论文标题
Batalin-Vilkovisky结构在类型$ \ widetilde {\ Mathbf {a}} _ {1} $的曲折代数的Hochschild同居
Batalin-Vilkovisky structure on Hochschild cohomology of zigzag algebra of type $\widetilde{\mathbf{A}}_{1}$
论文作者
论文摘要
在本文中，我们研究了量子Zigzag代数的Hochschild共同体上的Batalin-Vilkovisky结构。我们首先计算$ a_ {q} $的Hochschild同源群和Hochschild的共同体组的尺寸。基于这些计算，我们确定了$ a_ {q} $的Hochschild共同体戒指，并在Hochschild cology Cromology Ring ring $ a_ {q} $上明确地提供Batalin-Vilkovisky操作员和Gerstenhaber括号。
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.
