A braided interpretation of fractional supersymmetry in higher dimensions

TL;DR

This paper introduces a new mathematical framework using braided covector algebras to explore fractional supersymmetry in higher dimensions, connecting it to known supersymmetric theories.

Contribution

It develops a many-variable q-calculus formalism and relates it to fractional supersymmetry, especially at roots of unity, extending supersymmetric concepts to higher dimensions.

Findings

Properties of the q-calculus at roots of unity analyzed

Connections between braided covector algebras and fractional supersymmetry established

Special cases of 2D supersymmetry detailed

Abstract

A many variable $q$-calculus is introduced using the formalism of braided covector algebras. Its properties when certain of its deformation parameters are roots of unity are discussed in detail, and related to fractional supersymmetry. The special cases of two dimensional supersymmetry and fractional supersymmetry are developed in detail.