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  and by Doi-Takeuchi . 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)