In an earlier work extensions of supersymmetry and super Lie algebras were constructed consistently starting from any representation $\D$ of any Lie algebra $\g$. Here it is shown how infinite dimensional Lie algebras appear naturally within the framework of fractional supersymmetry. Using a differential realization of $\g$ this infinite dimensional Lie algebra, containing the Lie algebra $\g$ as a sub-algebra, is explicitly constructed.
Publié le : 2001-07-05
Classification:
[MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph],
[PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph],
[MATH.MATH-RT]Mathematics [math]/Representation Theory [math.RT],
[PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th]
@article{hal-00023291,
author = {De Traubenberg, M. Rausch},
title = {Fractional Supersymmetry and Infinite Dimensional Lie Algebras},
journal = {HAL},
volume = {2001},
number = {0},
year = {2001},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00023291}
}
De Traubenberg, M. Rausch. Fractional Supersymmetry and Infinite Dimensional Lie Algebras. HAL, Tome 2001 (2001) no. 0, . http://gdmltest.u-ga.fr/item/hal-00023291/