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...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 Podleśquantum spheres,and the Batalin–Vilkovisky algebra structures for them are described completely.展开更多
基金This work was supported by the National Natural Science Foundation of China(Grant No.11971418).
文摘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 Podleśquantum spheres,and the Batalin–Vilkovisky algebra structures for them are described completely.
