Deformations and homotopy theory of Rota-Baxter algebras of any weight

Abstract

This paper studies formal deformations and homotopy theory of Rota-Baxter algebras of any weight. We define an $L_{\infty }$-algebra, which controls simultaneous deformations of associative products and Rota-Baxter operators. As a consequence, we develop a cohomology theory of Rota-Baxter algebras of any weight and justify it by interpreting lower degree cohomology groups as formal deformations and abelian extensions. The notion of homotopy Rota-Baxter algebras is introduced and it is shown that the operad governing homotopy Rota-Baxter algebras is a minimal model of the operad of Rota-Baxter algebras.

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Cited by in corpus (2)

• Cohomology of weighted Rota-Baxter Lie algebras and Rota-Baxter paired operators
• Cohomologies of modified $\lambda$-differential Lie triple systems and applications