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The embedding ofU q(sl (2)) and sine algebras in generalized Clifford algebras

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Abstract

In this note, we establish the connection between certain quantum algebras and generalized Clifford algebras (GCA). Precisely, we embed the quantum tori Lie algebra andU q(sl (2)) in GCA.

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References

  1. Morris A. O.,Quar. J. Math., (Oxford),18 7–12 (1967);19 289, (1968).

    Article  MATH  ADS  Google Scholar 

  2. Fleury N. and M. Rausch de Traubenberg,J. Math. Phys.,33 3356, (1992);Advances in Appl. Cliff. Alg.,4 123, (1994), and references therein.

    Article  MATH  ADS  MathSciNet  Google Scholar 

  3. Fleury N., M. Rausch de Traubenberg and R. M. Yamaleev,Int. J. Theor. Phys.,32 (4) 503, (1993).

    Article  MATH  MathSciNet  Google Scholar 

  4. Fairlie D. B., P. Fletcher and C. K. Zachos,Phys. Lett.,B 218 203, (1989);J. Math. Phys.,31 1088, (1990).

    MATH  MathSciNet  Google Scholar 

  5. Golenisheva-Kutuzova M. I., D. R. Lebedev and M. A. Olshanetsky,Theor. Math. Phys.,100 (1995);Comm. Math. Phys.,148 403, (1992).

  6. Kogan I. I.,Int. J. Mod. Phys.,A 9 3887, (1994).

    Article  MATH  ADS  Google Scholar 

  7. El Kinani E. H.,Phys. Lett.,B 383 403, (1996).

    MathSciNet  Google Scholar 

  8. Weyl H., “The Theory of Groups and Quantum Mechanics,” E. P. Dutton 272–280, (1932) (Reprinted, Dover, New York 1950).

  9. Santhanam T. S.,Found. Phys.,7 121, (1977);Physica,A 114 4, (1982).

    Article  ADS  MathSciNet  Google Scholar 

  10. Jannathan R. and T. S. Santhanam,Theor. Phys.,21 363, (1982).

    Article  Google Scholar 

  11. See e.g. Durand S.,Mod. Phys. Lett.,A8 2323, (1993);A8 1195 (1993);A7 2904, (1992);Phys. Lett.,B 312 115, (1993).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  12. Perez A., M. Rausch de Traubenberg and P. Simon,Nuc. Phys.,B482 325, (1996).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  13. El Kinani E. H.,Mod. Phys. Lett.,A12 (18) 1589, (1997).

    MATH  ADS  Google Scholar 

  14. Connes A., “Noncommutative Geometry”, Academic Press London, (1994).

    MATH  Google Scholar 

  15. See e. g. Bernard D. and LeClaire,Comm. Math.,142 99, (1991).

    Article  MATH  ADS  Google Scholar 

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El Kinani, E.H., Ouarab, A. The embedding ofU q(sl (2)) and sine algebras in generalized Clifford algebras. AACA 9, 103–108 (1999). https://doi.org/10.1007/BF03041942

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  • DOI: https://doi.org/10.1007/BF03041942

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