Hochschild cohomology and graded Hecke algebras Academic Article uri icon

abstract

  • We develop and collect techniques for determining Hochschild cohomology of skew group algebras S(V )#G and apply our results to graded Hecke algebras. We discuss the explicit computation of certain types of invariants under centralizer subgroups, focusing on the infinite family of complex reflection groups G(r, p, n) to illustrate our ideas. Resulting formulas for Hochschild two-cocycles give information about deformations of S(V )#G and, in particular, about graded Hecke algebras. We expand the definition of a graded Hecke algebra to allow a nonfaithful action of G on V , and we show that there exist nontrivial graded Hecke algebras for G(r, 1, n), in contrast to the case of the natural reflection representation. We prove that one of these graded Hecke algebras is equivalent to an algebra that has appeared before in a different form. 2008 American Mathematical Society.

published proceedings

  • Transactions of the American Mathematical Society

author list (cited authors)

  • Shepler, A. V., & Witherspoon, S.

citation count

  • 12

complete list of authors

  • Shepler, Anne V||Witherspoon, Sarah

publication date

  • January 2008