12	case	case	NOUN
ijassa-1408	107	13	of	of	ADP
ijassa-1408	107	14	(	(	PUNCT
ijassa-1408	107	15	σ	σ	PROPN
ijassa-1408	107	16	,	,	PUNCT
ijassa-1408	107	17	τ)-derivations	τ)-derivations	PUNCT
ijassa-1408	107	18	it	it	PRON
ijassa-1408	107	19	is	be	AUX
ijassa-1408	107	20	clear	clear	ADJ
ijassa-1408	107	21	that	that	SCONJ
ijassa-1408	107	22	in	in	ADP
ijassa-1408	107	23	the	the	DET
ijassa-1408	107	24	proof	proof	NOUN
ijassa-1408	107	25	of	of	ADP
ijassa-1408	107	26	theorem	theorem	ADJ
ijassa-1408	107	27	1.1	1.1	NUM
ijassa-1408	107	28	the	the	DET
ijassa-1408	107	29	ability	ability	NOUN
ijassa-1408	107	30	to	to	PART
ijassa-1408	107	31	represent	represent	VERB
ijassa-1408	107	32	derivations	derivation	NOUN
ijassa-1408	107	33	via	via	ADP
ijassa-1408	107	34	groupoid	groupoid	PROPN
ijassa-1408	107	35	characters	character	NOUN
ijassa-1408	107	36	plays	play	VERB
ijassa-1408	107	37	the	the	DET
ijassa-1408	107	38	key	key	ADJ
ijassa-1408	107	39	role	role	NOUN
ijassa-1408	107	40	.	.	PUNCT
ijassa-1408	108	1	this	this	DET
ijassa-1408	108	2	construction	construction	NOUN
ijassa-1408	108	3	can	can	AUX
ijassa-1408	108	4	be	be	AUX
ijassa-1408	108	5	applied	apply	VERB
ijassa-1408	108	6	to	to	ADP
ijassa-1408	108	7	other	other	ADJ
ijassa-1408	108	8	structures	structure	NOUN
ijassa-1408	108	9	as	as	ADV
ijassa-1408	108	10	well	well	ADV
ijassa-1408	108	11	,	,	PUNCT
ijassa-1408	108	12	with	with	ADP
ijassa-1408	108	13	a	a	DET
ijassa-1408	108	14	corresponding	correspond	VERB
ijassa-1408	108	15	change	change	NOUN
ijassa-1408	108	16	in	in	ADP
ijassa-1408	108	17	the	the	DET
ijassa-1408	108	18	groupoid	groupoid	PROPN
ijassa-1408	108	19	structure	structure	NOUN
ijassa-1408	108	20	.	.	PUNCT
ijassa-1408	109	1	thus	thus	ADV
ijassa-1408	109	2	,	,	PUNCT
ijassa-1408	109	3	in	in	ADP
ijassa-1408	109	4	[	[	PUNCT
ijassa-1408	109	5	9	9	NUM
ijassa-1408	109	6	]	]	PUNCT
ijassa-1408	109	7	,	,	PUNCT
ijassa-1408	109	8	(	(	PUNCT
ijassa-1408	109	9	σ	σ	NOUN
ijassa-1408	109	10	,	,	PUNCT
ijassa-1408	109	11	τ)-derivations	τ)-derivation	NOUN
ijassa-1408	109	12	,	,	PUNCT
ijassa-1408	109	13	i.e.	i.e.	X
ijassa-1408	109	14	operators	operator	NOUN
ijassa-1408	109	15	satisfying	satisfy	VERB
ijassa-1408	109	16	a	a	DET
ijassa-1408	109	17	”	"	PUNCT
ijassa-1408	109	18	twisted	twisted	ADJ
ijassa-1408	109	19	”	"	PUNCT
ijassa-1408	109	20	leibniz	leibniz	NOUN
ijassa-1408	109	21	rule	rule	NOUN
ijassa-1408	109	22	,	,	PUNCT
ijassa-1408	109	23	were	be	AUX
ijassa-1408	109	24	investigated	investigate	VERB
ijassa-1408	109	25	.	.	PUNCT
ijassa-1408	110	1	conditions	condition	NOUN
ijassa-1408	110	2	and	and	CCONJ
ijassa-1408	110	3	applications	application	NOUN
ijassa-1408	110	4	of	of	ADP
ijassa-1408	110	5	(	(	PUNCT
ijassa-1408	110	6	σ	σ	PROPN
ijassa-1408	110	7	,	,	PUNCT
ijassa-1408	110	8	τ)-derivations	τ)-derivations	PROPN
ijassa-1408	110	9	can	can	AUX
ijassa-1408	110	10	be	be	AUX
ijassa-1408	110	11	found	find	VERB
ijassa-1408	110	12	in	in	ADP
ijassa-1408	110	13	[	[	X
ijassa-1408	110	14	10	10	NUM
ijassa-1408	110	15	,	,	PUNCT
ijassa-1408	110	16	11	11	NUM
ijassa-1408	110	17	]	]	PUNCT
ijassa-1408	110	18	.	.	PUNCT
ijassa-1408	111	1	let	let	VERB
ijassa-1408	111	2	us	we	PRON
ijassa-1408	111	3	give	give	VERB
ijassa-1408	111	4	a	a	DET
ijassa-1408	111	5	slightly	slightly	ADV
ijassa-1408	111	6	more	more	ADV
ijassa-1408	111	7	general	general	ADJ
ijassa-1408	111	8	definition	definition	NOUN
ijassa-1408	111	9	to	to	PART
ijassa-1408	111	10	fit	fit	VERB
ijassa-1408	111	11	our	our	PRON
ijassa-1408	111	12	case	case	NOUN
ijassa-1408	111	13	.	.	PUNCT
ijassa-1408	112	1	definition	definition	NOUN
ijassa-1408	112	2	4.1	4.1	NUM
ijassa-1408	112	3	:	:	PUNCT
ijassa-1408	112	4	a	a	DET
ijassa-1408	112	5	linear	linear	ADJ
ijassa-1408	112	6	bounded	bound	VERB
ijassa-1408	112	7	operator	operator	NOUN
ijassa-1408	112	8	d	d	NOUN
ijassa-1408	112	9	:	:	PUNCT
ijassa-1408	112	10	c[g	c[g	X
ijassa-1408	112	11	]	]	X
ijassa-1408	112	12	→	→	PUNCT
ijassa-1408	112	13	a	a	DET
ijassa-1408	112	14	such	such	ADJ
ijassa-1408	112	15	that	that	PRON
ijassa-1408	112	16	for	for	ADP
ijassa-1408	112	17	some	some	DET
ijassa-1408	112	18	endomorphisms	endomorphism	NOUN
ijassa-1408	112	19	σ	σ	PROPN
ijassa-1408	112	20	,	,	PUNCT
ijassa-1408	112	21	τ	τ	X
ijassa-1408	112	22	:	:	PUNCT
ijassa-1408	112	23	c[g	c[g	X
ijassa-1408	112	24	]	]	PUNCT
ijassa-1408	112	25	→	→	SYM
ijassa-1408	112	26	c[g	c[g	X
ijassa-1408	112	27	]	]	PUNCT
ijassa-1408	112	28	d(ab	d(ab	PROPN
ijassa-1408	112	29	)	)	PUNCT
ijassa-1408	112	30	=	=	SYM
ijassa-1408	112	31	d(a)σ(b	d(a)σ(b	PROPN
ijassa-1408	112	32	)	)	PUNCT
ijassa-1408	112	33	+	+	SYM
ijassa-1408	112	34	τ(a)d(v	τ(a)d(v	NOUN
ijassa-1408	112	35	)	)	PUNCT
ijassa-1408	112	36	,	,	PUNCT
ijassa-1408	112	37	a	a	DET
ijassa-1408	112	38	,	,	PUNCT
ijassa-1408	112	39	b	b	PROPN
ijassa-1408	112	40	∈	∈	PROPN
ijassa-1408	112	41	c[g	c[g	NOUN
ijassa-1408	112	42	]	]	X
ijassa-1408	112	43	,	,	PUNCT
ijassa-1408	112	44	(	(	PUNCT
ijassa-1408	112	45	4.7	4.7	NUM
ijassa-1408	112	46	)	)	PUNCT
ijassa-1408	112	47	let	let	VERB
