id	sid	eid	entity	type
ap-10605	1	1	acta polytechnica https://doi.org/10.14311/ap.2025.65.0554 acta polytechnica	PERSON
ap-10605	1	2	65(5):554–561	CARDINAL
ap-10605	1	3	2025	DATE
ap-10605	1	4	2025	CARDINAL
ap-10605	2	1	4.0	CARDINAL
ap-10605	2	2	the czech technical university	ORG
ap-10605	2	3	prague	GPE
ap-10605	2	4	severin poštab,∗	ORG
ap-10605	2	5	mykola	PERSON
ap-10605	2	6	ukraine	GPE
ap-10605	2	7	3	CARDINAL
ap-10605	2	8	st.	GPE
ap-10605	2	9	01004	CARDINAL
ap-10605	2	10	kyiv	GPE
ap-10605	2	11	ukraine	GPE
ap-10605	2	12	czech	NORP
ap-10605	2	13	prague	GPE
ap-10605	2	14	13	CARDINAL
ap-10605	2	15	120	CARDINAL
ap-10605	2	16	prague	GPE
ap-10605	2	17	czech	NORP
ap-10605	2	18	3	CARDINAL
ap-10605	2	19	st.	GPE
ap-10605	2	20	03113 kyiv	GPE
ap-10605	2	21	ukraine ∗	ORG
ap-10605	4	1	three	CARDINAL
ap-10605	4	2	algebras	ORG
ap-10605	4	3	three	CARDINAL
ap-10605	6	1	1.	CARDINAL
ap-10605	8	1	1	CARDINAL
ap-10605	8	2	2	CARDINAL
ap-10605	9	1	3	CARDINAL
ap-10605	10	1	algebras	ORG
ap-10605	12	1	algebras	ORG
ap-10605	15	1	first	ORDINAL
ap-10605	15	2	section 2	LAW
ap-10605	15	3	section 3	LAW
ap-10605	16	1	section 4	LAW
ap-10605	17	1	section 5	LAW
ap-10605	17	2	three	CARDINAL
ap-10605	17	3	algebras	ORG
ap-10605	17	4	appendix a. 2	PERSON
ap-10605	22	1	n∑ k=1	PERSON
ap-10605	22	2	∈ r. hereafter	PERSON
ap-10605	22	3	j̃	ORG
ap-10605	22	4	k̃	ORG
ap-10605	22	5	1	CARDINAL
ap-10605	23	1	linear	ORG
ap-10605	23	2	algebras	ORG
ap-10605	24	1	∈	ORG
ap-10605	25	1	⊆	CARDINAL
ap-10605	26	1	4	CARDINAL
ap-10605	29	1	⊂	GPE
ap-10605	30	1	1	CARDINAL
ap-10605	32	1	0	CARDINAL
ap-10605	33	1	554 https://doi.org/10.14311/ap.2025.65.0554 https://creativecommons.org/licenses/by/4.0/ https://www.cvut.cz/en	TIME
ap-10605	34	1	65	CARDINAL
ap-10605	35	1	5/2025	CARDINAL
ap-10605	35	2	first	ORDINAL
ap-10605	36	1	+ ξm(x	PERSON
ap-10605	36	2	∂xm	PERSON
ap-10605	36	3	1	CARDINAL
ap-10605	38	1	xm	ORG
ap-10605	45	1	2	CARDINAL
ap-10605	46	1	φ ∈ aut(g	ORG
ap-10605	46	2	∈	PRODUCT
ap-10605	47	1	φ	PERSON
ap-10605	48	1	3	CARDINAL
ap-10605	49	1	φ ∈ aut(g	ORG
ap-10605	49	2	∈	PRODUCT
ap-10605	50	1	φ	PERSON
ap-10605	52	1	two	CARDINAL
ap-10605	53	1	3	CARDINAL
ap-10605	53	2	two	CARDINAL
ap-10605	53	3	1	CARDINAL
ap-10605	54	1	2	CARDINAL
ap-10605	55	1	second	ORDINAL
ap-10605	55	2	one	CARDINAL
ap-10605	55	3	two	CARDINAL
ap-10605	56	1	second	ORDINAL
ap-10605	56	2	algebras	ORG
ap-10605	58	1	3.1	CARDINAL
ap-10605	59	1	first	ORDINAL
ap-10605	60	1	first	ORDINAL
ap-10605	60	2	4	CARDINAL
ap-10605	60	3	today	DATE
ap-10605	61	1	three	CARDINAL
