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This article is cited in 2 scientific papers (total in 2 papers)
The anick complex and the hochschild cohomology of the manturov (2,3)-group
H. Alhusseina, P. S. Kolesnikovb a Novosibirsk State University
b Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
Abstract:
The Manturov $(2,3)$-group $G_3^2$ is the group generated by three elements $a$, $b$, and $c$ with defining relations $a^2=b^2=c^2=(abc)^2=1$. We explicitly calculate the Anick chain complex for $G_3^2$ by algebraic discrete Morse theory and evaluate the Hochschild cohomology groups of the group algebra $\Bbbk G_3^2$ with coefficients in all 1-dimensional bimodules over a field $\Bbbk $ of characteristic zero.
Keywords:
hochschild cohomology, anick resolution, gröbner–Shirshov basis, morse matching.
Received: 26.03.2019 Revised: 09.07.2019 Accepted: 24.07.2019
Citation:
H. Alhussein, P. S. Kolesnikov, “The anick complex and the hochschild cohomology of the manturov (2,3)-group”, Sibirsk. Mat. Zh., 61:1 (2020), 17–28; Siberian Math. J., 61:1 (2020), 11–20
Linking options:
https://www.mathnet.ru/eng/smj5962 https://www.mathnet.ru/eng/smj/v61/i1/p17
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Abstract page: | 186 | Full-text PDF : | 52 | References: | 25 | First page: | 2 |
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