Rota-Baxter operators of weight zero on upper-triangular matrices of order three

2024/03/30 by Vsevolod Gubarev, Gubarev, Vsevolod
Computer Science · Mathematics · #Advanced Topics in Algebra #FOS: Mathematics #Holomorphic and Operator Theory #Matrix Theory and Algorithms #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2404.00289

openalex publication_date 2024/03/30 · 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 algebra U₃(F) of upper-triangular matrices of order three over a field of characteristic 0. For this, we apply the following three ingredients: properties of R(1), conjugation with suitable (anti)automorphisms of U₃(F), and computation with the help of Singular of the Gröbner basis for the system of the equations arisen on the coefficients of R.

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