ap-10605	61	2	1	CARDINAL
ap-10605	61	3	2	CARDINAL
ap-10605	63	1	3	CARDINAL
ap-10605	65	1	first	ORDINAL
ap-10605	65	2	•	CARDINAL
ap-10605	65	3	one	CARDINAL
ap-10605	65	4	∂x1	ORG
ap-10605	67	1	g. inequiva555 m. nesterenko	PERSON
ap-10605	67	2	s. pošta	PERSON
ap-10605	67	3	m. staryi acta polytechnica lence	PERSON
ap-10605	72	1	ξ1m(x	ORG
ap-10605	72	2	ξ22(x	DATE
ap-10605	73	1	ξ2m(x	PERSON
ap-10605	75	1	ξn1(x	PERSON
ap-10605	76	1	4	CARDINAL
ap-10605	77	1	r.	NORP
ap-10605	77	2	0 ≤	CARDINAL
ap-10605	78	1	second	ORDINAL
ap-10605	78	2	g0 ⊂	ORG
ap-10605	79	1	5	CARDINAL
ap-10605	80	1	⊂ g	GPE
ap-10605	87	1	algebras	ORG
ap-10605	88	1	4	CARDINAL
ap-10605	89	1	3.2	CARDINAL
ap-10605	90	1	blattner	PERSON
ap-10605	91	1	5	CARDINAL
ap-10605	91	2	1969	DATE
ap-10605	94	1	third	ORDINAL
ap-10605	95	1	zero	CARDINAL
ap-10605	96	1	only one	CARDINAL
ap-10605	109	1	i=1 li	PERSON
ap-10605	110	1	witt	PERSON
ap-10605	111	1	witt coefficient	PERSON
ap-10605	113	1	3.3	CARDINAL
ap-10605	114	1	shirokov	PERSON
ap-10605	114	2	algebraic	PERSON
ap-10605	115	1	1997	DATE
ap-10605	115	2	i. shirokov	PERSON
ap-10605	115	3	2013	DATE
ap-10605	115	4	6	CARDINAL
ap-10605	116	1	one	CARDINAL
ap-10605	116	2	one	CARDINAL
ap-10605	117	1	second	ORDINAL
ap-10605	117	2	one	CARDINAL
ap-10605	117	3	exp(−xiadei	DATE
ap-10605	119	1	556	CARDINAL
ap-10605	120	1	65	CARDINAL
ap-10605	121	1	5/2025	CARDINAL
ap-10605	121	2	algebras	ORG
ap-10605	121	3	k(x	PERSON
ap-10605	127	1	7	CARDINAL
ap-10605	127	2	d. gromada	PERSON
ap-10605	130	1	appendix	PERSON
ap-10605	130	2	three	CARDINAL
ap-10605	130	3	algebras c(3	ORG
ap-10605	130	4	1	CARDINAL
ap-10605	130	5	0	DATE
ap-10605	130	6	c(2	ORG
ap-10605	130	7	1	CARDINAL
ap-10605	131	1	3.4	CARDINAL
ap-10605	131	2	two	CARDINAL
ap-10605	132	1	linear	ORG
ap-10605	133	1		GPE
ap-10605	134	1	algebras	ORG
ap-10605	137	1	section 4	LAW
ap-10605	138	1	8	CARDINAL
ap-10605	139	1	4	CARDINAL
ap-10605	139	2	2	CARDINAL
ap-10605	139	3	0 1	CARDINAL
ap-10605	140	1	0	CARDINAL
ap-10605	140	2	1	CARDINAL
ap-10605	140	3	1	CARDINAL
ap-10605	142	1	2e	CARDINAL
ap-10605	142	2	2f	CARDINAL
ap-10605	143	1	2	CARDINAL
ap-10605	143	2	−e3	ORG
ap-10605	144	1	2e2	CARDINAL
ap-10605	144	2	3	CARDINAL
ap-10605	147	1	0	CARDINAL
ap-10605	148	1	0 0	DATE
ap-10605	149	1	φ2	GPE
ap-10605	149	2	1 2	CARDINAL
ap-10605	149	3	0	CARDINAL
ap-10605	149	4	0	CARDINAL
ap-10605	152	1	0	CARDINAL
ap-10605	154	1	1)xα−1∂α	CARDINAL
ap-10605	154	2	2	CARDINAL
ap-10605	154	3	1)xα+1∂α	CARDINAL
ap-10605	155	1	1	CARDINAL
ap-10605	157	1	2	CARDINAL
ap-10605	158	1	1 + x2 2)∂1 + 2x1x2∂2	QUANTITY
