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

Published online by Cambridge University Press:  18 May 2009

Hui-Xiang Chen
Hui-Xiang Chen
Affiliation:
Department of Mathematics, Teacher's College, Yangzhou University, Yangzhou, Jiangsu 225002, China Institute of Mathematics, Fudan University, Shanguai 200433, China
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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.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 40 , Issue 2 , May 1998 , pp. 147 - 160
Copyright
Copyright © Glasgow Mathematical Journal Trust 1998

References

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