Fractional Supersymmetry and Infinite Dimensional Lie Algebras

M. Rausch de Traubenberg (1)

1 PMT - Laboratoire de Physique Mathématique et Théorique

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.

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]; Théorie des représentations [math.RT]; Physique des Hautes Energies - Théorie [hep-th]

M. Rausch de Traubenberg. Fractional Supersymmetry and Infinite Dimensional Lie Algebras. Nuclear Physics B Proceedings Supplements, 2001, 102, pp.256-263. ⟨hal-00023291⟩