ap-10605	158	2	3	CARDINAL
ap-10605	159	1	4	CARDINAL
ap-10605	160	1	x1∂1	ORG
ap-10605	160	2	1∂1	CARDINAL
ap-10605	161	1	one	CARDINAL
ap-10605	161	2	4	CARDINAL
ap-10605	162	1	1	CARDINAL
ap-10605	162	2	2	CARDINAL
ap-10605	162	3	3	CARDINAL
ap-10605	164	1	one	CARDINAL
ap-10605	166	1	1	CARDINAL
ap-10605	166	2	3	CARDINAL
ap-10605	168	1	1 x2 1	CARDINAL
ap-10605	168	2	557	CARDINAL
ap-10605	168	3	s. pošta	PERSON
ap-10605	168	4	m. staryi acta polytechnica	PERSON
ap-10605	168	5	2	CARDINAL
ap-10605	168	6	2	CARDINAL
ap-10605	170	1	x̃3	ORG
ap-10605	171	1	1 x1	CARDINAL
ap-10605	172	1	3	CARDINAL
ap-10605	172	2	1	CARDINAL
ap-10605	173	1	three	CARDINAL
ap-10605	174	1	one	CARDINAL
ap-10605	174	2	4	CARDINAL
ap-10605	175	1	1	CARDINAL
ap-10605	179	1	xm	ORG
ap-10605	181	1	+ aαmx̃m)∂x̃α	PERSON
ap-10605	184	1	jacobian	NORP
ap-10605	184	2	zero	CARDINAL
ap-10605	186	1	5	CARDINAL
ap-10605	186	2	algebras	ORG
ap-10605	186	3	three	CARDINAL
ap-10605	186	4	1	CARDINAL
ap-10605	186	5	two	CARDINAL
ap-10605	186	6	0	DATE
ap-10605	186	7	c(2	ORG
ap-10605	186	8	1	CARDINAL
ap-10605	187	1	1	CARDINAL
ap-10605	187	2	0	DATE
ap-10605	187	3	c(2	ORG
ap-10605	187	4	1	CARDINAL
ap-10605	188	1	algebras	ORG
ap-10605	188	2	de sitter algebras	ORG
ap-10605	188	3	fifteen	CARDINAL
ap-10605	188	4	ten	CARDINAL
ap-10605	192	1	15	CARDINAL
ap-10605	192	2	1	CARDINAL
ap-10605	192	3	maxwell	ORG
ap-10605	193	1	lorentz	PERSON
ap-10605	193	2	de sitter	ORG
ap-10605	194	1	ten	CARDINAL
ap-10605	194	2	1	CARDINAL
ap-10605	194	3	2	DATE
ap-10605	194	4	3	DATE
ap-10605	194	5	4	DATE
ap-10605	195	1	nonzero	ORG
ap-10605	195	2	4	CARDINAL
ap-10605	196	1	− gνρpµ	PERSON
ap-10605	196	2	5	CARDINAL
ap-10605	196	3	6	CARDINAL
ap-10605	197	1	2(gµνd	CARDINAL
ap-10605	197	2	7	CARDINAL
ap-10605	197	3	9	CARDINAL
ap-10605	197	4	1	CARDINAL
ap-10605	198	1	10	CARDINAL
ap-10605	200	1	xµ∂ν	GPE
ap-10605	201	1	2xµxν∂ν	CARDINAL
ap-10605	201	2	− x2∂µ	PERSON
ap-10605	201	3	10	CARDINAL
ap-10605	202	1	1 +	CARDINAL
ap-10605	203	1	+ x2 n.	PERSON
ap-10605	203	2	de sitter algebras	ORG
ap-10605	204	1	3	CARDINAL
ap-10605	207	1	3	CARDINAL
ap-10605	208	1	4	CARDINAL
ap-10605	209	1	de sitter spaces	ORG
ap-10605	210	1	de sitter algebras	ORG
ap-10605	210	2	0	DATE
ap-10605	210	3	1	CARDINAL
ap-10605	210	4	c(2	ORG
ap-10605	210	5	1	CARDINAL
ap-10605	210	6	2	CARDINAL
ap-10605	210	7	4)–(9	CARDINAL
ap-10605	210	8	1	CARDINAL
ap-10605	210	9	2	DATE
ap-10605	210	10	3	CARDINAL
ap-10605	210	11	1	CARDINAL
ap-10605	210	12	1	CARDINAL
ap-10605	212	1	one	CARDINAL
ap-10605	214	1	the simons foundation	ORG
