Twisting on associative algebras and Rota-Baxter type operators

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