A generalization of super-Lie algebras is presented. It is then shown that all known examples of fractional supersymmetry can be understood in this formulation. However, the incorporation of three-dimensional fractional supersymmetry in this framework needs some care. The proposed solutions lead naturally to a formulation of a fractional supersymmetry starting from any representation 𝒟 of any Lie algebra This involves taking the -roots of 𝒟 in an appropriate sense. A fractional supersymmetry in any space–time dimension is then possible. This formalism finally leads to an infinite dimensional extension of reducing to the centerless Virasoro algebra when
REFERENCES
1.
2.
R.
Haag
, J. T.
Lopuszanski
, and M. F.
Sohnius
, Nucl. Phys. B
88
, 257
(1975
).3.
4.
5.
6.
J. L.
Matheus-Valle
and Marco A. R.
Monteiro
, Mod. Phys. Lett. A
7
, 3023
(1992
);L. P.
Colatto
and J. L.
Matheus-Valle
, J. Math. Phys.
37
, 6121
(1996
).7.
N.
Fleury
and M.
Rausch de Traubenberg
, Mod. Phys. Lett. A
11
, 899
(1996
).8.
J. A.
de Azcàrraga
and A. J.
Macfarlane
, J. Math. Phys.
37
, 1115
(1996
).9.
A.
Perez
, M.
Rausch de Traubenberg
, and P.
Simon
, Nucl. Phys. B
482
, 325
(1996
);M.
Rausch de Traubenberg
and P.
Simon
, Nucl. Phys. B
517
, 485
(1998
).10.
J. L.
Matheus-Valle
and Marco A. R.
Monteiro
, Phys. Lett. B
300
, 66
(1993
);E. H.
Saidi
, M. B.
Sedra
, and J.
Zerouaoui
, Class. Quantum Grav.
12
, 1567
(1995
);E. H.
Saidi
, M. B.
Sedra
, and J.
Zerouaoui
, Class. Quantum Grav.
12
, 2705
(1995
).11.
12.
M.
Rausch de Traubenberg
and M.
Slupinski
, Mod. Phys. Lett. A
12
, 3051
(1997
).13.
M.
Rausch de Traubenberg
, hep-th/9802141, Habilitation Thesis (in French).14.
J.
Leinaas
and J.
Myrheim
, Nuovo Cimento Soc. Ital. Fis., B
37
, 1
(1977
).15.
16.
17.
J. L.
Cortes
and M. S.
Plyushchay
, Int. J. Mod. Phys. A
11
, 3331
(1996
).18.
19.
20.
21.
N.
Fleury
and M.
Rausch de Traubenberg
, J. Math. Phys.
33
, 3356
(1992
);22.
23.
B. Wybourne, Classical Groups for Physicists (Wiley, New York, 1974).
24.
V. G. Kac and A. K. Raina, in Bombay Lectures on Highest Weight Representations of Infinite Dimensional Lie Algebras (World Scientific, Singapore, 1987).
25.
V. G. Kac, Infinite Dimensional Lie Algebras (Cambridge University Press, Cambridge, 1990).
26.
A. M. Polyakov, Gauge Fields and Strings (Harwood, Chur, 1987), Vol. 3.
This content is only available via PDF.
© 2000 American Institute of Physics.
2000
American Institute of Physics
You do not currently have access to this content.
