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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 4 scientific papers (total in 4 papers)

On nonconstant pre-Lie bimodules over M2(F)

A. P. Pozhidaev

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
Full-text PDF (368 kB) Citations (4)
References:
Abstract: We describe the unital finite-dimensional simple nonconstant bimodules W over the matrix algebra M2(F) over a field F of characteristic 0; i.e., the left action of the idempotents of M2(F) is diagonalizable and W does not contain constant bichains. Also, we construct an example of a nondiagonal bimodule and a series of constant right-symmetric bimodules over M2(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 M2(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}
\crossref{https://doi.org/10.33048/smzh.2022.63.210}
\mathscinet{http://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}
Linking options:
  • https://www.mathnet.ru/eng/smj7664
  • https://www.mathnet.ru/eng/smj/v63/i2/p391
  • This publication is cited in the following 4 articles:
    1. A. P. Pozhidaev, “Ob obobschennoi konstruktsii Mitsukhary”, Sib. matem. zhurn., 65:3 (2024), 545–559  mathnet  crossref
    2. A. P. Pozhidaev, “On a Generalized Mizuhara Construction”, Sib Math J, 65:3 (2024), 599  crossref
    3. A. P. Pozhidaev, “O diagonalnykh nekonstantnykh pravosimmetricheskikh algebrakh matrichnogo tipa M2(F)”, Sib. matem. zhurn., 64:4 (2023), 773–785  mathnet  crossref
    4. A. P. Pozhidaev, “On Diagonal Nonconstant Right-Symmetric Algebras of Matrix Type M2(F)”, Sib Math J, 64:4 (2023), 879  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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