@article{91f5803fe8a84d66bcbdcf3649642347,
title = "On the Right-Symmetric Algebras with a Unital Matrix Subalgebra",
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 anirreducible module over $ sl_{2}(F) $.",
keywords = "512.57, Koszul–Vinberg algebra, left-symmetric algebra, pre-Lie algebra, right-symmetric algebra, simple algebra",
author = "Pozhidaev, {A. P.} and Shestakov, {I. P.}",
note = "Funding Information: 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). Publisher Copyright: {\textcopyright} 2021, Pleiades Publishing, Ltd. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.",
year = "2021",
month = jan,
doi = "10.1134/S0037446621010158",
language = "English",
volume = "62",
pages = "138--147",
journal = "Siberian Mathematical Journal",
issn = "0037-4466",
publisher = "MAIK NAUKA/INTERPERIODICA/SPRINGER",
number = "1",
}