On Hopf Galois Hirata extensions

Abstract

Let H be a finite-dimensional Hopf algebra over a field K, H* the dual Hopf algebra of H, and B a right H*-Galois and Hirata separable extension of BH. Then B is characterized in terms of the commutator subring VB(BH) of BH in B and the smash product VB(BH)#H. A sufficient condition is also given for B to be an H*-Galois Azumaya extension of BH.