The Batalin-Vilkovisky Algebra on Hochschild Cohomology Induced by Infinity Inner Products

## Mathematics

### Journal of Generalized Lie Theory and Applications

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 Hochschild-cohomology of a unital $A ∞$-algebra with a symmetric and non-degenerate $∞$-inner product.