Symplectic reflection algebras in positive characteristic as Ore extensions

Abstract

We investigate PBW deformations of where G is the cyclic group of order p and the ground field k has characteristic p. The algebras are a version of symplectic reflection algebras that only exist in positive characteristic. They also admit a presentation as Ore extensions over and the combinatorics of the derivation used in this presentation is related to André and Eulerian polynomials. We find the center of and classify the simple modules. We also study a version of in which G is replaced by an elementary abelian p-group Gr.