Fractional Supersymmetry and Infinite Dimensional Lie Algebras

Abstract

In an earlier work extensions of supersymmetry and super Lie algebras were constructed consistently starting from any representation \D of any Lie algebra \g. Here it is shown how infinite dimensional Lie algebras appear naturally within the framework of fractional supersymmetry. Using a differential realization of \g this infinite dimensional Lie algebra, containing the Lie algebra \g as a sub-algebra, is explicitly constructed.Comment: 8 pages, D.V.Volkov Memorial Conference ``Supersymmetry and Quantum Field Theory'', Kharkov, July 25-29, 2000), two figure