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2 results

  • 10 - Quasitriangular Quasi-Hopf Algebras

  • Daniel Bulacu, Universitatea din Bucureşti, Romania, Stefaan Caenepeel, Vrije Universiteit Brussel, Florin Panaite, Freddy Van Oystaeyen, Universiteit Antwerpen, Belgium
  • Book:
    Quasi-Hopf Algebras
    Published online:
    21 February 2019
    Print publication:
    21 February 2019, pp 381-406

  • Summary

    By using categorical tools, we introduce the concept of quasitriangular (QT) quasi-bialgebras. For QT quasi-Hopf algebras we show that the square of the antipode is an inner automorphism, and therefore bijective. We uncover the QT structure of the quantum double D(H) of a finite-dimensional quasi-Hopf algebra H, and characterize D(H) as a biproduct quasi-Hopf algebra in the case when H itself is QT.

  • The Representation Ring of the Twisted Quantum Double of a Finite Group

  • S. J. Witherspoon
  • Journal:
    Canadian Journal of Mathematics / Volume 48 / Issue 6 / 01 December 1996
    Published online by Cambridge University Press:
    20 November 2018, pp. 1324-1338
    Print publication:
    01 December 1996
    • Article
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  • We provide an isomorphism between the Grothendieck ring of modules of the twisted quantum double of a finite group, and a product of centres of twisted group algebras of centralizer subgroups. It follows that this Grothendieck ring is semisimple. Another consequence is a formula for the characters of this ring in terms of representations of twisted group algebras of centralizer subgroups.