Semisimple weak Hopf algebras

Academic Article


  • We develop the theory of semisimple weak Hopf algebras and obtain analogues of a number of classical results for ordinary semisimple Hopf algebras. We prove a criterion for semisimplicity and analyze the square of the antipode S^2 of a semisimple weak Hopf algebra A. We explain how the Frobenius-Perron dimensions of irreducible A-modules and eigenvalues of S^2 can be computed using the inclusion matrix associated to A. A trace formula of Larson and Radford is extended to a relation between the global and Frobenius-Perron dimensions of A. Finally, an analogue of the Class Equation of Kac and Zhu is established and properties of $A$-module algebras and their dimensions are studied.
  • Status

    Publication Date

  • May 15, 2004
  • Has Subject Area

    Published In

  • Journal of Algebra  Journal
  • Keywords

  • math.QA
  • math.RA
  • Digital Object Identifier (doi)

    Start Page

  • 639
  • End Page

  • 667
  • Volume

  • 275
  • Issue

  • 2