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In this paper, we define the singular Hochschild cohomology groups$HH_{sg}^i(A, A)$ 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 $HH_{sg}^*(A, A)$ has a Gerstenhaber algebrastructure and in the case of a symmetric algebra $A$, $HH_{sg}^*(A, A)$ is aBatalin-Vilkovisky (BV) algebra.

Singular Hochschild Cohomology and Gerstenhaber Algebra Structure