Quantum differentiation and chain maps of bimodule complexes Academic Article uri icon


  • We consider a finite group acting on a vector space and the corresponding skew group algebra generated by the group and the symmetric algebra of the space. This skew group algebra illuminates the resulting orbifold and serves as a replacement for the ring of invariant polynomials, especially in the eyes of cohomology. One analyzes the Hochschild cohomology of the skew group algebra using isomorphisms which convert between resolutions. We present an explicit chain map from the bar resolution to the Koszul resolution of the symmetric algebra which induces various isomorphisms on Hochschild homology and cohomology, some of which have appeared in the literature before. This approach unifies previous results on homology and cohomology of both the symmetric algebra and skew group algebra. We determine induced combinatorial cochain maps which invoke quantum differentiation (expressed by Demazure-BGG operators). 2011 Mathematical Sciences Publishers.

published proceedings

  • Algebra & Number Theory

author list (cited authors)

  • Shepler, A., & Witherspoon, S.

citation count

  • 10

complete list of authors

  • Shepler, Anne||Witherspoon, Sarah

publication date

  • January 2011