Poisson orders, symplectic reflection algebras and representation theory

Details Poisson orders, symplectic reflection algebras and representation theory Poisson orders, symplectic reflection algebras and representation theory

2002-01-07

arxiv.org/abs/math/0201042v2

Mathematics

Representation Theory

Theorem 4.2 strengthened; example and reference added

Scientific paper

We introduce a new class of algebras called Poisson orders. This class includes the symplectic reflection algebras of Etingof and Ginzburg, many quantum groups at roots of unity, and enveloping algebras of restricted Lie algebras in positive characteristic. Quite generally, we study this class of algebras from the point of view of Poisson geometry, exhibiting connections between their representation theory and some well-known geometric constructions. As an application, we employ our results in the study of symplectic reflection algebras, completing work of Etingof and Ginzburg on when these algebras are finite over their centres, and providing a framework for the study of their representation theory in the latter case.

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