The commutator Hopf Galois extensions

Abstract

Let H be a finite dimentional Hopf algebra over a field k and H∗ the dual Hopf algebra of H. Then a commutator right H∗ -Galois extension B of BH is characterized in terms of the smash product B#H and some relationships between such a B and the Hopf Galois Azumaya or Hopf Galois Hirata extensions are also given.