Geodesic
On consecutive factors of the lower central series of right-angled Coxeter groups
Matematičeskie zametki, Tome 116 (2024) no. 1, pp. 10-33.

Voir la notice de l'article provenant de la source Math-Net.Ru

We study the lower central series of a right-angled Coxeter group $RC_{\mathcal K}$ and the corresponding associated graded Lie algebra $L(RC_{\mathcal K})$ and describe the basis of the fourth graded component of $L(RC_{\mathcal K})$ for any ${\mathcal K}$.
Keywords: right-angled Coxeter group, associated graded Lie algebra, graph, lower central series. 
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Ya. A. Veryovkin; T. A. Rahmatullaev. On consecutive factors of the lower central series of right-angled Coxeter groups. Matematičeskie zametki, Tome 116 (2024) no. 1, pp. 10-33. http://geodesic.mathdoc.fr/item/MZM_2024_116_1_a1/

[1] G. Duchamp, D. Krob, “The lower central series of the free partially commutative group”, Semigroup Forum, 45:3 (1992), 385–394 | MR

[2] R. D. Wade, “The lower central series of a right-angled Artin group”, Enseign. Math., 61:3–4 (2015), 343–371 | MR

[3] S. Papadima, A. I. Suciu, “Algebraic invariants for right-angled Artin groups”, Math. Ann., 334:3 (2006), 533–555 | DOI | MR

[4] R. R. Struik, “On nilpotent products of cyclic groups”, Canad. J. Math., 12 (1960), 447–462 | DOI | MR

[5] R. R. Struik, “On nilpotent products of cyclic groups. II”, Canad. J. Math., 13 (1961), 557–568 | DOI | MR

[6] Ya. A. Verevkin, “Prisoedinennaya algebra Li pryamougolnoi gruppy Kokstera”, Algebraicheskaya topologiya, kombinatorika i matematicheskaya fizika, Trudy MIAN, 305, MIAN, M., 2019, 61–70 | DOI | MR

[7] Ya. A. Verevkin, “Graduirovannye komponenty prisoedinennoi algebry Li pryamougolnoi gruppy Kokstera”, Toricheskaya topologiya, deistviya grupp, geometriya i kombinatorika. Chast 2, Trudy MIAN, 318, MIAN, M., 2022, 31–42 | DOI | MR

[8] H. V. Waldinger, “The lower central series of groups of a special class”, J. Algebra, 14:2 (1970), 229–244 | MR

[9] V. M. Bukhshtaber, T. E. Panov, “Deistviya torov, kombinatornaya topologiya i gomologicheskaya algebra”, UMN, 55:5 (335) (2000), 3–106 | DOI | MR | Zbl

[10] A. Bahri, M. Bendersky, F. R. Cohen, S. Gitler, “The polyhedral product functor: a method of decomposition for moment-angle complexes, arrangements and related spaces”, Adv. Math., 225:3 (2010), 1634–1668 | DOI | MR

[11] V. Buchstaber, T. Panov, Toric Topology, Math. Surveys Monogr., 204, Amer. Math. Soc., Providence, RI, 2015 | MR

[12] T. E. Panov, Ya. A. Verevkin, “Poliedralnye proizvedeniya i kommutanty pryamougolnykh grupp Artina i Koksetera”, Matem. sb., 207:11 (2016), 105–126 | DOI | MR

[13] V. Magnus, A. Karras, D. Soliter, Kombinatornaya teoriya grupp. Predstavlenie grupp v terminakh obrazuyuschikh i opredelyayuschikh sootnoshenii, Nauka, M., 1974 | MR

[14] N. Burbaki, Algebry i gruppy Li, Mir, M., 1976 | MR