Twisting on associative algebras and Rota–Baxter type operators

Abstract

We introduce an operation called “twisting” on the Hochschild complex by analogy with Drinfeld’s twisting operations. By using the twisting and derived bracket constructions, we study differential graded Lie algebra structures associated to the bi-graded Hochschild complex. We show that Rota–Baxter type operators are solutions of Maurer–Cartan equations. As an application of twisting, we give a construction of associative Nijenhuis operators.