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Batalin-Vilkovisky structure on Hochschild cohomology of zigzag algebra of type $\widetilde{\mathbf{A}}_{1}$
- Publication Year :
- 2022
-
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.
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2203.02306
- Document Type :
- Working Paper