Complex Quantum Groups and Their Dual Hopf Algebras

  • Bernhard Drabant
  • Michael Schlieker
  • Wolfgang Weich
  • Bruno Zumino
Part of the Mathematical Physics Studies book series (MPST, volume 13)


We construct complexified versions of the quantum groups associated with the Lie algebras of type A n-1. B n, C n and D n. Following the ideas of Faddeev, Reshetikhin and Takhtajan we obtain the Hopf algebras of regular functionals U R on these complexified quantum groups. In the special example A 1 we derive the q-deformed enveloping algebra U q(sl(2, )). In the limit q → 1 the undeformed U(sl(2, )) is recovered.


Hopf Algebra Quantum Group Complexify Version Algebra Relation Algebra Homomorphism 
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Copyright information

© Springer Science+Business Media Dordrecht 1992

Authors and Affiliations

  • Bernhard Drabant
    • 1
  • Michael Schlieker
    • 2
  • Wolfgang Weich
    • 2
  • Bruno Zumino
    • 3
  1. 1.Max-Planck-Institut für PhysikWerner-Heisenberg-InstitutMünchenGermany
  2. 2.Sektion Physik der Universität MünchenGermany
  3. 3.Department of PhysicsUniversity of CaliforniaBerkeleyUSA

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