Gerstenhaber brackets on Hochschild cohomology of quantum symmetric algebras and their group extensions
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We construct chain maps between the bar andKoszul 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.
author list (cited authors)
Witherspoon, S., & Zhou, G.
complete list of authors
Witherspoon, Sarah||Zhou, Guodong