Gerstenhaber brackets on Hochschild cohomology of quantum symmetric algebras and their group extensions
arXiv:1405.5465 · doi:10.2140/pjm.2016.283.223
Abstract
We construct chain maps between the bar and Koszul resolutions for a quantum symmetric algebra (skew polynomial ring). This construction uses a recursive technique involving explicit formulae for contracting homotopies. We use these chain maps to compute the Gerstenhaber bracket, obtaining a quantum version of the Schouten-Nijenhuis bracket on a symmetric algebra (polynomial ring). We compute brackets also in some cases for skew group algebras arising as group extensions of quantum symmetric algebras.
22 pages