ijassa-1408	112	48	’s	’s	PRON
ijassa-1408	112	49	call	call	VERB
ijassa-1408	112	50	a	a	DET
ijassa-1408	112	51	(	(	PUNCT
ijassa-1408	112	52	σ	σ	PROPN
ijassa-1408	112	53	,	,	PUNCT
ijassa-1408	112	54	τ)−derivation	τ)−derivation	PROPN
ijassa-1408	112	55	.	.	PUNCT
ijassa-1408	113	1	as	as	SCONJ
ijassa-1408	113	2	shown	show	VERB
ijassa-1408	113	3	in	in	ADP
ijassa-1408	113	4	[	[	NOUN
ijassa-1408	113	5	9	9	NUM
ijassa-1408	113	6	]	]	PUNCT
ijassa-1408	113	7	for	for	ADP
ijassa-1408	113	8	the	the	DET
ijassa-1408	113	9	”	"	PUNCT
ijassa-1408	113	10	twisted	twisted	ADJ
ijassa-1408	113	11	”	"	PUNCT
ijassa-1408	113	12	groupoid	groupoid	NOUN
ijassa-1408	113	13	(	(	PUNCT
ijassa-1408	113	14	see	see	VERB
ijassa-1408	113	15	[	[	X
ijassa-1408	113	16	9	9	NUM
ijassa-1408	113	17	]	]	PUNCT
ijassa-1408	113	18	,	,	PUNCT
ijassa-1408	113	19	section	section	NOUN
ijassa-1408	113	20	3	3	NUM
ijassa-1408	113	21	)	)	PUNCT
ijassa-1408	113	22	(	(	PUNCT
ijassa-1408	113	23	σ	σ	PROPN
ijassa-1408	113	24	,	,	PUNCT
ijassa-1408	113	25	τ)−derivation	τ)−derivation	NOUN
ijassa-1408	113	26	can	can	AUX
ijassa-1408	113	27	be	be	AUX
ijassa-1408	113	28	presented	present	VERB
ijassa-1408	113	29	by	by	ADP
ijassa-1408	113	30	its	its	PRON
ijassa-1408	113	31	characters	character	NOUN
ijassa-1408	113	32	(	(	PUNCT
ijassa-1408	113	33	[	[	X
ijassa-1408	113	34	9	9	NUM
ijassa-1408	113	35	]	]	PUNCT
ijassa-1408	113	36	,	,	PUNCT
ijassa-1408	113	37	theorem	theorem	VERB
ijassa-1408	113	38	1	1	NUM
ijassa-1408	113	39	)	)	PUNCT
ijassa-1408	113	40	.	.	PUNCT
ijassa-1408	114	1	applying	apply	VERB
ijassa-1408	114	2	the	the	DET
ijassa-1408	114	3	same	same	ADJ
ijassa-1408	114	4	reasoning	reasoning	NOUN
ijassa-1408	114	5	as	as	ADP
ijassa-1408	114	6	in	in	ADP
ijassa-1408	114	7	the	the	DET
ijassa-1408	114	8	proof	proof	NOUN
ijassa-1408	114	9	of	of	ADP
ijassa-1408	114	10	the	the	DET
ijassa-1408	114	11	theorem	theorem	ADJ
ijassa-1408	114	12	1.1	1.1	NUM
ijassa-1408	114	13	to	to	ADP
ijassa-1408	114	14	the	the	DET
ijassa-1408	114	15	case	case	NOUN
ijassa-1408	114	16	of	of	ADP
ijassa-1408	114	17	(	(	PUNCT
ijassa-1408	114	18	σ	σ	PROPN
ijassa-1408	114	19	,	,	PUNCT
ijassa-1408	114	20	τ)−derivations	τ)−derivation	NOUN
ijassa-1408	114	21	we	we	PRON
ijassa-1408	114	22	obtain	obtain	VERB
ijassa-1408	114	23	the	the	DET
ijassa-1408	114	24	”	"	PUNCT
ijassa-1408	114	25	twisted	twisted	ADJ
ijassa-1408	114	26	”	"	PUNCT
ijassa-1408	114	27	analog	analog	NOUN
ijassa-1408	114	28	of	of	ADP
ijassa-1408	114	29	our	our	PRON
ijassa-1408	114	30	theorem	theorem	PROPN
ijassa-1408	114	31	.	.	PROPN
ijassa-1408	114	32	example	example	NOUN
ijassa-1408	114	33	4.2	4.2	NUM
ijassa-1408	114	34	:	:	PUNCT
ijassa-1408	114	35	all	all	PRON
ijassa-1408	114	36	(	(	PUNCT
ijassa-1408	114	37	σ	σ	PROPN
ijassa-1408	114	38	,	,	PUNCT
ijassa-1408	114	39	τ)−derivations	τ)−derivations	PROPN
ijassa-1408	114	40	with	with	ADP
ijassa-1408	114	41	values	value	NOUN
ijassa-1408	114	42	in	in	ADP
ijassa-1408	114	43	bimodule	bimodule	NOUN
ijassa-1408	114	44	a	a	DET
ijassa-1408	114	45	generated	generate	VERB
ijassa-1408	114	46	by	by	ADP
ijassa-1408	114	47	a	a	DET
ijassa-1408	114	48	norm	norm	NOUN
ijassa-1408	114	49	subordinate	subordinate	NOUN
ijassa-1408	114	50	supremum	supremum	ADJ
ijassa-1408	114	51	–	–	PUNCT
ijassa-1408	114	52	are	be	AUX
ijassa-1408	114	53	(	(	PUNCT
ijassa-1408	114	54	σ	σ	PROPN
ijassa-1408	114	55	,	,	PUNCT
ijassa-1408	114	56	τ	τ	NOUN
ijassa-1408	114	57	)	)	PUNCT
ijassa-1408	114	58	-quasi	-quasi	PROPN
ijassa-1408	114	59	-	-	PUNCT
ijassa-1408	114	60	inner	inner	NOUN
ijassa-1408	114	61	.	.	PUNCT
ijassa-1408	115	1	here	here	ADV
ijassa-1408	115	2	(	(	PUNCT
ijassa-1408	115	3	σ	σ	PROPN
ijassa-1408	115	4	,	,	PUNCT
ijassa-1408	115	5	τ	τ	NOUN
ijassa-1408	115	6	)	)	PUNCT
ijassa-1408	115	7	-quasi	-quasi	PROPN
ijassa-1408	115	8	-	-	PUNCT
ijassa-1408	115	9	inner	inner	ADJ
ijassa-1408	115	10	derivations	derivation	NOUN
ijassa-1408	115	11	are	be	AUX
ijassa-1408	115	12	defined	define	VERB
ijassa-1408	115	13	similarly	similarly	ADV
ijassa-1408	115	14	as	as	ADP
ijassa-1408	115	15	(	(	PUNCT
ijassa-1408	115	16	σ	σ	PROPN
ijassa-1408	115	17	,	,	PUNCT
ijassa-1408	115	18	τ	τ	NOUN
ijassa-1408	115	19	)	)	PUNCT
ijassa-1408	115	20	-derivations	-derivation	NOUN
ijassa-1408	115	21	given	give	VERB
ijassa-1408	115	22	by	by	ADP
ijassa-1408	115	23	characters	character	NOUN
ijassa-1408	115	24	identically	identically	ADV
ijassa-1408	115	25	equal	equal	ADJ
ijassa-1408	115	26	to	to	ADP
ijassa-1408	115	27	zero	zero	NUM
ijassa-1408	115	28	on	on	ADP
ijassa-1408	115	29	loops	loop	NOUN
ijassa-1408	115	30	.	.	PUNCT
ijassa-1408	116	1	central	central	ADJ
ijassa-1408	116	2	derivations	derivation	NOUN
ijassa-1408	116	3	the	the	DET
ijassa-1408	116	4	proved	prove	VERB
ijassa-1408	116	5	theorem	theorem	NOUN
ijassa-1408	116	6	and	and	CCONJ
ijassa-1408	116	7	the	the	DET
ijassa-1408	116	8	proposed	propose	VERB
ijassa-1408	116	9	approach	approach	NOUN
ijassa-1408	116	10	also	also	ADV
ijassa-1408	116	11	suggest	suggest	VERB
