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In this paper, we study the Batalin-Vilkovisky structure on the Hochschildcohomology of quantum zigzag algebras $A_{q}$ of type$\widetilde{\mathbf{A}}_{1}$. We first calculate the dimensions of Hochschildhomology groups and Hochschild cohomology groups of $A_{q}$. Based on thesecomputations, we determine the Hochschild cohomology ring of $A_{q}$, and givethe Batalin-Vilkovisky operator and the Gerstenhaber bracket on Hochschildcohomology ring of $A_{q}$ explicitly.

Batalin-Vilkovisky structure on Hochschild cohomology of zigzag algebra of type $\widetilde{\mathbf{A}}_{1}$