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On Hopf Algebra Extensions Arising from Semi-Direct Products of Groups

  • Mitja Mastnak
Chapter
Part of the Mathematics and Its Applications book series (MAIA, volume 555)

Abstract

Hopf algebra extensions arising from a matched pair of groups were intro­duced by G.I. Kac ([Kac] ). He established an exact sequence (the Kac sequence) that connects group cohomology and Hopf algebra extensions. This was re­cently considered and generalized by other authors (for instance A. Masuoka in [Mal], [Ma2]).

Keywords

Hopf Algebra Cohomology Group Matched Pair Cohomology Class Semidirect Product 
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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    Irmengard Hofstetter, Extensions of Hopf Algebras and Their Cohomological Description, Journal of Algebra 164 (1994), 264–298MathSciNetMATHGoogle Scholar
  2. [Kac]
    G. I. Kac, Extensions of Groups to Ring Groups, Mat. USSR Sbornik Vol 5 (1968), 451–474Google Scholar
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    G. Karpilowsky, Group Representations, Volume 2, North-Holland, Amsterdam, London, New York, Tokyo, 1993Google Scholar
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    Mitja Mastnak, On Hopf Algebra Extensions, MSc. Thesis 1999Google Scholar
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    Mitja Mastnak, Hopf Algebra Extensions Arising From Semi Direct Products of Groups, to appear in the Journal of AlgebraGoogle Scholar
  6. [Ma1]
    Akira Masuoka, Calculations of Some Groups of Hopf Algebra Extensions, Journal of Algebra 191 (1997), 568–588MathSciNetMATHGoogle Scholar
  7. [Ma2]
    Akira Masuoka, Extensions of Hopf Algebras and Lie Bialgebras, Trans. AMS, 352 (2000), 3837–3879MathSciNetMATHGoogle Scholar
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    Susan Montgomery, Hopf algebras and Their Actions on Rings, CBMS Regional Conference Series in Math., Vol 82, Amer. Math. Soc., Providence, RI, 1993Google Scholar
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    Moss Eisenberg Sweedler, Hopf Algebras, Benjamin, New York, 1969Google Scholar
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    Ken-ichi Tahara, On the Second Cohomology Groups of Semidirect Products, Math. Z. 129 (1972), 365–379MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • Mitja Mastnak
    • 1
  1. 1.Department of Mathematics and StatisticsDalhousie UniversityHalifaxCanada

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