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Letters in Mathematical Physics

, Volume 82, Issue 2–3, pp 237–253 | Cite as

On Two Theorems about Symplectic Reflection Algebras

  • Georges PinczonEmail author
Article

Abstract

We give a new proof and an improvement of two Theorems of J. Alev, M.A. Farinati, T. Lambre and A.L. Solotar [1] : the first one about Hochschild cohomology spaces of some twisted bimodules of the Weyl Algebra W, and the second one about Hochschild cohomology spaces of the smash product G * W (G a finite subgroup of SP (2n)) and, as a consequence, we then give a new proof of a Theorem of P. Etingof and V. Ginzburg (Invent Math 147:243–348, 2002), which shows that the Symplectic Reflection Algebras are deformations of G * W (and, in fact, all possible ones).

Mathematics Subject Classification (2000)

16E40 16S80 53D55 81S10 

Keywords

deformations Hochschild cohomology Koszul complex Weyl Algebras Symplectic Reflection Algebras 

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Copyright information

© Springer 2007

Authors and Affiliations

  1. 1.Institut de Mathématiques de BourgogneUniversité de BourgogneDijon CedexFrance

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