Hopf Algebra Coaction and Its Application to Group-Graded Rings

  • Gui-Long Liu
Conference paper
Part of the Trends in Mathematics book series (TM)

Abstract

Let H be a Hopf algebra, A a right H-comodule algebra and A#H * a right smash product. Chen and Cai[5] give a Morita context connection between A coH and A#H *rat under the assumption that ∫ H* r = ∫ H* l ≠ 0. In this paper we form a Morita context connection between A coH and A#H *rat under the condition ∫ H* l ≠ 0. We apply the results to G-graded algebras and give a Maschke type theorem for G-graded algebras.

Keywords

ACOH 

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References

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    M. E. Sweedler, Hopf Algebras,Benjamin,New York, 1969.Google Scholar
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    C. Cai and H. Chen, Coactions, smash products and Hopf modules, J. Algebra 167 (1994), 85–99.MathSciNetMATHCrossRefGoogle Scholar
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    C. Cai and H. Chen, Hopf algebra coactions, Comm Algebra 22(1) (1994), 253–267.MathSciNetMATHCrossRefGoogle Scholar
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    D. Quinn, Group-graded ring and duality, Trans. Amer. Math. Soc. 292 (1985), 155–167.MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Gui-Long Liu
    • 1
  1. 1.Department of Mathematics and Computer Science BeijingLanguage and Culture UniversityBeijingP. R. China

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