ijassa-1408	116	12	examples	example	NOUN
ijassa-1408	116	13	of	of	ADP
ijassa-1408	116	14	norms	norm	NOUN
ijassa-1408	116	15	in	in	ADP
ijassa-1408	116	16	which	which	PRON
ijassa-1408	116	17	outer	outer	ADJ
ijassa-1408	116	18	derivations	derivation	NOUN
ijassa-1408	116	19	appear	appear	VERB
ijassa-1408	116	20	.	.	PUNCT
ijassa-1408	117	1	recall	recall	NOUN
ijassa-1408	117	2	(	(	PUNCT
ijassa-1408	117	3	[	[	X
ijassa-1408	117	4	5	5	NUM
ijassa-1408	117	5	]	]	PUNCT
ijassa-1408	117	6	,	,	PUNCT
ijassa-1408	117	7	section	section	NOUN
ijassa-1408	117	8	2.3	2.3	NUM
ijassa-1408	117	9	)	)	PUNCT
ijassa-1408	117	10	that	that	SCONJ
ijassa-1408	117	11	the	the	DET
ijassa-1408	117	12	central	central	ADJ
ijassa-1408	117	13	derivation	derivation	NOUN
ijassa-1408	117	14	dtz	dtz	PROPN
ijassa-1408	117	15	is	be	AUX
ijassa-1408	117	16	an	an	DET
ijassa-1408	117	17	operator	operator	NOUN
ijassa-1408	117	18	which	which	PRON
ijassa-1408	117	19	is	be	AUX
ijassa-1408	117	20	given	give	VERB
ijassa-1408	117	21	by	by	ADP
ijassa-1408	117	22	a	a	DET
ijassa-1408	117	23	center	center	ADJ
ijassa-1408	117	24	element	element	NOUN
ijassa-1408	117	25	of	of	ADP
ijassa-1408	117	26	the	the	DET
ijassa-1408	117	27	group	group	NOUN
ijassa-1408	117	28	z	z	PROPN
ijassa-1408	117	29	∈	∈	PROPN
ijassa-1408	117	30	z(g	z(g	NOUN
ijassa-1408	117	31	)	)	PUNCT
ijassa-1408	117	32	and	and	CCONJ
ijassa-1408	117	33	a	a	DET
ijassa-1408	117	34	non	non	ADJ
ijassa-1408	117	35	-	-	ADJ
ijassa-1408	117	36	trivial	trivial	ADJ
ijassa-1408	117	37	homomorphism	homomorphism	NOUN
ijassa-1408	117	38	τ	τ	X
ijassa-1408	117	39	:	:	PUNCT
ijassa-1408	117	40	g→	g→	NOUN
ijassa-1408	117	41	(	(	PUNCT
ijassa-1408	117	42	c,+	c,+	NOUN
ijassa-1408	117	43	)	)	PUNCT
ijassa-1408	117	44	into	into	ADP
ijassa-1408	117	45	the	the	DET
ijassa-1408	117	46	additive	additive	ADJ
ijassa-1408	117	47	group	group	NOUN
ijassa-1408	117	48	of	of	ADP
ijassa-1408	117	49	complex	complex	ADJ
ijassa-1408	117	50	numbers	number	NOUN
ijassa-1408	117	51	on	on	ADP
ijassa-1408	117	52	generators	generator	NOUN
ijassa-1408	117	53	g	g	PROPN
ijassa-1408	117	54	∈	∈	PROPN
ijassa-1408	117	55	g	g	PROPN
ijassa-1408	117	56	⊂	⊂	PROPN
ijassa-1408	117	57	c[g	c[g	PROPN
ijassa-1408	117	58	]	]	PUNCT
ijassa-1408	117	59	by	by	ADP
ijassa-1408	117	60	the	the	DET
ijassa-1408	117	61	formula	formula	NOUN
ijassa-1408	117	62	dtz	dtz	NOUN
ijassa-1408	117	63	:	:	PUNCT
ijassa-1408	117	64	g	g	PROPN
ijassa-1408	117	65	→	→	SYM
ijassa-1408	117	66	τ(g)gz	τ(g)gz	PROPN
ijassa-1408	117	67	.	.	PUNCT
ijassa-1408	118	1	(	(	PUNCT
ijassa-1408	118	2	4.8	4.8	NUM
ijassa-1408	118	3	)	)	PUNCT
ijassa-1408	118	4	central	central	ADJ
ijassa-1408	118	5	derivations	derivation	NOUN
ijassa-1408	118	6	form	form	VERB
ijassa-1408	118	7	a	a	DET
ijassa-1408	118	8	subalgebra	subalgebra	NOUN
ijassa-1408	118	9	(	(	PUNCT
ijassa-1408	118	10	[	[	X
ijassa-1408	118	11	5	5	NUM
ijassa-1408	118	12	]	]	PUNCT
ijassa-1408	118	13	,	,	PUNCT
ijassa-1408	118	14	theorem	theorem	VERB
ijassa-1408	118	15	2	2	NUM
ijassa-1408	118	16	)	)	PUNCT
ijassa-1408	118	17	.	.	PUNCT
ijassa-1408	119	1	it	it	PRON
ijassa-1408	119	2	is	be	AUX
ijassa-1408	119	3	easy	easy	ADJ
ijassa-1408	119	4	to	to	PART
ijassa-1408	119	5	see	see	VERB
ijassa-1408	119	6	that	that	SCONJ
ijassa-1408	119	7	the	the	DET
ijassa-1408	119	8	corresponding	correspond	VERB
ijassa-1408	119	9	character	character	NOUN
ijassa-1408	119	10	χt	χt	ADP
ijassa-1408	119	11	z	z	PROPN
ijassa-1408	119	12	in	in	ADP
ijassa-1408	119	13	the	the	DET
ijassa-1408	119	14	sense	sense	NOUN
ijassa-1408	119	15	of	of	ADP
ijassa-1408	119	16	the	the	DET
ijassa-1408	119	17	lemma	lemma	PROPN
ijassa-1408	119	18	2.1	2.1	NUM
ijassa-1408	119	19	is	be	AUX
ijassa-1408	119	20	non	non	ADJ
ijassa-1408	119	21	-	-	ADJ
ijassa-1408	119	22	trivial	trivial	ADJ
ijassa-1408	119	23	on	on	ADP
ijassa-1408	119	24	loops	loop	NOUN
ijassa-1408	119	25	(	(	PUNCT
ijassa-1408	119	26	see	see	VERB
ijassa-1408	119	27	[	[	X
ijassa-1408	119	28	5	5	NUM
ijassa-1408	119	29	]	]	PUNCT
ijassa-1408	119	30	,	,	PUNCT
ijassa-1408	119	31	proposition	proposition	NOUN
ijassa-1408	119	32	5	5	NUM
ijassa-1408	119	33	)	)	PUNCT
ijassa-1408	119	34	.	.	PUNCT
ijassa-1408	120	1	more	more	ADV
ijassa-1408	120	2	precisely	precisely	ADV
ijassa-1408	120	3	,	,	PUNCT
ijassa-1408	120	4	its	its	PRON
ijassa-1408	120	5	support	support	NOUN
ijassa-1408	120	6	is	be	AUX
ijassa-1408	120	7	a	a	DET
ijassa-1408	120	8	subgroupoid	subgroupoid	NOUN
ijassa-1408	120	9	with	with	ADP
ijassa-1408	120	10	one	one	NUM
ijassa-1408	120	11	object	object	NOUN
ijassa-1408	120	12	(	(	PUNCT
ijassa-1408	120	13	just	just	ADV
ijassa-1408	120	14	a	a	DET
ijassa-1408	120	15	fixed	fix	VERB
ijassa-1408	120	16	central	central	ADJ
ijassa-1408	120	17	element	element	NOUN
ijassa-1408	120	18	)	)	PUNCT
ijassa-1408	120	19	.	.	PUNCT
ijassa-1408	121	1	from	from	ADP
ijassa-1408	121	2	which	which	PRON
ijassa-1408	121	3	we	we	PRON
ijassa-1408	121	4	obtain	obtain	VERB
ijassa-1408	121	5	that	that	SCONJ
ijassa-1408	121	6	the	the	DET
ijassa-1408	121	7	central	central	ADJ
