Rota–Baxter operators of nonzero weight on the matrix algebra of order three

Abstract

We classify all Rota–Baxter operators of nonzero weight on the matrix algebra of order three over an algebraically closed field of characteristic zero which do not arise from the decompositions of the entire algebra into a direct vector space sum of two subalgebras.

Keywords:

• Rota–Baxter operator
• matrix algebra
• sum of fields

AMS Classification:

• 16W99

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

M. Goncharov was supported by Russian Science Foundation (RSF) (project N 19-11-00039). V. Gubarev was supported by the Program of fundamental scientific researches of the Siberian Branch of Russian Academy of Sciences, I.1.1, project 0314-2019-0001.