The Batalin-Vilkovisky algebra on Hochschild cohomology induced by infinity inner products. (Q999684)

Let \(A\) be an associative algebra; then its Hochschild cohomology \(H^*(A,A)\) has a Gerstenhaber structure [\textit{M. Gerstenhaber}, Ann. Math. (2) 78, 267-288 (1963; Zbl 0131.27302)]. In this paper the author shows that this Gerstenhaber structure on \(H^*(A,A)\) comes from a BV-structure if the algebra has a unit and a symmetric, invariant and non-degenerate inner product (the author studies both cases: when the algebra is associative and when it is homotopy associative).