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arXiv 2009.059102020-09math.RAmath.KT

Batalin--Vilkovisky algebra structures on the Hochschild cohomology of generalized Weyl algebras

Liyu Liu, Wen Ma

备注：: 22 pages, containing the most part of the second author's master thesis

英文摘要：

This paper is devoted to the calculation of Batalin-Vilkovisky algebra structures on the Hochschild cohomology of skew Calabi-Yau generalized Weyl algebras. We firstly 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.

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