Fractional supersymmetry and Fthroots of representations
Abstract
A generalization of superLie algebras is presented. It is then shown that all known examples of fractional supersymmetry can be understood in this formulation. However, the incorporation of threedimensional 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 Fthroots of D in an appropriate sense. A fractional supersymmetry in any spacetime 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:hepth/9904126
 Bibcode:
 2000JMP....41.4556R
 Keywords:

 11.30.Pb;
 02.10.Sp;
 Supersymmetry;
 High Energy Physics  Theory
 EPrint:
 23 pages, 1 figure, LaTex file with epsf.sty