Rota-Baxter operators on a sum of fields

Abstract

We count the number of all Rota-Baxter operators on a finite direct sum $A=F\oplus F\oplus \dots \oplus F$ of fields and count all of them up to conjugation with an automorphism. We also study Rota-Baxter 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 Rota-Baxter of nonzero weight is isomorphic to $A$.

11 p., 2 figures, 2 tables

References in corpus (2)

• From Rota-Baxter Algebras to Pre-Lie Algebras
• Rota-Baxter Operators on Quadratic Algebras

Cited by in corpus (5)

• Rota-Baxter groups, skew left braces, and the Yang-Baxter equation
• Rota-Baxter operators on groups
• Rota-Baxter operators on Turaev's Hopf group (co)algebras I: Basic definitions and related algebraic structures
• Double Lie algebras of a nonzero weight
• Rota-Baxter operators of nonzero weight on the matrix algebra of order three