International Journal of Mathematics and Mathematical Sciences 
Volume 2003 (2003), Issue 69, Pages 4325-4345
doi:10.1155/S0161171203212400

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

Abstract

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.