Gerstenhaber brackets on Hochschild cohomology of quantum symmetric algebras and their group extensions Academic Article uri icon

abstract

  • 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.

published proceedings

  • Pacific Journal of Mathematics

altmetric score

  • 0.25

author list (cited authors)

  • Witherspoon, S., & Zhou, G.

citation count

  • 2

complete list of authors

  • Witherspoon, Sarah||Zhou, Guodong

publication date

  • January 2016