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arXiv · 2412.00825

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

Vsevolod Gubarev
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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 $R(1)\neq0$. 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.

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Vsevolod Gubarev. 2024-12-01. Rota-Baxter operators of weight zero on the matrix algebra of order three without unit in kernel. https://doi.org/10.1016/j.jalgebra.2025.06.019

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