Poincaŕ and sl(2) algebras of order 3

Journal of Mathematical Physics

Volumn 48, Issue 9, 2007, Pages

  Goze, M ^a   De Traubenberg, M Rausch ^b   Tanasa, A ^c  

^a UNIVERSITÉ DE HAUTE ALSACE   (France)

^b CNRS   (France)

^c UNIVERSITÉ PARIS SACLAY   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 34848832027     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2779956     Document Type: Article

References (44)

1. Ahmedov, H., Yildiz, A., and Ucan, Y., " Fractional Super Lie Algebras and Groups., " J. Phys. A 34, 6413-6423 (2001), e-print arXiv:math.RT/0012058.
2. Ahmedov, H., Yildiz, A., and Ucan, Y., " Fractional Super Lie Algebras and Groups., " J. Phys. A 34, 6413-6423 (2001), e-print arXiv:math.RT/0012058.
3. Coleman, S. and Mandula, J., " All Possible Symmetries of the S Matrix., " Phys. Rev. 159, 1251-1256 (1967).
4. de Azc̀rraga, J. A. and Macfarlane, A. J., " Group theoretical foundations of fractional supersymmetry., " J. Math. Phys. 37, 1115-1127 (1996), e-print arXiv:hep-th/9506177.
5. de Azc̀rraga, J. A. and Macfarlane, A. J., " Group theoretical foundations of fractional supersymmetry., " J. Math. Phys. 37, 1115-1127 (1996), e-print arXiv:hep-th/9506177.
6. Dunne, R. S., Macfarlane, A. J., de Azcarraga, J. A., and Perez Bueno, J. C., " Geometrical foundations of fractional supersymmetry., " Int. J. Mod. Phys. A 12, 3275-3306 (1997), e-print arXiv:hep-th/9610087.
7. Dunne, R. S., Macfarlane, A. J., de Azcarraga, J. A., and Perez Bueno, J. C., " Geometrical foundations of fractional supersymmetry., " Int. J. Mod. Phys. A 12, 3275-3306 (1997), e-print arXiv:hep-th/9610087.
8. Durand, S., " Extended fractional supersymmetric quantum mechanics., " Mod. Phys. Lett. A 8, 1795-1804 (1993), e-print arXiv:hep-th/9305130.
9. Durand, S., " Extended fractional supersymmetric quantum mechanics., " Mod. Phys. Lett. A 8, 1795-1804 (1993), e-print arXiv:hep-th/9305130.
10. Fleury, N., and Rausch de Traubenberg, M., " Local Fractional Supersymmetry for Alternative Statistics., " Mod. Phys. Lett. A 11, 899-914 (1996), e-print arXiv:hep-th/9510108.
11. Fleury, N., and Rausch de Traubenberg, M., " Local Fractional Supersymmetry for Alternative Statistics., " Mod. Phys. Lett. A 11, 899-914 (1996), e-print arXiv:hep-th/9510108.
12. Folly, Y., " Sur la rigidit́ des repŕsentations de sl(2)., " Rend. Sem. Fac. Sci. Univ. Cagliari 67, 1-8 (1997).
13. Fulton, W., Harris, J., Representation theory, (Springer, New York, 1991).
14. Gerstenhaber, M., " On the deformation of rings and algebras., " Ann. Math. 79, 59-103 (1964).
15. Gerstenhaber, M., " The cohomology structure of an associative ring., " Ann. Math. 78, 267-288 (1963).
16. Goze, M., " Perturbation des superalg̀bres de Lie., " J. Geom. Phys. 6, 583-593 (1989).
17. Goze, M., in Deformation Theory of Algebras and Structures and Applications (Il Ciocco1986), NATO Advanced Studies Institute Series C: Mathematical and Physical Sciences, edited by, M. Hazewinkel, and, M. Gerstenhaber, (Kluwer Academic Dordrecht, 1988), Vol. 247, pp. 265-355.
18. Goze, M., and Ancochea Bermudez, J. M., " On the classification of rigid Lie algebras., " J. Algebra 245, 68-91 (2001).
19. Goze, M., and Remm, E., " Valued deformations of algebras., " J. Algebra Appl. 3, 345-365 (2004).
20. Haag, R., Lopuszanski, J. T., and Sohnius, M. F., " All Possible Generators of Supersymmetries of The S Matrix., " Nucl. Phys. B 88, 257-302 (1975).
21. Inönü, E. and Wigner, E. P., " On the contraction of groups and their representations., " Proc. Natl. Acad. Sci. U.S.A. 39, 510-524 (1953).
22. Kerner, R., " Z(3) graded algebras and the cubic root of the supersymmetry translations., " J. Math. Phys. 33, 403-411 (1992).
23. Matheus-Valle, J. L. and Monteiro, A. R., " Quantum group generalization of the classical supersymmetric point particle., " Mod. Phys. Lett. A 7, 3023-3028 (1992).
