Fractional Supersymmetry and Lie Algebras

Details Fractional Supersymmetry and Lie Algebras Fractional Supersymmetry and Lie Algebras

2000-07-19

arxiv.org/abs/hep-th/0007150v1

Physics

High Energy Physics

High Energy Physics - Theory

16 pages, 1 figure, LaTex file with epsf.sty, Lecture given at the Workshop on Non Commutative Geometry and Superstring Theory

Scientific paper

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 $F^{\mathrm th}$ 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.

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