On Diagonal Nonconstant Right-Symmetric Algebras of Matrix Type M2(F)

On Diagonal Nonconstant Right-Symmetric Algebras of Matrix Type M2(F) Full article

Journal

Siberian Mathematical Journal
ISSN: 0037-4466 , E-ISSN: 1573-9260

Output data

Year: 2023, Volume: 64, Number: 4, Pages: 879-889 Pages count : 11 DOI: 10.1134/s0037446623040109

Funding (1)

Russian Science Foundation

21-11-00286

We describe the right-symmetric algebras of matrix type M2(F)overafieldF of characteristic 0 such that the left action of the orthogonal idempotents of M2(F) is diagonalizable, and the right-module part W includes no constant bichains. We construct some wide class of nonassociative algebras Eψ,∂(W,A ), where W is a subalgebra and a right module over an associative algebra A. We give a criterion for these algebras to be right-symmetric. Assuming that WA = W, we show that the algebras of this class are either simple or local. We exhibit some examples of simple right-symmetric algebras and right-symmetric algebras without nilpotent right ideals whose right-module part is not an irreducible module over M2(F).

Pozhidaev A.P.
On Diagonal Nonconstant Right-Symmetric Algebras of Matrix Type M2(F)
Siberian Mathematical Journal. 2023. V.64. N4. P.879-889. DOI: 10.1134/s0037446623040109 WOS Scopus РИНЦ OpenAlex

Пожидаев А.П.
О диагональных неконстантных правосимметрических алгебрах матричного типа M2(F)
Сибирский математический журнал. 2023. Т.64. №4. С.773-785. DOI: 10.33048/smzh.2023.64.410 РИНЦ

Accepted:	May 16, 2023
Submitted:	May 28, 2023
Published print:	Jul 24, 2023
Published online:	Jul 24, 2023

Web of science:	WOS:001035552800010
Scopus:	2-s2.0-85165573494
Elibrary:	63273716
OpenAlex:	W4385192316

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