Batalin-Vilkovisky algebra structures on Hochschild cohomology of generalized Weyl algebras
Batalin-Vilkovisky algebra structures on Hochschild cohomology of generalized Weyl algebras
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DOI：
10.1007/s11464-021-0978-6
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发表时间：
2020-09
期刊：
影响因子：
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通讯作者：
Liyu Liu;Wen Ma
中科院分区：
文献类型：
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作者：
Liyu Liu;Wen Ma
我们致力于计算斜Calabi-Yau广义Weyl代数的Hochschild上同调上的Batalin-Vilkovisky代数结构。我们首先在复合体水平上建立了Van den Bergh二元性。然后，在Solotar等人的结果的基础上，我们将Kosalzig和Krähmer的方法应用于广义Weyl代数的Hochschild同调，并利用Van den Bergh对偶将同调信息转化为上同调信息，得到了所需的Batalin-Vilkovisky代数结构。最后，我们将我们的结果应用于量子加权投影线和Podleś量子球，并完整地描述了它们的代数结构。
We devote to the calculation of Batalin—Vilkovisky algebra structures on the Hochschild cohomology of skew Calabi—Yau generalized Weyl algebras. We first establish a Van den Bergh duality at the level of complex. Then based on the results of Solotar et al., we apply Kowalzig and Krähmer’s method to the Hochschild homology of generalized Weyl algebras, and translate the homological information into cohomological one by virtue of the Van den Bergh duality, obtaining the desired Batalin—Vilkovisky algebra structures. Finally, we apply our results to quantum weighted projective lines and Podleś quantum spheres, and the Batalin—Vilkovisky algebra structures for them are described completely.