On the structure of weak Hopf algebras

Academic Article


  • We study the group of group-like elements of a weak Hopf algebra and derive an analogue of Radford's formula for the fourth power of the antipode S, which implies that the antipode has a finite order modulo a trivial automorphism. We find a sufficient condition in terms of Tr(S^2) for a weak Hopf algebra to be semisimple, discuss relation between semisimplicity and cosemisimplicity, and apply our results to show that a dynamical twisting deformation of a semisimple Hopf algebra is cosemisimple.
  • Status

    Publication Date

  • September 25, 2002
  • Has Subject Area

    Published In


  • math.QA
  • Digital Object Identifier (doi)

    Start Page

  • 257
  • End Page

  • 286
  • Volume

  • 170
  • Issue

  • 2