Clifford Correspondence for Finite Dimensional Hopf Algebras
Academic Article
Overview
Identity
Additional Document Info
Other
View All
Overview
abstract
Let B#H 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#H-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#H-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. 1999 Academic Press.