International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 69, Pages 4325-4345

Twistings, crossed coproducts, and Hopf-Galois coextensions

S. Caenepeel,1 Dingguo Wang,2 and Yanxin Wang3

1Faculty of Applied Sciences, Vrije Universiteit Brussel (VUB), Brussels B-1050, Belgium
2Department of Mathematics, Qufu Normal University, Shandong, Qufu 273165, China
3Department of Mathematics, Tsinghua University, Beijing 100084, China

Received 1 December 2002

Copyright © 2003 S. Caenepeel et al. 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 Hopf algebra. Ju and Cai (2000) introduced the notion of twisting of an H-module coalgebra. In this paper, we study the relationship between twistings, crossed coproducts, and Hopf-Galois coextensions. In particular, we show that a twisting of an H-Galois coextension remains H-Galois if the twisting is invertible.