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

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.

Growth of generalized Weyl algebras over polynomial algebras and Laurent polynomial algebras

“…GWAs were introduced by Bavula [7] in early 1990s. Since then their structures and representations have been studied intensively, for example, their dimension and growth [8,10,9,55]; their derivations, isomorphisms and automorphisms [6,47,1,21,25]; and their homological and geometric properties [16,51,36,19,37,30].…”