Rota–Baxter operators on a sum of fields

Abstract

We count the number of all Rota–Baxter operators (RB-operators) on a finite direct sum [Formula: see text] of fields and count all of them up to conjugation with an automorphism. We also study RB-operators on [Formula: see text] corresponding to a decomposition of [Formula: see text] into a direct vector space sum of two subalgebras. We show that every algebra structure induced on [Formula: see text] by a RB-operator of nonzero weight is isomorphic to [Formula: see text].