24. Mohammedi, N., " Fractional supersymmetry., " Mod. Phys. Lett. A 10, 1287-1292 (1995), e-print arXiv:hep-th/9412133.
25. Mohammedi, N., " Fractional supersymmetry., " Mod. Phys. Lett. A 10, 1287-1292 (1995), e-print arXiv:hep-th/9412133.
26. Mohammedi, N., Moultaka, G., Rausch de Traubenberg, M., " Field theoretic realizations for cubic supersymmetry., " Int. J. Mod. Phys. A 19, 5585-5608 (2004), e-print arXiv:hep-th/0305172.
27. Mohammedi, N., Moultaka, G., Rausch de Traubenberg, M., " Field theoretic realizations for cubic supersymmetry., " Int. J. Mod. Phys. A 19, 5585-5608 (2004), e-print arXiv:hep-th/0305172.
28. Moultaka, G., Rausch de Traubenberg, M., and Tanasa, A., " Cubic supersymmetry and abelian gauge invariance., " Int. J. Mod. Phys. A 20, 5779-5806 (2005), e-print arXiv:hep-th/0411198.
29. Moultaka, G., Rausch de Traubenberg, M., and Tanasa, A., " Cubic supersymmetry and abelian gauge invariance., " Int. J. Mod. Phys. A 20, 5779-5806 (2005), e-print arXiv:hep-th/0411198.
30. Moultaka, G., Rausch de Traubenberg, M., Tanasa, A., Proceedings of the XIth International Conference Symmetry Methods in Physics, Prague, 21-24 June 2004, (unpublished). e-print arXiv:hep-th/0407168.
31. Moultaka, G., Rausch de Traubenberg, M., Tanasa, A., Proceedings of the XIth International Conference Symmetry Methods in Physics, Prague, 21-24 June 2004, (unpublished). e-print arXiv:hep-th/0407168.
32. Nijenhuis, A., and Richardson, R. W., " Cohomology and deformations in graded Lie algebras., " Bull. Am. Math. Soc. 72, 1-29 (1966).
33. Perez, A., Rausch de Traubenberg, M., and Simon, P., " 2D Fractional Supersymmetry for Rational Conformal Field Theory. Application for Third-Integer Spin States., " Nucl. Phys. B 482, 325-344 (1996), e-print arXiv:hep-th/9603149.
34. Perez, A., Rausch de Traubenberg, M., and Simon, P., " 2D Fractional Supersymmetry for Rational Conformal Field Theory. Application for Third-Integer Spin States., " Nucl. Phys. B 482, 325-344 (1996), e-print arXiv:hep-th/9603149.
35. Rausch de Traubenberg, M., and Simon, P., " 2-D fractional supersymmetry and conformal field theory for alternative statistics., " Nucl. Phys. B 517, 485-505 (1998), e-print arXiv:hep-th/9606188.
36. Rausch de Traubenberg, M., and Simon, P., " 2-D fractional supersymmetry and conformal field theory for alternative statistics., " Nucl. Phys. B 517, 485-505 (1998), e-print arXiv:hep-th/9606188.
37. Rausch de Traubenberg, M., and Slupinski, M. J., " Finite-dimensional Lie algebras of order F., " J. Math. Phys. 43, 5145-5160 (2002), e-print arXiv:hep-th/0205113.
38. Rausch de Traubenberg, M., and Slupinski, M. J., " Finite-dimensional Lie algebras of order F., " J. Math. Phys. 43, 5145-5160 (2002), e-print arXiv:hep-th/0205113.
39. Rausch de Traubenberg, M., and Slupinski, M. J., " Fractional supersymmetry and F(th) roots of representations., " J. Math. Phys. 41, 4556-4579 (2000), e-print arXiv:hep-th/9904126.
40. Rausch de Traubenberg, M., and Slupinski, M. J., " Fractional supersymmetry and F(th) roots of representations., " J. Math. Phys. 41, 4556-4579 (2000), e-print arXiv:hep-th/9904126.
41. Rausch de Traubenberg, M., and Slupinski, M., " Non-trivial extensions of the 3D-Poincare algebra and fractional supersymmetry for anyons., " Mod. Phys. Lett. A 12, 3051-3066 (1997), e-print arXiv:hep-th/9609203.
42. Rausch de Traubenberg, M., and Slupinski, M., " Non-trivial extensions of the 3D-Poincare algebra and fractional supersymmetry for anyons., " Mod. Phys. Lett. A 12, 3051-3066 (1997), e-print arXiv:hep-th/9609203.
43. Tanasa, A., e-print arXiv:hep-th/0509174 (Ph-D thesis).
44. Weimar-Woods, E., " Contractions, generalised Inönü-Wigner contractions and deformations of finite-dimensional Lie algebras., " Rev. Math. Phys. 12, 1505-1529 (2000).