Hochschild cohomology and graded Hecke algebras
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- by Anne V. Shepler and Sarah Witherspoon PDF
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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.References
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Additional Information
- Anne V. Shepler
- Affiliation: Department of Mathematics, University of North Texas, Denton, Texas 76203
- Email: ashepler@unt.edu
- Sarah Witherspoon
- Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843
- MR Author ID: 364426
- Email: sjw@math.tamu.edu
- Received by editor(s): January 20, 2006
- Published electronically: March 20, 2008
- Additional Notes: The first author was partially supported by NSF grant #DMS-0402819
The second author was partially supported by NSF grant #DMS-0443476 and the Alexander von Humboldt Foundation - © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 360 (2008), 3975-4005
- MSC (2000): Primary 16E40, 16S80
- DOI: https://doi.org/10.1090/S0002-9947-08-04396-1
- MathSciNet review: 2395161
Dedicated: We dedicate this article to Sergey Yuzvinsky on the occasion of his 70th birthday.