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Sibirskii Matematicheskii Zhurnal, 2021, Volume 62, Number 1, Pages 173–184
DOI: https://doi.org/10.33048/smzh.2021.62.115 (Mi smj7547) 		 
This article is cited in 6 scientific papers (total in 6 papers)

On the right-symmetric algebras with a unital matrix subalgebra

A. P. Pozhidaevab, I. P. Shestakovca

a Sobolev Institute of Mathematics, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia
c Departamento de Matemática, Universidade de São Paulo, São Paulo, Brasil
Full-text PDF (457 kB) Citations (6) English version article
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DOI: https://doi.org/10.33048/smzh.2021.62.115
Abstract: Under study are the right-symmetric algebras over a field $F$ which possess a “unital” matrix subalgebra $M_n(F)$. We classify all these finite-dimensional right-symmetric algebras $\mathcal{A}=W\oplus M_2(F)$ in the case when $W$ is an irreducible module over $sl_2(F)$.
Keywords: right-symmetric algebra, left-symmetric algebra, simple algebra, Koszul–Vinberg algebra, pre-Lie algebra.
Funding agency Grant number
Fundação de Amparo à Pesquisa do Estado de São Paulo 2018/05372-7
2018/23690-6
National Council for Scientific and Technological Development (CNPq) 304313/2019-0
Ministry of Science and Higher Education of the Russian Federation 0314-2019-0001
A. P. Pozhidaev was supported by the FAPESP (2018/05372–7) and I. P. Shestakov by the FAPESP (2018/23690–6) and CNPq 304313/2019–0. The work was carried out in the framework of the State Task to the Sobolev Institute of Mathematics (Project 0314–2019–0001).
Received: 18.05.2020
Revised: 14.09.2020
Accepted: 09.10.2020
English version:
Siberian Mathematical Journal, 2021, Volume 62, Issue 1, Pages 138–147
DOI: https://doi.org/10.1134/S0037446621010158
Bibliographic databases:
Document Type: Article
UDC: 512.57
MSC: 35R30
Language: Russian
Citation: A. P. Pozhidaev, I. P. Shestakov, “On the right-symmetric algebras with a unital matrix subalgebra”, Sibirsk. Mat. Zh., 62:1 (2021), 173–184; Siberian Math. J., 62:1 (2021), 138–147
Citation in format AMSBIB
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