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.
Acknowledgements
I would like to thank Victor Ginzburg for suggesting the problem and for useful conversations, and the anonymous referee for suggesting many improvements to the text.
Notes
1 See [Citation9, Section 2.5], where the statement is attributed to Dixmier.