Azumaya Extensions and Galois Correspondence

Abstract

For H a finite-dimensional Hopf algebra over a field k, we study H*-Galois Azumaya extensions A, i.e., A is an H-module algebra which is H*-Galois with A/A^H separable and A^H Azumaya. We prove that there is a Galois correspondence between a set of separable subalgebras of A and a set of separable subalgebras of C _A (A^H), thus generalizing the work of Alfaro and Szeto for H a group algebra. We also study Galois bases and Hirata systems.