The batalin-vilkovisky algebra on hochschild cohomology induced by infinity inner products

Abstract

We define a BV-structure on the Hochschild cohomology of a unital, associative algebra A with a symmetric, invariant and non-degenerate inner product. The induced Gerstenhaber algebra is the one described in Gerstenhaber's original paper on Hochschild-cohomology. We also prove the corresponding theorem in the homotopy case, namely we define the BV-structure on the Hochschildcohomology of a unital A∞-algebra with a symmetric and non-degenerate ∞-inner product.