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Jordanian Uh,sgl(2) and its Coloured Realization

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Abstract

A two-parametric nonstandard (Jordanian) deformation of the Lie algebra gl(2) is constructed and then, exploited to obtain a new, triangular R-matrix solution of the coloured Yang–Baxter equation. The corresponding coloured quantum group is presented explicitly.

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References

  1. Demidov, E. E., Manin, Yu. I, Mukhin, E. E. and Zhdanovich, D. V.: Prog. Theoret Phys. Suppl. 102(1990), 203.

    Google Scholar 

  2. Zakrzewski, S.: Lett. Math. Phys. 22(1991), 287.

    Google Scholar 

  3. Aghamohammadi, A.: Modern. Phys. Lett. A 8(1993), 2607.

    Google Scholar 

  4. Dabrowski, L. and Parashar, P.: Lett. Math. Phys. 38(1996), 331.

    Google Scholar 

  5. Ohn, C.: Lett. Math. Phys. 25(1992), 85.

    Google Scholar 

  6. Vladimirov, A. A.: Phys. Lett. A 8(1993), 2573.

    Google Scholar 

  7. Shariati, A., Aghamohammadi, A. and Khorrami, M.: Modern. Phys. Lett. A 11(1996), 187.

    Google Scholar 

  8. Ballesteros, A. and Herranz, F. J.: J. Phys. A 29(1996), L311.

    Google Scholar 

  9. Dobrev, V. K.: Representations of the Jordanian quantum algebra U h sl(2), ICTP Preprint IC/96/14, 1996.

  10. Abdessalam, B., Chakrabarti, A. and Chakrabarti, R.: Irreducible representations of Jordanian quantum algebra U h sl(2) via a nonlinear Map, q-alg/9606014 (1997).

  11. Murakami, J.: Proc. Internat. Conf. Euler Mathematical School: Quantum Groups (Leningrad), Lecture Notes in Phys., Springer, Berlin, 1990, p. 350.

    Google Scholar 

  12. Burdík, C. and Hellinger, P.: J. Phys. A 25(1992), L1023.

    Google Scholar 

  13. Faddeev, L. D., Reshetikhin, N. Yu. and Takhtajan, L. A.: in: M. Jimbo (ed.), Yang-Baxter Equation in Integrable Systems, Adv. Series in Math. Phys. 10, World Scientific, Singapore, 1990, p. 299.

    Google Scholar 

  14. Akutsu, Y. and Deguchi, T.: Phys. Rev. Lett 67(1991), 777.

    Google Scholar 

  15. Ge, M. L. and Xue, K.: J. Phys. A24(1991), L895; J. Phys. A 26(1993), 281.

    Google Scholar 

  16. Gómez, C. and Sierra, G.: J. Math. Phys 34(1993), 2119.

    Google Scholar 

  17. Kundu, A. and Basu-Mallick, B.: J. Phys. A 25(1992), 6307; J. Phys. A 27(1994), 3091.

    Google Scholar 

  18. Bonatsos, D., Daskaloyannis, C., Kolokotronis, P., Ludu, A. and Quesne, C.: A nonlinear su(2) algebra with a two-colour quasitriangular Hopf algebra, q-alg/9701029 (1997).

  19. Schirrmacher, A., Wess, J. and Zumino, B.: Z. Phys. C 49(1991), 317.

    Google Scholar 

  20. Hlavatý, L.: J. Phys. A 25(1992), L63.

    Google Scholar 

  21. Basu-Mallick, B.: Internat J. Modern Phys. A 10(1995), 2851.

    Google Scholar 

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Parashar, P. Jordanian Uh,sgl(2) and its Coloured Realization. Letters in Mathematical Physics 45, 105–112 (1998). https://doi.org/10.1023/A:1007441904626

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