L. I. Murakami, S. V. Pchelintsev, O. V. Shashkov, “Right alternative unital bimodules over the matrix algebras of order <nobr>$\geq 3$</nobr>”, Sibirsk. Mat. Zh., 2022, Volume 63, Number 4,Pages <nobr>893

This article is cited in 2 papers

Right alternative unital bimodules over the matrix algebras of order $\geq 3$

L. I. Murakami^a, S. V. Pchelintsev^b, O. V. Shashkov^b

^a Universidade de São Paulo, Instituto de Matemática e Estatística
^b Financial University under the Government of the Russian Federation, Moscow

Abstract: We address the unital right alternative bimodules over the matrix algebras $\mathrm{M}_n(\Phi)$ of order $n\ge3$, prove that each of these bimodules is the direct sum of an associative bimodule and a Graves bimodule, and fully describe the structure of twisted Graves bimodules. Also, we construct an irreducible right alternative $\mathrm{M}_n(\Phi)$-bimodule of minimal dimension $n(n-1)$. Furthermore, we show that no element $f(x,y)$ of the free right alternative algebra of rank 3 is its nuclear element. The results of this article are needed for the study of the right alternative superalgebras whose even part includes $\mathrm{M}_n(\Phi)$ with $n\ge3$.

Keywords: right alternative algebra, Jordan algebra, right alternative bimodule, Jordan bimodule.

UDC: 512.554.5

MSC: 35R30

Received: 01.11.2021
Revised: 20.05.2022
Accepted: 15.06.2022

DOI: 10.33048/smzh.2022.63.415