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.

References in corpus (4)

• Twisted relative Rota-Baxter operators on Leibniz algebras and NS-Leibniz algebras
• Homotopy relative Rota-Baxter Lie algebras, triangular $L_{\infty }$-bialgebras and higher derived brackets
• Relative Rota-Baxter systems on Leibniz algebras
• Cohomology theory of averaging algebras, $L_{\infty }$-structures and homotopy averaging algebras

Cited by in corpus (1)

• Cohomology of weighted Rota-Baxter Lie algebras and Rota-Baxter paired operators