带弱内射的Hopf代数结构

Abstract

Abstract:

Constructing a new Hopf algebra with known Hopf algebras is one of the most important problems in studying Hopf algebra. In this paper, the authors derive necessary and sufficient conditions for the smash product algebra A#H to be a Hopf algebra with a Hopf quotient algebra H
and a weak injection from H to A#H. It is easy to find that this structure includes the Radford’s biproduct and Majid’s bicrossed product as special cases.


Key words: Hopf algebra,Crossed product,Smash product, Weak injection

CLC Number:

16W30

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LE Jue, ZHANG Yong. The Structure of Hopf Algebras with a Weak Injection[J].Acta mathematica scientia,Series A, 2005, 25(2): 201-212.

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References

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[2]Schauenburg P.The structure of Hopf algebras with a weak projection. Algebras and Representation Theory,2000, 3: 187-211

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[4]Chen H X.Faithful flatness and coflatness of Hopf algebras. Algebra Colloquium, 1999, 6(4): 369-376

[5]Schauenburg P. A bialgebra that admits a HopfGalois extension is a Hopf algebra. Proceedi ngs of the AmericanMathematical society,1997, 125: 83-85

[6]Montgomery S. Hopf algebras and their actions onrings. CBMS Series in Math, Am Math Soc, Providence, 1993

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The Structure of Hopf Algebras with a Weak Injection

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