A Duality Theorem for Hopf Algebras

Abstract

Let k be a commutative ring. All objects we consider are k objects. Let H be a finite Hopf algebra over k (i.e. is f. g. and projective over k). There is a natural action H*⊗ (R #H) → R #H. In [3] corollary 12.7 S. Montgomery and R. Blatter proved that the natural map (R # H) # H* → End _R(R # H) is an algebra isomorphism. We consider R # H as a right as a right R module via the map R → R # H). We will give a different proof using non-commutative Galois theory.