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

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Abstract

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.

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Acknowledgements

The authors are very grateful to the anonymous referees for their valuable comments, and to Guodong Zhou for pointing out an inaccuracy in the early version of this article. This work was supported by the National Natural Science Foundation of China (Grant No. 11971418).

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  1. School of Mathematical Sciences, Yangzhou University, Yangzhou, 225002, China

    Liyu Liu & Wen Ma

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  1. Liyu Liu
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  2. Wen Ma
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Correspondence to Liyu Liu.

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Liu, L., Ma, W. Batalin-Vilkovisky algebra structures on Hochschild cohomology of generalized Weyl algebras. Front. Math 17, 915–941 (2022). https://doi.org/10.1007/s11464-021-0978-6

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