ijassa-1408	121	8	derivation	derivation	NOUN
ijassa-1408	121	9	can	can	AUX
ijassa-1408	121	10	not	not	PART
ijassa-1408	121	11	be	be	AUX
ijassa-1408	121	12	quasi	quasi	ADJ
ijassa-1408	121	13	-	-	ADJ
ijassa-1408	121	14	inner	inner	ADJ
ijassa-1408	121	15	.	.	PUNCT
ijassa-1408	122	1	a	a	DET
ijassa-1408	122	2	simple	simple	ADJ
ijassa-1408	122	3	calculation	calculation	NOUN
ijassa-1408	122	4	shows	show	VERB
ijassa-1408	122	5	that	that	SCONJ
ijassa-1408	122	6	the	the	DET
ijassa-1408	122	7	central	central	ADJ
ijassa-1408	122	8	derivations	derivation	NOUN
ijassa-1408	122	9	are	be	AUX
ijassa-1408	122	10	not	not	PART
ijassa-1408	122	11	bounded	bound	VERB
ijassa-1408	122	12	in	in	ADP
ijassa-1408	122	13	the	the	DET
ijassa-1408	122	14	supremum	supremum	ADJ
ijassa-1408	122	15	norm	norm	NOUN
ijassa-1408	122	16	.	.	PUNCT
ijassa-1408	123	1	it	it	PRON
ijassa-1408	123	2	follows	follow	VERB
ijassa-1408	123	3	from	from	ADP
ijassa-1408	123	4	the	the	DET
ijassa-1408	123	5	theorem	theorem	ADJ
ijassa-1408	123	6	1.1	1.1	NUM
ijassa-1408	123	7	but	but	CCONJ
ijassa-1408	123	8	this	this	PRON
ijassa-1408	123	9	also	also	ADV
ijassa-1408	123	10	can	can	AUX
ijassa-1408	123	11	easily	easily	ADV
ijassa-1408	123	12	be	be	AUX
ijassa-1408	123	13	checked	check	VERB
ijassa-1408	123	14	by	by	ADP
ijassa-1408	123	15	direct	direct	ADJ
ijassa-1408	123	16	calculation	calculation	NOUN
ijassa-1408	123	17	.	.	PUNCT
ijassa-1408	124	1	however	however	ADV
ijassa-1408	124	2	,	,	PUNCT
ijassa-1408	124	3	it	it	PRON
ijassa-1408	124	4	is	be	AUX
ijassa-1408	124	5	possible	possible	ADJ
ijassa-1408	124	6	to	to	PART
ijassa-1408	124	7	choose	choose	VERB
ijassa-1408	124	8	a	a	DET
ijassa-1408	124	9	norm	norm	NOUN
ijassa-1408	124	10	which	which	PRON
ijassa-1408	124	11	is	be	AUX
ijassa-1408	124	12	not	not	PART
ijassa-1408	124	13	subordinate	subordinate	ADJ
ijassa-1408	124	14	to	to	ADP
ijassa-1408	124	15	the	the	DET
ijassa-1408	124	16	supremum	supremum	NOUN
ijassa-1408	124	17	.	.	PUNCT
ijassa-1408	125	1	this	this	DET
ijassa-1408	125	2	case	case	NOUN
ijassa-1408	125	3	was	be	AUX
ijassa-1408	125	4	discussed	discuss	VERB
ijassa-1408	125	5	in	in	ADP
ijassa-1408	125	6	more	more	ADJ
ijassa-1408	125	7	detail	detail	NOUN
ijassa-1408	125	8	in	in	ADP
ijassa-1408	125	9	the	the	DET
ijassa-1408	125	10	joint	joint	ADJ
ijassa-1408	125	11	paper	paper	NOUN
ijassa-1408	125	12	with	with	ADP
ijassa-1408	125	13	a.	a.	NOUN
ijassa-1408	125	14	najanzin	najanzin	PROPN
ijassa-1408	126	1	[	[	X
ijassa-1408	126	2	7	7	NUM
ijassa-1408	126	3	]	]	PUNCT
ijassa-1408	126	4	.	.	PUNCT
ijassa-1408	127	1	let	let	VERB
ijassa-1408	127	2	us	we	PRON
ijassa-1408	127	3	briefly	briefly	ADV
ijassa-1408	127	4	describe	describe	VERB
ijassa-1408	127	5	one	one	NUM
ijassa-1408	127	6	example	example	NOUN
ijassa-1408	127	7	of	of	ADP
ijassa-1408	127	8	a	a	DET
ijassa-1408	127	9	norm	norm	NOUN
ijassa-1408	127	10	in	in	ADP
ijassa-1408	127	11	which	which	PRON
ijassa-1408	127	12	the	the	DET
ijassa-1408	127	13	central	central	ADJ
ijassa-1408	127	14	differentials	differential	NOUN
ijassa-1408	127	15	are	be	AUX
ijassa-1408	127	16	bounded	bound	VERB
ijassa-1408	127	17	.	.	PUNCT
ijassa-1408	128	1	we	we	PRON
ijassa-1408	128	2	define	define	VERB
ijassa-1408	128	3	the	the	DET
ijassa-1408	128	4	norm	norm	NOUN
ijassa-1408	128	5	∥	∥	X
ijassa-1408	128	6	·	·	PUNCT
ijassa-1408	128	7	∥∗α	∥∗α	VERB
ijassa-1408	128	8	for	for	ADP
ijassa-1408	128	9	ω	ω	PROPN
ijassa-1408	128	10	=	=	SYM
ijassa-1408	128	11	∑	∑	PUNCT
ijassa-1408	128	12	g∈g	g∈g	PROPN
ijassa-1408	128	13	x(g)g	x(g)g	PROPN
ijassa-1408	128	14	as	as	SCONJ
ijassa-1408	128	15	follows	follow	VERB
ijassa-1408	128	16	∥ω∥∗α	∥ω∥∗α	PROPN
ijassa-1408	128	17	:	:	PUNCT
ijassa-1408	128	18	=	=	PUNCT
ijassa-1408	128	19	∑	∑	PUNCT
ijassa-1408	128	20	g∈g	g∈g	PROPN
ijassa-1408	128	21	|x(g)|e−α|g|	|x(g)|e−α|g|	NOUN
ijassa-1408	128	22	.	.	PUNCT
ijassa-1408	129	1	(	(	PUNCT
ijassa-1408	129	2	4.9	4.9	NUM
ijassa-1408	129	3	)	)	PUNCT
ijassa-1408	129	4	we	we	PRON
ijassa-1408	129	5	denote	denote	VERB
ijassa-1408	129	6	the	the	DET
ijassa-1408	129	7	closure	closure	NOUN
ijassa-1408	129	8	of	of	ADP
ijassa-1408	129	9	c[g	c[g	NOUN
ijassa-1408	129	10	]	]	PUNCT
ijassa-1408	129	11	by	by	ADP
ijassa-1408	129	12	this	this	DET
ijassa-1408	129	13	norm	norm	NOUN
ijassa-1408	129	14	as	as	ADP
ijassa-1408	129	15	a∗	a∗	PROPN
ijassa-1408	129	16	α	α	PROPN
ijassa-1408	129	17	.	.	PROPN
ijassa-1408	129	18	example	example	NOUN
ijassa-1408	129	19	4.3	4.3	NUM
ijassa-1408	129	20	(	(	PUNCT
ijassa-1408	129	21	theorem	theorem	VERB
ijassa-1408	129	22	2.1	2.1	NUM
ijassa-1408	129	23	,	,	PUNCT
ijassa-1408	129	24	[	[	X
ijassa-1408	129	25	7	7	NUM
ijassa-1408	129	26	]	]	PUNCT
ijassa-1408	129	27	):	):	PUNCT
ijassa-1408	129	28	for	for	ADP
ijassa-1408	129	29	all	all	DET
ijassa-1408	129	30	sufficiently	sufficiently	ADV
ijassa-1408	129	31	large	large	ADJ
ijassa-1408	129	32	α	α	PROPN
ijassa-1408	129	33	>	>	X
ijassa-1408	129	34	0	0	NUM
ijassa-1408	129	35	,	,	PUNCT
ijassa-1408	129	36	central	central	ADJ
