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1 results

  • 7 - Finite-Dimensional 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 253-304

  • Summary

    We show that for a finite-dimensional quasi-Hopf algebra H the space of integrals in H, and the space of cointegrals on H, have dimension 1. We characterize semisimple and symmetric quasi-Hopf algebras with the help of integrals, and prove a formula for the fourth power of the antipode in terms of the modular elements by using the machinery provided by Frobenius algebras. The chapter ends with a freeness theorem stating that any finite-dimenisonal quasi-Hopf algebra is free over any quasi-Hopf subalgebra.