Morphisms of Relative Hopf Modules, Smash Products, and Duality

Abstract

The aim of this paper is to extend a result of H.-J. Schneider on endomorphism rings of relative Hopf modules [17, Theorem 3.2] to the case of projective Hopf algebras with bijective antipode, and to show the connection between this extension and several duality theorems for Hopf algebras. A consequence of this generalization is the following: if H is a co-Frobenius Hopf algebra over the field k, A/B is a Hopf-Galois extension and M is a right (A,H)-Hopf module, then, considering the usual ring embeddings