ijassa-1408	129	37	derivations	derivation	NOUN
ijassa-1408	129	38	with	with	ADP
ijassa-1408	129	39	values	value	NOUN
ijassa-1408	129	40	in	in	ADP
ijassa-1408	129	41	the	the	DET
ijassa-1408	129	42	bimodule	bimodule	NOUN
ijassa-1408	129	43	a∗	a∗	PROPN
ijassa-1408	129	44	α	α	PROPN
ijassa-1408	129	45	are	be	AUX
ijassa-1408	129	46	bounded	bound	VERB
ijassa-1408	129	47	.	.	PUNCT
ijassa-1408	130	1	copyright	copyright	NOUN
ijassa-1408	130	2	©	©	PROPN
ijassa-1408	130	3	2023	2023	NUM
ijassa-1408	130	4	assa	assa	NOUN
ijassa-1408	130	5	.	.	PUNCT
ijassa-1408	131	1	adv	adv	PROPN
ijassa-1408	131	2	syst	syst	PROPN
ijassa-1408	131	3	sci	sci	PROPN
ijassa-1408	131	4	appl	appl	PROPN
ijassa-1408	131	5	(	(	PUNCT
ijassa-1408	131	6	2023	2023	NUM
ijassa-1408	131	7	)	)	PUNCT
ijassa-1408	131	8	a	a	DET
ijassa-1408	131	9	combinatorial	combinatorial	ADJ
ijassa-1408	131	10	view	view	NOUN
ijassa-1408	131	11	on	on	ADP
ijassa-1408	131	12	derivations	derivation	NOUN
ijassa-1408	131	13	in	in	ADP
ijassa-1408	131	14	bimodules	bimodule	NOUN
ijassa-1408	131	15	183	183	NUM
ijassa-1408	131	16	in	in	ADP
ijassa-1408	131	17	the	the	DET
ijassa-1408	131	18	case	case	NOUN
ijassa-1408	131	19	of	of	ADP
ijassa-1408	131	20	a	a	DET
ijassa-1408	131	21	group	group	NOUN
ijassa-1408	131	22	ring	ring	NOUN
ijassa-1408	131	23	(	(	PUNCT
ijassa-1408	131	24	i.e.	i.e.	X
ijassa-1408	131	25	the	the	DET
ijassa-1408	131	26	case	case	NOUN
ijassa-1408	131	27	of	of	ADP
ijassa-1408	131	28	finite	finite	PROPN
ijassa-1408	131	29	linear	linear	PROPN
ijassa-1408	131	30	combinations	combination	NOUN
ijassa-1408	131	31	without	without	ADP
ijassa-1408	131	32	topological	topological	ADJ
ijassa-1408	131	33	space	space	NOUN
ijassa-1408	131	34	structure	structure	NOUN
ijassa-1408	131	35	)	)	PUNCT
ijassa-1408	131	36	the	the	DET
ijassa-1408	131	37	ideals	ideal	NOUN
ijassa-1408	131	38	of	of	ADP
ijassa-1408	131	39	inner	inner	ADJ
ijassa-1408	131	40	and	and	CCONJ
ijassa-1408	131	41	quasi	quasi	ADJ
ijassa-1408	131	42	-	-	ADJ
ijassa-1408	131	43	inner	inner	ADJ
ijassa-1408	131	44	derivations	derivation	NOUN
ijassa-1408	131	45	do	do	AUX
ijassa-1408	131	46	not	not	PART
ijassa-1408	131	47	coincide	coincide	VERB
ijassa-1408	131	48	(	(	PUNCT
ijassa-1408	131	49	see	see	VERB
ijassa-1408	131	50	[	[	X
ijassa-1408	131	51	5	5	NUM
ijassa-1408	131	52	]	]	PUNCT
ijassa-1408	131	53	,	,	PUNCT
ijassa-1408	131	54	the	the	DET
ijassa-1408	131	55	case	case	NOUN
ijassa-1408	131	56	of	of	ADP
ijassa-1408	131	57	heisenberg	heisenberg	PROPN
ijassa-1408	131	58	group	group	PROPN
ijassa-1408	131	59	)	)	PUNCT
ijassa-1408	131	60	.	.	PUNCT
ijassa-1408	132	1	moreover	moreover	ADV
ijassa-1408	132	2	,	,	PUNCT
ijassa-1408	132	3	the	the	DET
ijassa-1408	132	4	difference	difference	NOUN
ijassa-1408	132	5	between	between	ADP
ijassa-1408	132	6	inner	inner	ADJ
ijassa-1408	132	7	and	and	CCONJ
ijassa-1408	132	8	quasi	quasi	ADJ
ijassa-1408	132	9	-	-	ADJ
ijassa-1408	132	10	inner	inner	ADJ
ijassa-1408	132	11	derivations	derivation	NOUN
ijassa-1408	132	12	is	be	AUX
ijassa-1408	132	13	determined	determine	VERB
ijassa-1408	132	14	by	by	ADP
ijassa-1408	132	15	the	the	DET
ijassa-1408	132	16	combinatorial	combinatorial	ADJ
ijassa-1408	132	17	properties	property	NOUN
ijassa-1408	132	18	of	of	ADP
ijassa-1408	132	19	the	the	DET
ijassa-1408	132	20	group	group	NOUN
ijassa-1408	132	21	.	.	PUNCT
ijassa-1408	133	1	as	as	ADP
ijassa-1408	133	2	the	the	DET
ijassa-1408	133	3	proof	proof	NOUN
ijassa-1408	133	4	of	of	ADP
ijassa-1408	133	5	the	the	DET
ijassa-1408	133	6	theorem	theorem	ADJ
ijassa-1408	133	7	1.1	1.1	NUM
ijassa-1408	133	8	shows	show	NOUN
ijassa-1408	133	9	in	in	ADP
ijassa-1408	133	10	the	the	DET
ijassa-1408	133	11	case	case	NOUN
ijassa-1408	133	12	of	of	ADP
ijassa-1408	133	13	normalized	normalize	VERB
ijassa-1408	133	14	bimodules	bimodule	NOUN
ijassa-1408	133	15	,	,	PUNCT
ijassa-1408	133	16	this	this	DET
ijassa-1408	133	17	dependence	dependence	NOUN
ijassa-1408	133	18	vanishes	vanish	VERB
ijassa-1408	133	19	.	.	PUNCT
ijassa-1408	134	1	so	so	ADV
ijassa-1408	134	2	the	the	DET
ijassa-1408	134	3	following	follow	VERB
ijassa-1408	134	4	assumption	assumption	NOUN
ijassa-1408	134	5	seems	seem	VERB
ijassa-1408	134	6	plausible	plausible	ADJ
ijassa-1408	134	7	:	:	PUNCT
ijassa-1408	134	8	whether	whether	SCONJ
ijassa-1408	134	9	all	all	DET
ijassa-1408	134	10	derivations	derivation	NOUN
ijassa-1408	134	11	in	in	ADP
ijassa-1408	134	12	ℓp(g	ℓp(g	NOUN
ijassa-1408	134	13	)	)	PUNCT
ijassa-1408	134	14	are	be	AUX
ijassa-1408	134	15	inner	inner	ADJ
ijassa-1408	134	16	.	.	PUNCT
ijassa-1408	135	1	acknowledgements	acknowledgement	NOUN
ijassa-1408	135	2	the	the	DET
ijassa-1408	135	3	research	research	NOUN
ijassa-1408	135	4	is	be	AUX
ijassa-1408	135	5	supported	support	VERB
ijassa-1408	135	6	by	by	ADP
ijassa-1408	135	7	the	the	DET
ijassa-1408	135	8	ministry	ministry	PROPN
ijassa-1408	135	9	of	of	ADP
ijassa-1408	135	10	science	science	PROPN
ijassa-1408	135	11	and	and	CCONJ
ijassa-1408	135	12	higher	high	ADJ
ijassa-1408	135	13	education	education	NOUN