ap-10605	214	2	sfi-pd-ukraine-00014586	ORG
ap-10605	214	3	m.n.	GPE
ap-10605	214	4	m.s.	GPE
ap-10605	215	1	1	CARDINAL
ap-10605	215	2	r. l. anderson	PERSON
ap-10605	215	3	s. m. davison	PERSON
ap-10605	216	1	second	ORDINAL
ap-10605	217	1	48(1):301–315, 1974	DATE
ap-10605	218	1	558	CARDINAL
ap-10605	220	1	65	CARDINAL
ap-10605	221	1	5/2025	CARDINAL
ap-10605	221	2	2	CARDINAL
ap-10605	221	3	f. schwarz	PERSON
ap-10605	222	1	second	ORDINAL
ap-10605	223	1	mathematica 60(1):39–113, 2000	ORG
ap-10605	224	1	3	CARDINAL
ap-10605	224	2	h. makaruk	PERSON
ap-10605	226	1	32(3):375–383, 1993.	DATE
ap-10605	228	1	4	CARDINAL
ap-10605	228	2	m. boyko	PERSON
ap-10605	228	3	m. o. nesterenko	PERSON
ap-10605	228	4	m. w. lutfullin	PERSON
ap-10605	229	1	algebras	ORG
ap-10605	230	1	journal of physics	ORG
ap-10605	230	2	2003	DATE
ap-10605	231	1	5	CARDINAL
ap-10605	231	2	r. j. blattner	PERSON
ap-10605	232	1	algebras	ORG
ap-10605	233	1	american	NORP
ap-10605	233	2	1969	DATE
ap-10605	235	1	6	CARDINAL
ap-10605	235	2	a. a. magazev	PERSON
ap-10605	235	3	b. mikheyev	PERSON
ap-10605	235	4	i. v. shirokov	PERSON
ap-10605	236	1	algebras	ORG
ap-10605	236	2	11:66, 2015	DATE
ap-10605	237	1	https://doi.org/10.3842/sigma.2015.066	NORP
ap-10605	237	2	7	CARDINAL
ap-10605	237	3	d. gromada	PERSON
ap-10605	238	1	algebras	ORG
ap-10605	239	1	czech technical university	ORG
ap-10605	239	2	prague	GPE
ap-10605	239	3	2017	CARDINAL
ap-10605	240	1	2025	CARDINAL
ap-10605	241	1	2017	CARDINAL
ap-10605	241	2	8	CARDINAL
ap-10605	241	3	m. havlíček	PERSON
ap-10605	241	4	w. lassner	PERSON
ap-10605	243	1	i.	PERSON
ap-10605	244	1	8(3):391–399, 1975	DATE
ap-10605	245	1	559	CARDINAL
ap-10605	246	1	s. pošta	PERSON
ap-10605	246	2	m. staryi acta polytechnica appendix a.	PERSON
ap-10605	246	3	three	CARDINAL
ap-10605	246	4	1	CARDINAL
ap-10605	246	5	two	CARDINAL
ap-10605	246	6	0	DATE
ap-10605	246	7	c(2	ORG
ap-10605	246	8	1	CARDINAL
ap-10605	248	1	generic	PERSON
ap-10605	248	2	1	CARDINAL
ap-10605	249	1	= ci	PERSON
ap-10605	250	1	1	CARDINAL
ap-10605	253	1	10	CARDINAL
ap-10605	254	1	rgeneric(c(3	ORG
ap-10605	254	2	1	CARDINAL
ap-10605	255	1	∂2	CARDINAL
ap-10605	256	1	j13 = x3∂1	PERSON
ap-10605	260	1	+ 2 s5 ch6 ∂8	QUANTITY
ap-10605	267	1	∂10	GPE
ap-10605	269	1	x2∂3	GPE
ap-10605	274	1	∂9 − s5s6c8	ORG
ap-10605	279	1	∂10	PERSON
ap-10605	279	2	2	CARDINAL
ap-10605	281	1	2	CARDINAL
ap-10605	282	1	2x4c5c6∂7	CARDINAL
ap-10605	284	1	+ 2(c5s6s8	CARDINAL
ap-10605	285	1	2(s5s8	CARDINAL
ap-10605	285	2	2x1x11	CARDINAL
ap-10605	285	3	sh7sh9c5c6	ORG
