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

TL;DR

This paper classifies all nonzero weight Rota-Baxter operators on 3x3 matrix algebras over an algebraically closed field, focusing on those not derived from algebra decompositions.

Contribution

It provides a complete classification of such operators, highlighting those not resulting from algebra decompositions, which was previously uncharacterized.

Findings

Complete list of Rota-Baxter operators of nonzero weight on 3x3 matrices

Identification of operators not arising from algebra decompositions

Advancement in understanding Rota-Baxter structures on matrix algebras

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 are not arisen from the decompositions of the entire algebra into a direct vector space sum of two subalgebras.