ijassa-1408	135	14	of	of	ADP
ijassa-1408	135	15	the	the	DET
ijassa-1408	135	16	russian	russian	PROPN
ijassa-1408	135	17	federation	federation	PROPN
ijassa-1408	135	18	(	(	PUNCT
ijassa-1408	135	19	goszadanie	goszadanie	PROPN
ijassa-1408	135	20	n.	n.	PROPN
ijassa-1408	135	21	075	075	NUM
ijassa-1408	135	22	-	-	PUNCT
ijassa-1408	135	23	00337	00337	NUM
ijassa-1408	135	24	-	-	PUNCT
ijassa-1408	135	25	20	20	NUM
ijassa-1408	135	26	-	-	PUNCT
ijassa-1408	135	27	03	03	NUM
ijassa-1408	135	28	,	,	PUNCT
ijassa-1408	135	29	project	project	NOUN
ijassa-1408	135	30	0714	0714	NUM
ijassa-1408	135	31	-	-	SYM
ijassa-1408	135	32	2020	2020	NUM
ijassa-1408	135	33	-	-	SYM
ijassa-1408	135	34	0005	0005	NUM
ijassa-1408	135	35	)	)	PUNCT
ijassa-1408	135	36	.	.	PUNCT
ijassa-1408	136	1	references	reference	NOUN
ijassa-1408	136	2	1	1	NUM
ijassa-1408	136	3	.	.	PUNCT
ijassa-1408	137	1	dales	dale	NOUN
ijassa-1408	137	2	,	,	PUNCT
ijassa-1408	137	3	h.	h.	PROPN
ijassa-1408	137	4	g.	g.	PROPN
ijassa-1408	137	5	(	(	PUNCT
ijassa-1408	137	6	2000	2000	NUM
ijassa-1408	137	7	)	)	PUNCT
ijassa-1408	137	8	.	.	PUNCT
ijassa-1408	138	1	banach	banach	NOUN
ijassa-1408	138	2	algebras	algebra	NOUN
ijassa-1408	138	3	and	and	CCONJ
ijassa-1408	138	4	automatic	automatic	ADJ
ijassa-1408	138	5	continuity	continuity	NOUN
ijassa-1408	138	6	,	,	PUNCT
ijassa-1408	138	7	oxford	oxford	PROPN
ijassa-1408	138	8	,	,	PUNCT
ijassa-1408	138	9	uk	uk	PROPN
ijassa-1408	138	10	:	:	PUNCT
ijassa-1408	138	11	oxford	oxford	PROPN
ijassa-1408	138	12	university	university	PROPN
ijassa-1408	138	13	press	press	NOUN
ijassa-1408	138	14	.	.	PUNCT
ijassa-1408	139	1	2	2	X
ijassa-1408	139	2	.	.	X
ijassa-1408	139	3	johnson	johnson	PROPN
ijassa-1408	139	4	,	,	PUNCT
ijassa-1408	139	5	b.	b.	PROPN
ijassa-1408	139	6	e.	e.	PROPN
ijassa-1408	139	7	(	(	PUNCT
ijassa-1408	139	8	2001	2001	NUM
ijassa-1408	139	9	)	)	PUNCT
ijassa-1408	139	10	.	.	PUNCT
ijassa-1408	140	1	the	the	DET
ijassa-1408	140	2	derivation	derivation	NOUN
ijassa-1408	140	3	problem	problem	NOUN
ijassa-1408	140	4	for	for	ADP
ijassa-1408	140	5	group	group	NOUN
ijassa-1408	140	6	algebras	algebra	NOUN
ijassa-1408	140	7	of	of	ADP
ijassa-1408	140	8	connected	connect	VERB
ijassa-1408	140	9	locally	locally	ADV
ijassa-1408	140	10	compact	compact	ADJ
ijassa-1408	140	11	groups	group	NOUN
ijassa-1408	140	12	,	,	PUNCT
ijassa-1408	140	13	j.	j.	PROPN
ijassa-1408	140	14	london	london	PROPN
ijassa-1408	140	15	math	math	PROPN
ijassa-1408	140	16	.	.	PUNCT
ijassa-1408	141	1	soc	soc	PROPN
ijassa-1408	141	2	.	.	PUNCT
ijassa-1408	141	3	,	,	PUNCT
ijassa-1408	141	4	63(2	63(2	NUM
ijassa-1408	141	5	)	)	PUNCT
ijassa-1408	141	6	,	,	PUNCT
ijassa-1408	141	7	441–452	441–452	NUM
ijassa-1408	141	8	.	.	NOUN
ijassa-1408	142	1	3	3	X
ijassa-1408	142	2	.	.	X
ijassa-1408	142	3	losert	losert	PROPN
ijassa-1408	142	4	,	,	PUNCT
ijassa-1408	142	5	v.	v.	PROPN
ijassa-1408	142	6	(	(	PUNCT
ijassa-1408	142	7	2008	2008	NUM
ijassa-1408	142	8	)	)	PUNCT
ijassa-1408	142	9	.	.	PUNCT
ijassa-1408	143	1	the	the	DET
ijassa-1408	143	2	derivation	derivation	NOUN
ijassa-1408	143	3	problem	problem	NOUN
ijassa-1408	143	4	for	for	ADP
ijassa-1408	143	5	group	group	NOUN
ijassa-1408	143	6	algebras	algebra	NOUN
ijassa-1408	143	7	,	,	PUNCT
ijassa-1408	143	8	ann	ann	PROPN
ijassa-1408	143	9	.	.	PROPN
ijassa-1408	143	10	of	of	ADP
ijassa-1408	143	11	math	math	NOUN
ijassa-1408	143	12	.	.	PUNCT
ijassa-1408	143	13	,	,	PUNCT
ijassa-1408	143	14	168(1	168(1	NUM
ijassa-1408	143	15	)	)	PUNCT
ijassa-1408	143	16	,	,	PUNCT
ijassa-1408	143	17	221–246	221–246	NUM
ijassa-1408	143	18	.	.	NOUN
ijassa-1408	143	19	4	4	X
ijassa-1408	143	20	.	.	X
ijassa-1408	143	21	arutyunov	arutyunov	PROPN
ijassa-1408	143	22	,	,	PUNCT
ijassa-1408	143	23	a.	a.	NOUN
ijassa-1408	143	24	a.	a.	PROPN
ijassa-1408	143	25	,	,	PUNCT
ijassa-1408	143	26	&	&	CCONJ
ijassa-1408	143	27	mishchenko	mishchenko	PROPN
ijassa-1408	143	28	,	,	PUNCT
ijassa-1408	143	29	a.	a.	PROPN
ijassa-1408	143	30	s.	s.	PROPN
ijassa-1408	143	31	(	(	PUNCT
ijassa-1408	143	32	2019	2019	NUM
ijassa-1408	143	33	)	)	PUNCT
ijassa-1408	143	34	.	.	PUNCT
ijassa-1408	144	1	a	a	DET
ijassa-1408	144	2	smooth	smooth	ADJ
ijassa-1408	144	3	version	version	NOUN
ijassa-1408	144	4	of	of	ADP
ijassa-1408	144	5	johnson	johnson	PROPN
ijassa-1408	144	6	’s	’s	PART
ijassa-1408	144	7	problem	problem	NOUN
ijassa-1408	144	8	on	on	ADP
ijassa-1408	144	9	derivations	derivation	NOUN
ijassa-1408	144	10	of	of	ADP
ijassa-1408	144	11	group	group	NOUN
ijassa-1408	144	12	algebras	algebra	NOUN
ijassa-1408	144	13	,	,	PUNCT
ijassa-1408	144	14	mat	mat	PROPN
ijassa-1408	144	15	.	.	PUNCT
ijassa-1408	144	16	sb	sb	PROPN
ijassa-1408	144	17	.	.	PROPN
ijassa-1408	144	18	,	,	PUNCT
ijassa-1408	144	19	210(6	210(6	NUM
ijassa-1408	144	20	)	)	PUNCT
ijassa-1408	144	21	,	,	PUNCT
ijassa-1408	144	22	3–29	3–29	PROPN
ijassa-1408	144	23	,	,	PUNCT
ijassa-1408	144	24	doi	doi	NOUN
ijassa-1408	144	25	:	:	PUNCT
ijassa-1408	144	26	https://doi.org/10.4213/sm9119	https://doi.org/10.4213/sm9119	NOUN
