Fractional Supersymmetry and Lie Algebras

Abstract

Supersymmetry and super-Lie algebras have been consistently generalized previously. The so-called fractional supersymmetry and $F-$Lie algebras could be constructed starting from any representation $\D$ of any Lie algebra $g$. This involves taking the $F^{\mathrm{t}h}$ root of $\D$ in some sense. We show, after having constructed differential realization(s) of any Lie algebra, how fractional supersymmetry can be explicitly realized in terms of appropriate homogeneous monomials.

16 pages, 1 figure, LaTex file with epsf.sty, Lecture given at the Workshop on Non Commutative Geometry and Superstring Theory, Rabat 16-17 June 2000, to appear in the proceedings