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Rota-Baxter operators on a sum of fields. (English) Zbl 1472.16044

Summary: We count the number of all Rota-Baxter operators (RB-operators) on a finite direct sum \(A=F\oplus F\oplus\cdots\oplus F\) of fields and count all of them up to conjugation with an automorphism. We also study RB-operators on \(A\) corresponding to a decomposition of \(A\) into a direct vector space sum of two subalgebras. We show that every algebra structure induced on \(A\) by a RB-operator of nonzero weight is isomorphic to \(A\).

MSC:

16W99 Associative rings and algebras with additional structure
05C30 Enumeration in graph theory
17B38 Yang-Baxter equations and Rota-Baxter operators

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References:

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