Fractional Supersymmetry and Fth-Roots of Representations

Details Fractional Supersymmetry and Fth-Roots of Representations Fractional Supersymmetry and Fth-Roots of Representations

1999-04-19

arxiv.org/abs/hep-th/9904126v1

J.Math.Phys.41:4556,2000

Physics

High Energy Physics

High Energy Physics - Theory

23 pages, 1 figure, LaTex file with epsf.sty

Scientific paper

10.1063/1.533362

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 g. This involves taking the Fth-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 g, reducing to the centerless Virasoro algebra when g=sl(2,R).

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