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

Convolution 

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References

  1. [Ho]
    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
  3. [Kar]
    G. Karpilowsky, Group Representations, Volume 2, North-Holland, Amsterdam, London, New York, Tokyo, 1993Google Scholar
  4. [M]
    Mitja Mastnak, On Hopf Algebra Extensions, MSc. Thesis 1999Google Scholar
  5. [M1]
    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
  8. [Mo]
    Susan Montgomery, Hopf algebras and Their Actions on Rings, CBMS Regional Conference Series in Math., Vol 82, Amer. Math. Soc., Providence, RI, 1993Google Scholar
  9. [S]
    Moss Eisenberg Sweedler, Hopf Algebras, Benjamin, New York, 1969Google Scholar
  10. [Ta]
    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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