Batalin--Vilkovisky algebra structures on the Hochschild cohomology of generalized Weyl algebras
From MaRDI portal
Publication:6348977
DOI10.1007/S11464-021-0978-6arXiv2009.05910MaRDI QIDQ6348977
Publication date: 12 September 2020
Abstract: 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 Kr"ahmer'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 Podle's quantum spheres, and the Batalin-Vilkovisky algebra structures for them are described completely.
Noncommutative algebraic geometry (14A22) (Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.) (16E40) Duality in applied homological algebra and category theory (aspects of algebraic topology) (55U30)
This page was built for publication: Batalin--Vilkovisky algebra structures on the Hochschild cohomology of generalized Weyl algebras
Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6348977)
