Communications in Mathematical Physics

, Volume 194, Issue 1, pp 71–86

Classification of Bicovariant Differential Calculi on Quantum Groups (a Representation-Theoretic Approach)

  • Pierre Baumann
  • Frédéric Schmitt

DOI: 10.1007/s002200050349

Cite this article as:
Baumann, P. & Schmitt, F. Comm Math Phys (1998) 194: 71. doi:10.1007/s002200050349

Abstract:

The restricted dual of a quantized enveloping algebra can be viewed as the algebra of functions on a quantum group. According to Woronowicz, there is a general notion of bicovariant differential calculus on such an algebra. We give a classification theorem of these calculi. The proof uses the notion (due to Reshetikhin and Semenov-Tian-Shansky) of a factorizable quasi-triangular Hopf algebra and relies on results of Joseph and Letzter. On the way, we also give a new formula for Rosso's bilinear form.

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Pierre Baumann
    • 1
  • Frédéric Schmitt
    • 1
  1. 1.U.F.R. de Mathématique, Université Louis Pasteur, 7 rue René Descartes, F-67084 Strasbourg Cedex, FranceFR