REPRESENTATION-THEORY OF HOPF GALOIS EXTENSIONS

Let H be a Hopf algebra over the field k and B subset-of A a right faithfully flat right H-Galois extension. The aim of this paper is to study some questions of representation theory connected with the ring extension B subset-of A, such as induction and restriction of simple or indecomposable modules. In particular, generalizations are given of classical results of Clifford, Green and Blattner on representations of groups and Lie algebras. The stabilizer of a left B-module is introduced as a subcoalgebra of H. Very often the stabilizer is a Hopf subalgebra. The special case when A is a finite dimensional cocommutative Hopf algebra over an algebraically closed field, B is a normal Hopf subalgebra and H is the quotient Hopf algebra was studied before by Voigt using the language of finite group schemes.