Hochschild Cohomology and Graded Hecke Algebras

Details Hochschild Cohomology and Graded Hecke Algebras Hochschild Cohomology and Graded Hecke Algebras

2006-03-09

arxiv.org/abs/math/0603231v2

Mathematics

Rings and Algebras

35 pages, minor changes, to appear in Transactions of the American Mathematical Society

Scientific paper

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 constrast 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.

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