International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 64, Pages 4033-4039

On Hopf Galois Hirata extensions

George Szeto and Lianyong Xue

Department of Mathematics, Bradley University, Peoria 61625, IL, USA

Received 17 March 2003

Copyright © 2003 George Szeto and Lianyong Xue. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.