κ-Deformation of (Super)Poincaré Algebra

  • J. Lukierski
Conference paper


The notion of quantum groups and quantum algebras (see e.g. ref. [1]-[6]) can be used in order to study the deformations of space-time symmetries as well as their supersymmetric extensions. In order to obtain the quantum deformation of semisimple Lie algebras describing Minkowski or Euclidean group of motions mostly the contraction techniques have been used. In particular there were obtained:
  1. a)

    quantum deformation of D = 2 and D = 3 Euclidean and Minkowski geometries, described as quantum Lie algebra or quantum Lie group [7], [8]

  2. b)

    quantum deformation of D = 4 Poincaré algebra [9], [10]

  3. c)

    quantum deformations of D = 2 supersymmetry algebra in its Minkowski as well as its Euclidean version [11]–[13].



Quantum Group Quantum Deformation Supersymmetric Extension Supersymmetry Algebra Minkowski Geometry 
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.


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  1. 1.
    Faddeev, L., Reshetikhin, N., Takhtajan, L.: Algebra i Analiz 1, 178 (1989)MathSciNetGoogle Scholar
  2. 2.
    Woronowicz, L.: Comm.Math.Phys. 111, 613 (1987).MathSciNetCrossRefMATHADSGoogle Scholar
  3. 2a.
    Woronowicz, L.: Comm.Math.Phys. 122, 125 (1989)MathSciNetCrossRefMATHADSGoogle Scholar
  4. 3.
    Drinfeld, V.G.: Quantum groups. In: Proceedings of the International Congress of Math. Berkeley, USA (1986). p. 793Google Scholar
  5. 4.
    Jimbo, M.: Lett.Math.Phys. 10, 63 (1985).MathSciNetCrossRefMATHADSGoogle Scholar
  6. 4a.
    Jimbo, M.: Lett.Math.Phys. 11, 247 (1986)MathSciNetCrossRefMATHADSGoogle Scholar
  7. 5.
    Manin, Yu.T.: Quantum groups and non-commutative geometry. Centre de Recherches Math., Univ. de Montreal, 1989Google Scholar
  8. 6.
    Proceedings of First EIMI Workshop on Quantum Groups, October-December 1990, ed. P. Kulish, Springer Verlag, 1991Google Scholar
  9. 7.
    Celeghini, E., Giacchetti, R., Sorace, E., Tarlini, M.: J.Math.Phys. 32, (1991) 1155; ibid. 1159MathSciNetCrossRefMATHADSGoogle Scholar
  10. 8.
    Celeghini, E., Giacchetti, R., Sorace, E., Tarlini, M.: Contraction of quantum groups. Contribution to [6]Google Scholar
  11. 9.
    Lukierski, J., Nowicki, A., Ruegg, H., Tolstoy, V.N.: Phys.Lett.B 264, 331 (1991)MathSciNetCrossRefADSGoogle Scholar
  12. 10.
    Lukierski, J., Nowicki, A., Ruegg, H.: Geneve Univ. preprint UGVA/DPT-08–740Google Scholar
  13. 11.
    Schmidke, W.P., Vokos, S.P., Zumino, B.: Z.Phys.C 48, 249 (1990)MathSciNetCrossRefMATHGoogle Scholar
  14. 12.
    Lukierski, J., Nowicki, A.: Wroclaw Univ. preprint UWr 777/91, June 1991Google Scholar
  15. 13.
    Celeghini, E., Giacchetti, R., Kulish, P.P., Sorace, E., Tarlini, M.: Firenze Univ. preprint DFF 139/6/91Google Scholar
  16. 14.
    Chakrabarti, A.: J.Math.Phys. 32, 1227 (1991)MathSciNetCrossRefMATHADSGoogle Scholar
  17. 15.
    Schlieker, M., Weich, W., Weixler, R.: Munich University preprint LMU-TPW 1991–3, April 1991Google Scholar
  18. 16.
    Tolstoy, V.N.: Proceedings of Summer Workshop “Quantum Groups”, Clausthal, Germany, July 1989. Springer VerlagGoogle Scholar
  19. 17.
    Kulish, P.P., Chaichian, M.: Phys.Lett.B 234, 72 (1990)MathSciNetCrossRefMATHADSGoogle Scholar
  20. 18.
    Koroshkin, S.M., Tolstoy, V.N.: Nuclear Physics Institute, Moscov State University, preprint 91–13/217Google Scholar
  21. 19.
    Lukierski, J., Nowicki, A., Ruegg, H.: Quantum Deformations of Poincaré Algebra and the Supersymmetric Extensions. Bordeaux Univ. preprint, October 1991; to be published in Proceedings of the International Symposium on Topological and Geometrical Methods in Field Theory, Turku, May 1991Google Scholar
  22. 20.
    Podleś, P., Woronowicz, S.L.: Comm.Math.Phys. 130, 381 (1990)MathSciNetCrossRefMATHADSGoogle Scholar
  23. 21.
    Carow-Watamura, V., Schlieker, M., Scholl, M., Watamura, S.: Z.Phys.C 48, 159 (1990)MathSciNetCrossRefGoogle Scholar
  24. 22.
    Carow-Watamura, V., Schlieker, M., Scholl, M., Watamura, S.: Internat.J.Modern Phys.A 6, 3081 (1991)MathSciNetCrossRefMATHADSGoogle Scholar
  25. 23.
    Woronowicz, S.L.:New Quantum Deformation of SL(2; C) — Hopf Algebra Level. Warsaw University preprint, 1990Google Scholar
  26. 24.
    Schmidke, W.P., Wess, L., Zumino, B.: Max Planck Institute preprint MPI-Ph/91–15, March 1991Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • J. Lukierski
    • 1
  1. 1.Institute of Theoretical PhysicsUniversity of WroclawWroclawPoland

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