Formal deformations and cohomology theory of Rota-Baxter algebras of any weight

Abstract: This paper studies Rota-Baxter algebras of any weight, say, associative algebras endowed with Rota-Baxter operators. We develop a cohomology theory for Rota-Baxter algebras of any weight and justify it by interpreting lower degree cohomology groups as formal deformations and abelian extensions of Rota-Baxter algebras. We make explicit the $L_\infty$-algebra structure over the cochain complex defining cohomology groups and introduce the notion of homotopy Rota-Baxter algebras as Maurer-Cartan elements of this $L_\infty$-algebra.

Mathematics

Audience: researchers in the topic

ICCM 2020