Advertisement

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)

Abstract

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.

Keywords

Hopf Algebra Quantum Group Complexify Version Algebra Relation Algebra Homomorphism 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [Abe]
    E. Abe, Hopf Algebras, Cambridge Tracts in Mathematics, vol. 74, Cambridge Univ. Press (1980).Google Scholar
  2. [CSSW]
    U. Carow-Watamura, M. Schlieker, M. Scholl and S. Watamura, Z. Phys. C48, 159 (1990). U. Carow-Watamura, M. Schlieker, M. Scholl und S. Watamura, Int. J. Mod. Phys. A, Vol. 6, No. 17,3081 (1991).MathSciNetGoogle Scholar
  3. [CSWW]
    U. Carow-Watamura, M. Schlieker, S. Watamura and W. Weich, preprint KATHEP-1990–26 (1990), to appear in Comm. Math. Phys.. Google Scholar
  4. [CW]
    U. Carow-Watamura and S. Watamura, Tohku preprint (1991).Google Scholar
  5. [Dri]
    V.G. Drinfel’d, Proceedings of the International Congress of Mathematicians, Berkeley, California, USA, 798 (1986).Google Scholar
  6. [DSWZ]
    B. Drabant, M. Schlieker, W. Weich and B. Zumino, in preparation.Google Scholar
  7. [FRT]
    L.D. Faddeev, N. Yu. Reshetikhin and L.A. Takhtajan, Algebra and Analysis 1, 178 (1987).MathSciNetGoogle Scholar
  8. [Jur]
    B. Jurco, Lett. Math. Phys. 22, 177 (1991).MathSciNetADSzbMATHCrossRefGoogle Scholar
  9. [LNRT]
    J. Lukierski, A. Nowicki, H. Ruegg, V. N. Tolstoy, Geneva preprints VGVA-DPT 1991/02–710, VGVA-DPT 1991/08–740 to appear in Phys. Lett. B (1991).Google Scholar
  10. [Ogi]
    O. Ogievetsky, private communication.Google Scholar
  11. [OSWZ]
    O. Ogievetsky, W.B. Schmidke, J. Wess and B. Zumino, MPI-Ph/91–51 (1991).Google Scholar
  12. [Pod]
    P. Podleś, preprint RIMS 754 (1991).Google Scholar
  13. [PW]
    P. Podleś and S.L. Woronowicz, Comm. Math. Phys. 130, 381 (1990).MathSciNetADSzbMATHCrossRefGoogle Scholar
  14. [SWZ]
    W.B. Schmidke, J. Wess and B. Zumino, preprint MPI-Ph/91–15 (1991).Google Scholar
  15. [Wor]
    S.L. Woronowicz, Comm. Math. Phys. 122, 125 (1989).MathSciNetADSzbMATHCrossRefGoogle Scholar

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

Personalised recommendations