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