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arXiv · 1811.08219

Rota-Baxter operators on a sum of fields

Vsevolod Gubarev
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Abstract

We count the number of all Rota-Baxter operators on a finite direct sum $A = F\oplus F\oplus \ldots \oplus F$ 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 $A$.

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Vsevolod Gubarev. 2018-11-20. Rota-Baxter operators on a sum of fields. https://doi.org/10.1142/s0219498820501182

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