English

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

Rings and Algebras 2025-08-20 v1

Abstract

We describe all Rota-Baxter operators RR of weight zero on the algebra U3(F)U_3(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)R(1), conjugation with suitable (anti)automorphisms of U3(F)U_3(F), and computation with the help of \texttt{Singular} of the Gr\"{o}bner basis for the system of the equations arisen on the coefficients of RR.

Keywords

Cite

@article{arxiv.2404.00289,
  title  = {Rota-Baxter operators of weight zero on upper-triangular matrices of order three},
  author = {Vsevolod Gubarev},
  journal= {arXiv preprint arXiv:2404.00289},
  year   = {2025}
}

Comments

22 p