Algebraic versions of a finite-dimensional quantum groupoid

Academic Article


  • We establish the equivalence of three versions of a finite dimensional quantum groupoid: a generalized Kac algebra introduced by T. Yamanouchi, a weak $C^*$-Hopf algebra introduced by G. Bohm, F. Nill and K. Szlachanyi (with an involutive antipode), and a Kac bimodule -- an algebraic version of a Hopf bimodule, the notion introduced by J.-M. Vallin. We also study the structure and construct examples of finite dimensional quantum groupoids.
  • Authors

  • Nikshych, Dmitri
  • Vainerman, L
  • Status

    Publication Date

  • 2000
  • Keywords

  • 16W30(Primary); 81R50(Secondary)
  • math.OA
  • math.QA
  • Start Page

  • 189
  • End Page

  • 220
  • Volume

  • 209