Sugawara Construction and the Q-Deformation of Virasoro Algebra

  • M. Chaichian
  • P. Prešnajder
Part of the Mathematical Physics Studies book series (MPST, volume 13)


The q-deformed Virasoro algebra is obtained using the annihilation and creation operators of the q-deformed infinite Heisenberg algebra, which has the Hopf structure. The generators of the q-deformed Virasoro algebra are expressed as a Sugawara construction in terms of normal ordered binomials in these annihilation and creation operators, and become double-indexed as the reminder of a degeneracy removal. The obtained q-deformed Virasoro algebra with central extension reduces to the standard one in the non-deformed limit.


Central Extension Creation Operator Heisenberg Algebra Virasoro Algebra Virasoro Generator 
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  1. [1]
    M.B. Green, J.H. Schwarz and E. Witten, Superstring theory (Cambridge Univ. Press, 1987).Google Scholar
  2. [2]
    L.D. Fadeev in Les Bouches Lectures 1982 (North Holland, Amsterdam, 1984). P.P. Kulish and E.K. Sklyanin, Lecture Notes in Physics (Springer, Berlin, 1982), Vol. 151. P. Kulish and N. Reshetikin, J.Sov.Math 23 (1983) 2435.Google Scholar
  3. [3]
    W.G. Drinfeld, Sov. Mat. Doklady 32 (1985) 254. Proc. ICM, Berkeley (AcademicPress, New York, 1986), vol. 1, p. 793. M. Jimbo, Lett. Math. Phys. 11 (1986) 247 and Commun. Math. Phys. 102 (1986) 537.Google Scholar
  4. [4]
    M. Chaichian, P. Kulish and J. Lukierski, Phys.Lett B237 (1990) 401.MathSciNetADSGoogle Scholar
  5. [5]
    T. Curtright and C. Zachos, Phys. Lett. B243 (1990) 237.MathSciNetADSGoogle Scholar
  6. [6]
    F.J. Narganes-Quijano, J.Phys. A24 (1991) 593.MathSciNetADSGoogle Scholar
  7. [7]
    A.P. Polychronakos, Phys.Lett. B256 (1991),35.MathSciNetADSGoogle Scholar
  8. [8]
    M. Chaichian, Q. Ellinas and Z. Popowicz, Phys.Lett. B248 (1990) 95.MathSciNetADSGoogle Scholar
  9. [9]
    M. Chaichian, A.P. Isaev, J. Lukierski, Z. Popowicz, Phys.Lett. B248 (1990) 95.ADSGoogle Scholar
  10. [10]
    N. Aizawa and H. Sato, Phys.Lett. B256(1991) 185. H. Sato, Kyoto Ulliv. preprint YITP /K–930, HUPD–9108, May 1991.MathSciNetADSGoogle Scholar
  11. [11]
    A.J. Mcfarlane, J. Phys. A22 (1989) 4581. L.C. Biederharn, J.Phys. A22 (1989), L 873. T. Hayashi, Commun. Math. Phys. 127 (1990 129. M. Chaichian and P. Kulish, Phys. lett B234 (1990) 72.ADSGoogle Scholar
  12. [12]
    E. Abe, Hopf algebras, Cambridge Tracts in Mathematics (Cambridge Univ., Press, 1980).Google Scholar
  13. [13]
    Yu. I. Manin, Commun. Math. Phys. 123 (1989) 163.MathSciNetADSzbMATHCrossRefGoogle Scholar
  14. [14]
    L.D. Fadeev, N.Y. Reshetikin and L.A. Takhtajan, Advanced Series in Mathema-tical Physics (World Scientific, Singapore, 1989), eds. C.N. Yang and M.L. Ge, Vol. 9.Google Scholar
  15. [15]
    M. Chaichian and P. Presnajder, preprint CERN-TH.6225/91,august 1991.Google Scholar
  16. [16]
    E. Celeghini, R. Giachetti, E. Sorace and M. Tarlini, J. Math. Phys. 31 (1991) 1155.MathSciNetADSCrossRefGoogle Scholar
  17. [17]
    D.B. Fairlie, P. Fletcher and C.K. Zachos, Phys. Lett,. B218 (1989) 203MathSciNetADSGoogle Scholar
  18. [18]
    A.N. Kirillov and N. Yu. Reshetikin, LOMI preprint E-9–88, 1988.Google Scholar
  19. [19]
    H. Hiro-Oka, O. Matsui, T. Naito and S. Saito, Tokyo Metropolitan Univ, preprint TMUP-HEL.9004, March 1990. S. Saito in Karpacz 91, XXVII Winter School or Theoretical Physics (World Scientific, 1991).Google Scholar
  20. [20]
    E. Celeghini, R. Giacchetti, P.P. Kulish, E. Sorace and M. Tarlini, preprint Ulliv. Florence, DFF 139/6/91, July 1991.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1992

Authors and Affiliations

  • M. Chaichian
    • 1
  • P. Prešnajder
    • 2
  1. 1.Department of High Energy, PhysicsUniversity of HelsinkiHelsinkiFinland
  2. 2.Department of Theoretical PhysicsComenius UniversityBratislavaCzechoslovakia

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