Fractional Supersymmetry and Infinite Dimensional Lie Algebras

TL;DR

This paper demonstrates how infinite dimensional Lie algebras naturally emerge within fractional supersymmetry frameworks, extending previous work on supersymmetry and super Lie algebras by explicitly constructing these algebras using differential realizations.

Contribution

It introduces a method to explicitly construct infinite dimensional Lie algebras within fractional supersymmetry, expanding the understanding of algebraic structures in supersymmetric theories.

Findings

Infinite dimensional Lie algebras appear naturally in fractional supersymmetry.

Construction of these algebras uses differential realizations of Lie algebras.

The resulting algebra contains the original Lie algebra as a sub-algebra.

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.