Rota-Baxter operators of weight zero on upper-triangular matrices of order three
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 Gr\"obner basis for the system of the equations arisen on the coefficients of R.
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