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

2024/12/01 by Vsevolod Gubarev, Gubarev, Vsevolod
Computer Science · Mathematics · #16W99 #Advanced Topics in Algebra #FOS: Mathematics #Fixed Point Theorems Analysis #Matrix Theory and Algorithms #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2412.00825

openalex publication_date 2024/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We describe all Rota-Baxter operators R of weight zero on the matrix algebra M₃(F) over a quadratically closed field F of characteristic not 2 or 3 such that R(1)≠0. Thus, we get a partial classification of solutions to the associative Yang-Baxter equation on M₃(F). For the solution, the computer algebra system Singular was involved.

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