Fractional supersymmetry and Fth-roots of representations
Abstract
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).
- Publication:
-
Journal of Mathematical Physics
- Pub Date:
- July 2000
- DOI:
- 10.1063/1.533362
- arXiv:
- arXiv:hep-th/9904126
- Bibcode:
- 2000JMP....41.4556R
- Keywords:
-
- 11.30.Pb;
- 02.10.Sp;
- Supersymmetry;
- High Energy Physics - Theory
- E-Print:
- 23 pages, 1 figure, LaTex file with epsf.sty