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Sibirskii Matematicheskii Zhurnal, 2022, Volume 63, Number 2, Pages 391–402
DOI: https://doi.org/10.33048/smzh.2022.63.210 (Mi smj7664) 		 
This article is cited in 2 scientific papers (total in 2 papers)

On nonconstant pre-Lie bimodules over $M_2(F)$

A. P. Pozhidaev

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
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DOI: https://doi.org/10.33048/smzh.2022.63.210
Abstract: We describe the unital finite-dimensional simple nonconstant bimodules $\mathcal{W}$ over the matrix algebra $M_2(F)$ over a field $F$ of characteristic $0$; i.e., the left action of the idempotents of $M_2(F)$ is diagonalizable and $\mathcal{W}$ does not contain constant bichains. Also, we construct an example of a nondiagonal bimodule and a series of constant right-symmetric bimodules over $M_2(F)$.
Keywords: right-symmetric algebra, left-symmetric algebra, irreducible bimodule, simple algebra, pre-Lie algebra.
Funding agency Grant number
Russian Science Foundation 21-11-00286
Research was supported by the Russian Science Foundation (Project no. 21–11–00286).
Received: 10.09.2021
Revised: 10.09.2021
Accepted: 10.12.2021
English version:
Siberian Mathematical Journal, 2022, Volume 63, Issue 2, Pages 326–335
DOI: https://doi.org/10.1134/S0037446622020100
Bibliographic databases:
Document Type: Article
UDC: 512.57
Language: Russian
Citation: A. P. Pozhidaev, “On nonconstant pre-Lie bimodules over $M_2(F)$”, Sibirsk. Mat. Zh., 63:2 (2022), 391–402; Siberian Math. J., 63:2 (2022), 326–335
Citation in format AMSBIB
\Bibitem{Poz22}
\by A.~P.~Pozhidaev
\paper On nonconstant pre-Lie bimodules over $M_2(F)$
\jour Sibirsk. Mat. Zh.
\yr 2022
\vol 63
\issue 2
\pages 391--402
\mathnet{http://mi.mathnet.ru/smj7664}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=4440288}
\transl
\jour Siberian Math. J.
\yr 2022
\vol 63
\issue 2
\pages 326--335
\crossref{https://doi.org/10.1134/S0037446622020100}
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