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ISSN 1088-6850(e) ISSN 0002-9947(p)

Hochschild cohomology and graded Hecke algebras

Author(s): Anne V. Shepler; Sarah Witherspoon
Journal: Trans. Amer. Math. Soc. 360 (2008), 3975-4005.
MSC (2000): Primary 16E40, 16S80
Posted: March 20, 2008
MathSciNet review: 2395161
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Abstract: We develop and collect techniques for determining Hochschild cohomology of skew group algebras $S(V)\char93 G$ 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 to illustrate our ideas. Resulting formulas for Hochschild two-cocycles give information about deformations of $S(V)\char93 G$ and, in particular, about graded Hecke algebras. We expand the definition of a graded Hecke algebra to allow a nonfaithful action of on , and we show that there exist nontrivial graded Hecke algebras for , 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.

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