Advertisement

A Rigidity Property for Quantum SU(3) Groups

  • Gabriel Nagy
Part of the Progress in Mathematics book series (PM, volume 172)

Abstract

Quantum groups were introduced by Drinfeld in the mid 80’s (see [4]). Originally these objects were studied in connection with the inverse scattering problem. Later quantum groups became interesting objects in themselves and today make up a distinct field in mathematics.

Keywords

Quantum Group Short Exact Sequence Poisson Structure Maximal Torus Polar Decomposition 
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.

Bibliography

  1. [1]
    B. BlackadarK-theory for operator algebrasSpringer Verlag, 1986MATHCrossRefGoogle Scholar
  2. [2]
    K. BragielThe twisted SU(N) On the C*-algebra C(SU μ (N)Letters. Math. Phys.20(1990), 251–157MathSciNetMATHCrossRefGoogle Scholar
  3. [3]
    J. DixmierC*-algebrasNorth Holland, 1977Google Scholar
  4. [4]
    V. DrinfeldQuantum Croups I.C.M.Berkeley, 1986Google Scholar
  5. [5]
    H.T. KoelinkOn *-representations of the Hopf *-algebra associated with the quantum group U q (N)Compositio Math.77(1991), 199–231MathSciNetMATHGoogle Scholar
  6. [6]
    S. Levendorskii, Ya. SoibelmanAlgebras of functions on compact quantum groups Schubert cells and quantum toriComm Math. Phys.139(1991), 141–170.MathSciNetCrossRefGoogle Scholar
  7. [7]
    G. NagyOn the Haar measure of quantum SU(N) groupsComm Math. Phys.153(1993), 217–228MathSciNetMATHCrossRefGoogle Scholar
  8. [8]
    G. NagyA framework for deformation quantizationPh.D. thesis, University of California, Berkeley, 1992.Google Scholar
  9. [9]
    G. NagyDeformation quantization and K-theorypreprint 1996Google Scholar
  10. [10]
    G. Nagy, A. NicaOn the “quantum disk” and a “non-commutative circle”Algebraic Methods in Operator Theory (R. Curto and P. E. T. Jorgensen eds.), Birkhäuser, 1994, 276–290CrossRefGoogle Scholar
  11. [11]
    M. Pimsner, S. Popa, D. VoiculescuHomogeneous C*-extensions of \(C(X) \otimes K \) I, J.Operator.Theory 1 (1979), 55–108; II, ibid.4(1980), 211–249MathSciNetMATHGoogle Scholar
  12. [12]
    M. A. RieffelQuantization and C*-algebrasC*-algebras 1943–1993: A 50 year celebration (R. Doran ed) Contemp. Math.167(1994), Amer. Math. Soc., Providence RI, 66–97Google Scholar
  13. [13]
    A. J.-L. SheuThe structure of twisted SU(3) groupsPacific J. Math151(1991), 307–315MathSciNetMATHGoogle Scholar
  14. [14]
    A. J.-L. SheuCompact quantum groups and groupoid C*-algebraspreprint 1995Google Scholar
  15. [15]
    Ya. SoibelmanIrreducible representations of the function algebra on the quantum SU(n) and Schubert cellsSoviet. Math. Dokl.40(1990), 34–38MathSciNetMATHGoogle Scholar
  16. [16]
    Ya. SoibelmanThe algebra of functions on a compact quantum group and its representationsLeningrad Math. J.2(1990), 161–178MathSciNetGoogle Scholar
  17. [17]
    L. Vaksman, Ya SoibelmanAlgebra of functions on quantum SU(2)Funkt. Anal. i ego Priloz.22(1988), 1–14MathSciNetMATHCrossRefGoogle Scholar
  18. [18]
    S.L. WoronowiczTwisted SU(2) group. An example of non-commutative differential calculusPubl. RIMS32(1987), 117–181MathSciNetCrossRefGoogle Scholar
  19. [19]
    S.L. WoronowiczCompact matrix pseudogroupsComm. Math. Phys.111(1987), 613–665MathSciNetMATHCrossRefGoogle Scholar
  20. [20]
    S.L. WoronowiczTannaka-Krein duality for compact matrix pseudogroups. Twisted SU(N) groupInvent. Math.93(1988), 35–76MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1999

Authors and Affiliations

  • Gabriel Nagy
    • 1
  1. 1.Department of MathematicsKansas State UniversityManhattanUSA

Personalised recommendations