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. Caenepeel1
, Dingguo Wang2
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
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.