  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.
