Rank of quantum groups and braided groups in dual form

  • Shahn Majid
I. Quantum Groups, Deformation Theory And Representation Theory
Part of the Lecture Notes in Mathematics book series (LNM, volume 1510)


We give a dual formulation of recent work on the representation theory of general quantum groups. These form a rigid quasitensor category C to which is associated a braided group Aut(C) of braided-commutative “co-ordinate functions” analogous to the ring of functions on a group or supergroup. Every dual quasitriangular Hopf algebra A gives rise to such a braided group A. We give the example of the braided group BSL(2) in detail. We also give the rank of quantum groups in dual form and explain its connection with the partition function of simple quantum systems.


Partition Function Hopf Algebra Quantum Group Braided Group Monoidal Category 
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Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • Shahn Majid
    • 1
  1. 1.Department of Applied Mathematics & Theoretical Physics University of CambridgeCambridgeU.K.

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