Clifford Correspondence for Finite Dimensional Hopf Algebras

Abstract

Let B#σH be a crossed product algebra over an algebraically closed field, with H a finite dimensional Hopf algebra. We give an explicit equivalence between the category of finite dimensional B#σH-modules whose restriction to B is a direct sum of copies of a stable irreducible B-module, and the category of modules for a twisted product of H with the field. This describes all finite dimensional irreducible B#σH-modules containing a stable irreducible B-submodule, and thus generalizes the classical stable Clifford correspondence for groups. In case H is cocommutative, we extend this correspondence to the nonstable case.