ijassa-1408	144	27	.	.	PUNCT
ijassa-1408	145	1	5	5	X
ijassa-1408	145	2	.	.	X
ijassa-1408	145	3	arutyunov	arutyunov	PROPN
ijassa-1408	145	4	,	,	PUNCT
ijassa-1408	145	5	a.	a.	NOUN
ijassa-1408	145	6	a.	a.	NOUN
ijassa-1408	145	7	(	(	PUNCT
ijassa-1408	145	8	2020	2020	NUM
ijassa-1408	145	9	)	)	PUNCT
ijassa-1408	145	10	.	.	PUNCT
ijassa-1408	146	1	derivation	derivation	NOUN
ijassa-1408	146	2	algebra	algebra	PROPN
ijassa-1408	146	3	in	in	ADP
ijassa-1408	146	4	noncommutative	noncommutative	ADJ
ijassa-1408	146	5	group	group	PROPN
ijassa-1408	146	6	algebras	algebra	NOUN
ijassa-1408	146	7	,	,	PUNCT
ijassa-1408	146	8	proc	proc	PROPN
ijassa-1408	146	9	.	.	PUNCT
ijassa-1408	147	1	steklov	steklov	PROPN
ijassa-1408	147	2	inst	inst	PROPN
ijassa-1408	147	3	.	.	PUNCT
ijassa-1408	148	1	math	math	NOUN
ijassa-1408	148	2	.	.	PUNCT
ijassa-1408	149	1	,	,	PUNCT
ijassa-1408	149	2	308	308	NUM
ijassa-1408	149	3	,	,	PUNCT
ijassa-1408	149	4	22–34	22–34	NUM
ijassa-1408	149	5	,	,	PUNCT
ijassa-1408	149	6	doi	doi	NOUN
ijassa-1408	149	7	:	:	PUNCT
ijassa-1408	149	8	https://doi.org/10.1134/s0081543820010022	https://doi.org/10.1134/s0081543820010022	NUM
ijassa-1408	149	9	6	6	NUM
ijassa-1408	149	10	.	.	PUNCT
ijassa-1408	150	1	arutyunov	arutyunov	PROPN
ijassa-1408	150	2	,	,	PUNCT
ijassa-1408	150	3	a.	a.	NOUN
ijassa-1408	150	4	a.	a.	PROPN
ijassa-1408	150	5	,	,	PUNCT
ijassa-1408	150	6	&	&	CCONJ
ijassa-1408	150	7	alekseev	alekseev	PROPN
ijassa-1408	150	8	,	,	PUNCT
ijassa-1408	150	9	a.	a.	NOUN
ijassa-1408	150	10	v.	v.	PROPN
ijassa-1408	150	11	(	(	PUNCT
ijassa-1408	150	12	2019	2019	NUM
ijassa-1408	150	13	)	)	PUNCT
ijassa-1408	150	14	.	.	PUNCT
ijassa-1408	151	1	cohomology	cohomology	NOUN
ijassa-1408	151	2	of	of	ADP
ijassa-1408	151	3	n	n	CCONJ
ijassa-1408	151	4	-	-	PUNCT
ijassa-1408	151	5	categories	category	NOUN
ijassa-1408	151	6	and	and	CCONJ
ijassa-1408	151	7	derivations	derivation	NOUN
ijassa-1408	151	8	in	in	ADP
ijassa-1408	151	9	group	group	NOUN
ijassa-1408	151	10	algebras	algebra	NOUN
ijassa-1408	151	11	,	,	PUNCT
ijassa-1408	151	12	topology	topology	NOUN
ijassa-1408	151	13	and	and	CCONJ
ijassa-1408	151	14	its	its	PRON
ijassa-1408	151	15	applications	application	NOUN
ijassa-1408	151	16	,	,	PUNCT
ijassa-1408	151	17	275	275	NUM
ijassa-1408	151	18	,	,	PUNCT
ijassa-1408	151	19	107002	107002	NUM
ijassa-1408	151	20	doi	doi	NOUN
ijassa-1408	151	21	:	:	PUNCT
ijassa-1408	151	22	https://doi.org/10.1016/j.topol.2019.107002	https://doi.org/10.1016/j.topol.2019.107002	NOUN
ijassa-1408	151	23	.	.	PUNCT
ijassa-1408	152	1	7	7	X
ijassa-1408	152	2	.	.	X
ijassa-1408	152	3	arutyunov	arutyunov	PROPN
ijassa-1408	152	4	,	,	PUNCT
ijassa-1408	152	5	a.	a.	NOUN
ijassa-1408	152	6	a.	a.	PROPN
ijassa-1408	152	7	,	,	PUNCT
ijassa-1408	152	8	&	&	CCONJ
ijassa-1408	152	9	naianzin	naianzin	ADV
ijassa-1408	152	10	,	,	PUNCT
ijassa-1408	152	11	a.	a.	NOUN
ijassa-1408	152	12	v.	v.	PROPN
ijassa-1408	152	13	(	(	PUNCT
ijassa-1408	152	14	2022	2022	NUM
ijassa-1408	152	15	)	)	PUNCT
ijassa-1408	152	16	.	.	PUNCT
ijassa-1408	153	1	nontrivial	nontrivial	ADJ
ijassa-1408	153	2	outer	outer	ADJ
ijassa-1408	153	3	derivations	derivation	NOUN
ijassa-1408	153	4	in	in	ADP
ijassa-1408	153	5	bimodules	bimodule	NOUN
ijassa-1408	153	6	over	over	ADP
ijassa-1408	153	7	group	group	NOUN
ijassa-1408	153	8	rings	ring	NOUN
ijassa-1408	153	9	,	,	PUNCT
ijassa-1408	153	10	eurasian	eurasian	ADJ
ijassa-1408	153	11	mathemeatical	mathemeatical	ADJ
ijassa-1408	153	12	journal	journal	NOUN
ijassa-1408	153	13	,	,	PUNCT
ijassa-1408	153	14	13(4	13(4	NUM
ijassa-1408	153	15	)	)	PUNCT
ijassa-1408	153	16	,	,	PUNCT
ijassa-1408	153	17	8–17	8–17	PROPN
ijassa-1408	153	18	,	,	PUNCT
ijassa-1408	153	19	doi	doi	NOUN
ijassa-1408	153	20	:	:	PUNCT
ijassa-1408	153	21	https://doi.org/10.32523/2077-9879-2022-13-4-08-17	https://doi.org/10.32523/2077-9879-2022-13-4-08-17	NOUN
ijassa-1408	153	22	.	.	PUNCT
ijassa-1408	154	1	8	8	X
ijassa-1408	154	2	.	.	X
ijassa-1408	154	3	johnson	johnson	PROPN
ijassa-1408	154	4	,	,	PUNCT
ijassa-1408	154	5	b.	b.	PROPN
ijassa-1408	154	6	e.	e.	PROPN
ijassa-1408	154	7	,	,	PUNCT
ijassa-1408	154	8	&	&	CCONJ
ijassa-1408	154	9	ringrose	ringrose	PROPN
ijassa-1408	154	10	,	,	PUNCT
ijassa-1408	154	11	j.	j.	PROPN
ijassa-1408	154	12	r.	r.	PROPN
ijassa-1408	154	13	(	(	PUNCT
ijassa-1408	154	14	1969	1969	NUM
ijassa-1408	154	15	)	)	PUNCT
ijassa-1408	154	16	.	.	PUNCT
ijassa-1408	155	1	derivations	derivation	NOUN
ijassa-1408	155	2	of	of	ADP
ijassa-1408	155	3	operator	operator	NOUN
ijassa-1408	155	4	algebras	algebra	NOUN
ijassa-1408	155	5	and	and	CCONJ
ijassa-1408	155	6	discrete	discrete	ADJ
ijassa-1408	155	7	group	group	NOUN
ijassa-1408	155	8	algebras	algebra	NOUN
ijassa-1408	155	9	,	,	PUNCT
ijassa-1408	155	10	bull	bull	PROPN
ijassa-1408	155	11	.	.	PUNCT
ijassa-1408	156	1	london	london	PROPN
ijassa-1408	156	2	math	math	PROPN
ijassa-1408	156	3	.	.	PUNCT
ijassa-1408	157	1	soc	soc	PROPN
ijassa-1408	157	2	.	.	PUNCT
ijassa-1408	157	3	,	,	PUNCT
ijassa-1408	157	4	1	1	NUM
ijassa-1408	157	5	,	,	PUNCT