ap-10605	285	4	2x1x12)∂12 +	DATE
ap-10605	285	5	2x1x13)∂13 +	DATE
ap-10605	287	1	2 + x2 2	QUANTITY
ap-10605	293	1	2(c5c8	DATE
ap-10605	294	1	2x2x11 + ch7s5c6)∂11 +	QUANTITY
ap-10605	295	1	2x2x12	CARDINAL
ap-10605	296	1	+	DATE
ap-10605	296	2	ch10s5s6c8	ORG
ap-10605	297	1	2x2x13	CARDINAL
ap-10605	298	1	sh9ch10(c5c8 + s5s6c8	DATE
ap-10605	299	1	− s5s6c8	ORG
ap-10605	299	2	2x2x14	CARDINAL
ap-10605	305	1	+ 2x3x4∂4	DATE
ap-10605	305	2	2th6(x1s5	CARDINAL
ap-10605	306	1	2(x4t7c6	CARDINAL
ap-10605	314	1	2x3x13	CARDINAL
ap-10605	315	1	2x3x14	CARDINAL
ap-10605	316	1	560	CARDINAL
ap-10605	317	1	65	CARDINAL
ap-10605	318	1	5/2025	CARDINAL
ap-10605	318	2	2x1x4∂1	ORDINAL
ap-10605	319	1	2x2x4∂x2	CARDINAL
ap-10605	325	1	x3c6)∂6	ORG
ap-10605	325	2	2(x2c6s5	CARDINAL
ap-10605	326	1	+ 2	DATE
ap-10605	326	2	x2s5s6c8 − x1s6c5c8	PERSON
ap-10605	329	1	x1s5c8	DATE
ap-10605	330	1	+ 2	DATE
ap-10605	332	1	2x4x11 + sh7)∂11 +	QUANTITY
ap-10605	332	2	2x4x12	CARDINAL
ap-10605	332	3	2x4x13 + ch7ch9sh10)∂13 +	QUANTITY
ap-10605	332	4	2x4x14	CARDINAL
ap-10605	338	1	x12∂12	DATE
ap-10605	342	1	rgeneric(c(3	PRODUCT
ap-10605	342	2	0	DATE
ap-10605	343	1	∂2	CARDINAL
ap-10605	349	1	x2∂3 −	ORG
ap-10605	351	1	c4 ch5	PERSON
ap-10605	352	1	2	CARDINAL
ap-10605	352	2	− x2 3	PERSON
ap-10605	353	1	2x3c4∂5	CARDINAL
ap-10605	353	2	2x3s4	CARDINAL
ap-10605	353	3	c4s5c6	NORP
ap-10605	357	1	+ 2x3s4∂5	TIME
ap-10605	357	2	2x3c4	CARDINAL
ap-10605	358	1	2x8x2)∂8	CARDINAL
ap-10605	360	1	2(x1s4 + x2c4)th5∂4	DATE
ap-10605	360	2	+ 2(x1c4	CARDINAL
ap-10605	360	3	2x9x3)∂9 + 2x3∂10	DATE
ap-10605	367	1	1	CARDINAL
ap-10605	368	1	∂2	CARDINAL
ap-10605	379	1	c4 c5	PERSON
ap-10605	380	1	x3s4t5)∂4	ORG
ap-10605	380	2	2x3c4∂5	CARDINAL
ap-10605	380	3	2x3s4	CARDINAL
ap-10605	380	4	c5	ORG
ap-10605	383	1	∂2	CARDINAL
ap-10605	384	1	2(x3c4t5	CARDINAL
ap-10605	385	1	+ 2x3s4∂5	TIME
ap-10605	385	2	2x3c4	CARDINAL
ap-10605	385	3	2x2x7 + s4ch5)∂7 +	DATE
ap-10605	385	4	2x2x8)∂8	CARDINAL
ap-10605	385	5	2x1x3∂1	CARDINAL
ap-10605	389	1	+ 2(t5(x1s4 +	DATE
ap-10605	390	1	+ 2(x1c4	DATE
ap-10605	392	1	c5	ORG
ap-10605	392	2	2x3x7 + sh5)∂7 +	QUANTITY
ap-10605	392	3	+ 2x3x8)∂8 +	DATE
ap-10605	392	4	2x3∂10	CARDINAL
ap-10605	400	1	561	CARDINAL
ap-10605	400	2	65(5):554–561	CARDINAL
ap-10605	400	3	2025	CARDINAL
ap-10605	400	4	1	CARDINAL
ap-10605	400	5	2	CARDINAL
ap-10605	400	6	3	CARDINAL
ap-10605	400	7	3.1	CARDINAL
ap-10605	400	8	3.2	CARDINAL
ap-10605	400	9	3.3	CARDINAL
ap-10605	400	10	3.4	CARDINAL
ap-10605	400	11	4	CARDINAL
ap-10605	400	12	5	CARDINAL
ap-10605	400	13	algebras	ORG