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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

Hopf Algebra Direct Summand Sition Inverse Smash Product Nonzero Idempotent 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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    M. E. Sweedler, Hopf Algebras,Benjamin,New York, 1969.Google Scholar
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    M. Beattie, A generalization of smash product of a graded ring, J. Pure and Applied Algebra 52 (1988), 219–226.MathSciNetMATHCrossRefGoogle Scholar
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    M. Beattie, Strongly inner actions, coactions and duality theorems, Tsu-kuba J. Math. 16 (1992), 279–293.MathSciNetMATHGoogle 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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