Key points are not available for this paper at this time.
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.
Vsevolod Gubarev (Sat,) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: