  We define Drinfeld orbifold algebras as filtered algebras deforming the skew
group algebra (semi-direct product) arising from the action of a finite group
on a polynomial ring. They simultaneously generalize Weyl algebras, graded (or
Drinfeld) Hecke algebras, rational Cherednik algebras, symplectic reflection
algebras, and universal enveloping algebras of Lie algebras with group actions.
We give necessary and sufficient conditions on defining parameters to obtain
Drinfeld orbifold algebras in two general formats, both algebraic and
homological. We explain the connection between Hochschild cohomology and a
Poincare-Birkhoff-Witt property explicitly (using Gerstenhaber brackets). We
also classify those deformations of skew group algebras which arise as Drinfeld
orbifold algebras and give applications for abelian groups.
