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

Bo Hou; Jin Gao

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arXiv · 2203.02306

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

Bo Hou·Jin Gao

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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.

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BibTeX RIS

Bo Hou, Jin Gao. 2022-03-04. Batalin-Vilkovisky structure on Hochschild cohomology of zigzag algebra of type $\widetilde{\mathbf{A}}_{1}$. https://arxiv.org/abs/2203.02306

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