Glasgow Mathematical Journal

Table of Contents - 1998 - Volume 40, Issue 02  

Research Article

Cleft extensions for a Hopf algebrakq[X,X−1, Y]

Hui-Xiang Chena1a2

a1 Department of Mathematics, Teacher's College, Yangzhou University, Yangzhou, Jiangsu 225002, China

a2 Institute of Mathematics, Fudan University, Shanguai 200433, China

The concept of cleft extensions, or equivalently of crossed products, for a Hopf algebra is a generalization of Galois extensions with normal basis and of crossed products for a group. The study of these subjects was founded independently by Blattner-Cohen-Montgomery [1] and by Doi-Takeuchi [4]. In this paper, we determine the isomorphic classes of cleft extensions for a infinite dimensional non-commutative, non-cocommutative Hopf algebra kq[X, X–l, Y], which is generated by a group-like element X and a (1,X)-primitive element Y. We also consider the quotient algebras of the cleft extensions.

(Received June 25 1996)

(Revised December 05 1996)