ijassa-1408	157	6	70–74	70–74	NUM
ijassa-1408	157	7	.	.	NOUN
ijassa-1408	157	8	9	9	NUM
ijassa-1408	157	9	.	.	X
ijassa-1408	157	10	alekseev	alekseev	PROPN
ijassa-1408	157	11	,	,	PUNCT
ijassa-1408	157	12	a.	a.	NOUN
ijassa-1408	157	13	,	,	PUNCT
ijassa-1408	157	14	arutyunov	arutyunov	PROPN
ijassa-1408	157	15	,	,	PUNCT
ijassa-1408	157	16	a.	a.	NOUN
ijassa-1408	157	17	,	,	PUNCT
ijassa-1408	157	18	&	&	CCONJ
ijassa-1408	157	19	silvestrov	silvestrov	PROPN
ijassa-1408	157	20	,	,	PUNCT
ijassa-1408	157	21	s.	s.	PROPN
ijassa-1408	157	22	(	(	PUNCT
ijassa-1408	157	23	2020	2020	NUM
ijassa-1408	157	24	)	)	PUNCT
ijassa-1408	157	25	.	.	PUNCT
ijassa-1408	158	1	on	on	ADP
ijassa-1408	158	2	(	(	PUNCT
ijassa-1408	158	3	σ	σ	NOUN
ijassa-1408	158	4	,	,	PUNCT
ijassa-1408	158	5	τ)-derivations	τ)-derivation	NOUN
ijassa-1408	158	6	of	of	ADP
ijassa-1408	158	7	group	group	NOUN
ijassa-1408	158	8	algebra	algebra	NOUN
ijassa-1408	158	9	as	as	ADP
ijassa-1408	158	10	category	category	NOUN
ijassa-1408	158	11	characters	character	NOUN
ijassa-1408	158	12	.	.	PUNCT
ijassa-1408	159	1	arxiv	arxiv	NOUN
ijassa-1408	159	2	:	:	PUNCT
ijassa-1408	159	3	2008.00390	2008.00390	NUM
ijassa-1408	159	4	,	,	PUNCT
ijassa-1408	159	5	[	[	X
ijassa-1408	159	6	online	online	X
ijassa-1408	159	7	]	]	X
ijassa-1408	159	8	.	.	PUNCT
ijassa-1408	160	1	available	available	ADJ
ijassa-1408	160	2	:	:	PUNCT
ijassa-1408	160	3	https://arxiv.org/abs/2008.00390	https://arxiv.org/abs/2008.00390	ADJ
ijassa-1408	160	4	10	10	NUM
ijassa-1408	160	5	.	.	PUNCT
ijassa-1408	160	6	hartwig	hartwig	PROPN
ijassa-1408	160	7	,	,	PUNCT
ijassa-1408	160	8	j.	j.	PROPN
ijassa-1408	160	9	t.	t.	PROPN
ijassa-1408	160	10	,	,	PUNCT
ijassa-1408	160	11	larsson	larsson	PROPN
ijassa-1408	160	12	,	,	PUNCT
ijassa-1408	160	13	d.	d.	PROPN
ijassa-1408	160	14	,	,	PUNCT
ijassa-1408	160	15	&	&	CCONJ
ijassa-1408	160	16	silvestrov	silvestrov	PROPN
ijassa-1408	160	17	,	,	PUNCT
ijassa-1408	160	18	s.	s.	PROPN
ijassa-1408	160	19	d.	d.	PROPN
ijassa-1408	160	20	(	(	PUNCT
ijassa-1408	160	21	2006	2006	NUM
ijassa-1408	160	22	)	)	PUNCT
ijassa-1408	160	23	.	.	PUNCT
ijassa-1408	161	1	deformations	deformation	NOUN
ijassa-1408	161	2	of	of	ADP
ijassa-1408	161	3	lie	lie	NOUN
ijassa-1408	161	4	algebras	algebra	NOUN
ijassa-1408	161	5	using	use	VERB
ijassa-1408	161	6	σ	σ	PROPN
ijassa-1408	161	7	derivations	derivation	NOUN
ijassa-1408	161	8	,	,	PUNCT
ijassa-1408	161	9	j.	j.	PROPN
ijassa-1408	161	10	algebra	algebra	PROPN
ijassa-1408	161	11	,	,	PUNCT
ijassa-1408	161	12	295(2	295(2	NUM
ijassa-1408	161	13	)	)	PUNCT
ijassa-1408	161	14	,	,	PUNCT
ijassa-1408	161	15	314–361	314–361	NUM
ijassa-1408	161	16	.	.	PUNCT
ijassa-1408	161	17	11	11	NUM
ijassa-1408	161	18	.	.	PUNCT
ijassa-1408	161	19	elchinger	elchinger	NOUN
ijassa-1408	161	20	,	,	PUNCT
ijassa-1408	161	21	o.	o.	PROPN
ijassa-1408	161	22	,	,	PUNCT
ijassa-1408	161	23	lundengard	lundengard	PROPN
ijassa-1408	161	24	,	,	PUNCT
ijassa-1408	161	25	k.	k.	PROPN
ijassa-1408	161	26	,	,	PUNCT
ijassa-1408	161	27	makhlouf	makhlouf	PROPN
ijassa-1408	161	28	,	,	PUNCT
ijassa-1408	161	29	a.	a.	PROPN
ijassa-1408	161	30	,	,	PUNCT
ijassa-1408	161	31	&	&	CCONJ
ijassa-1408	161	32	silvestrov	silvestrov	PROPN
ijassa-1408	161	33	,	,	PUNCT
ijassa-1408	161	34	s.	s.	PROPN
ijassa-1408	161	35	d.	d.	PROPN
ijassa-1408	161	36	(	(	PUNCT
ijassa-1408	161	37	2016	2016	NUM
ijassa-1408	161	38	)	)	PUNCT
ijassa-1408	161	39	.	.	PUNCT
ijassa-1408	162	1	brackets	bracket	NOUN
ijassa-1408	162	2	with	with	ADP
ijassa-1408	162	3	(	(	PUNCT
ijassa-1408	162	4	τ	τ	PROPN
ijassa-1408	162	5	,	,	PUNCT
ijassa-1408	162	6	σ)-derivations	σ)-derivation	NOUN
ijassa-1408	162	7	and	and	CCONJ
ijassa-1408	162	8	(	(	PUNCT
ijassa-1408	162	9	p	p	NOUN
ijassa-1408	162	10	,	,	PUNCT
ijassa-1408	162	11	q)-deformations	q)-deformation	NOUN
ijassa-1408	162	12	of	of	ADP
ijassa-1408	162	13	witt	witt	PROPN
ijassa-1408	162	14	and	and	CCONJ
ijassa-1408	162	15	virasoro	virasoro	PROPN
ijassa-1408	162	16	algebras	algebras	PROPN
ijassa-1408	162	17	,	,	PUNCT
ijassa-1408	162	18	forum	forum	PROPN
ijassa-1408	162	19	math	math	PROPN
ijassa-1408	162	20	.	.	PUNCT
ijassa-1408	162	21	,	,	PUNCT
ijassa-1408	162	22	28(4	28(4	NUM
ijassa-1408	162	23	)	)	PUNCT
ijassa-1408	162	24	,	,	PUNCT
ijassa-1408	162	25	657–673	657–673	NUM
ijassa-1408	162	26	.	.	PUNCT
ijassa-1408	163	1	copyright	copyright	NOUN
ijassa-1408	163	2	©	©	PROPN
ijassa-1408	163	3	2023	2023	NUM
ijassa-1408	163	4	assa	assa	NOUN
ijassa-1408	163	5	.	.	PUNCT
ijassa-1408	164	1	adv	adv	PROPN
ijassa-1408	164	2	syst	syst	PROPN
ijassa-1408	164	3	sci	sci	PROPN
ijassa-1408	164	4	appl	appl	PROPN
ijassa-1408	164	5	(	(	PUNCT
ijassa-1408	164	6	2023	2023	NUM
ijassa-1408	164	7	)	)	PUNCT
ijassa-1408	164	8	introduction	introduction	NOUN
ijassa-1408	164	9	preliminaries	preliminary	NOUN
ijassa-1408	164	10	derivations	derivation	NOUN
ijassa-1408	164	11	in	in	ADP
ijassa-1408	164	12	bimodules	bimodule	NOUN
ijassa-1408	164	13	examples	example	NOUN
ijassa-1408	164	14	and	and	CCONJ
ijassa-1408	164	15	applications	application	NOUN