AUSLANDER'S THEOREM FOR PERMUTATION ACTIONS ON NONCOMMUTATIVE ALGEBRAS.

When A = k[x₁, . . . ,x_n] and G is a small subgroup of GL_n(k), Auslander's Theorem says that the skew group algebra A#G is isomorphic to End_A^G(A) as graded algebras. We prove a generalization of Auslander's Theorem for permutation actions on (-1)-skew polynomial rings, (-1)-quantum Weyl algebras, three-dimensional Sklyanin algebras, and a certain homogeneous down-up algebra. We also show that certain fixed rings A^G are graded isolated singularities in the sense of Ueyama. [ABSTRACT FROM AUTHOR]