Hochschild Cohomology and Graded Hecke AlgebrasReport as inadecuate



 Hochschild Cohomology and Graded Hecke Algebras


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We develop and collect techniques for determining Hochschild cohomology of skew group algebras SV#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 Gr,p,n to illustrate our ideas. Resulting formulas for Hochschild two-cocycles give information about deformations of SV#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 Gr,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.



Author: Anne V. Shepler; Sarah Witherspoon

Source: https://archive.org/







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