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Batalin-Vilkovisky structure on Hochschild cohomology of zigzag algebra of type $\widetilde{\mathbf{A}}_{1}$ (2203.02306v1)
Published 4 Mar 2022 in math.RA, math.KT, and math.RT
Abstract: In this paper, we study the Batalin-Vilkovisky structure on the Hochschild cohomology of quantum zigzag algebras $A_{q}$ of type $\widetilde{\mathbf{A}}{1}$. We first calculate the dimensions of Hochschild homology groups and Hochschild cohomology groups of $A{q}$. Based on these computations, we determine the Hochschild cohomology ring of $A_{q}$, and give the Batalin-Vilkovisky operator and the Gerstenhaber bracket on Hochschild cohomology ring of $A_{q}$ explicitly.