Singular Hochschild Cohomology and Gerstenhaber Algebra Structure

Abstract

In this paper, we define the singular Hochschild cohomology groups $H{H}_{sg}^i(A,A)$ of an associative $k$-algebra $A$ as morphisms from $A$ to $A[i]$ in the singular category $D_{sg}(A{\otimes }_k{A}^{op})$ for $i\in \mathbb{Z}$. We prove that $H{H}_{sg}^{\ast }(A,A)$ has a Gerstenhaber algebra structure and in the case of a symmetric algebra $A$, $H{H}_{sg}^{\ast }(A,A)$ is a Batalin-Vilkovisky (BV) algebra.

Preliminary version, comments welcome

References in corpus (1)

• Gerstenhaber-Batalin-Vilkoviski structures on coisotropic intersections

Cited by in corpus (3)

• Singular Hochschild cohomology and algebraic string operations
• Invariance of the Gerstenhaber algebra structure on Tate-Hochschild cohomology
• Tate-Hochschild Cohomology of Radical Square Zero Algebras