Rota-Baxter operators of weight zero on the matrix algebra of order three without unit in kernel

Abstract

We describe all Rota-Baxter operators $R$ of weight zero on the matrix algebra $M_3(F)$ over a quadratically closed field $F$ of characteristic not 2 or 3 such that $R(1)\ne 0$. Thus, we get a partial classification of solutions to the associative Yang-Baxter equation on $M_3(F)$. For the solution, the computer algebra system Singular was involved.

arXiv comment21 p

References in corpus (6)

• Simple finite-dimensional double algebras
• Classification of constant solutions for associative Yang-Baxter equation on $gl(3)$
• Rota-Baxter Operators on Quadratic Algebras
• Spectrum of Rota-Baxter operators
• Nonunital decompositions of the matrix algebra of order three
• Rota-Baxter operators of weight zero on upper-triangular matrices of order three