Braided structure of fractional $Z_3$-supersymmetry

TL;DR

The paper demonstrates that fractional $Z_3$-supersymmetry can be understood through the braided line framework, revealing a deep connection between supersymmetry and quantum algebra structures.

Contribution

It establishes an isomorphism between fractional $Z_3$-superspace and the braided line at a specific quantum parameter limit, providing a new geometric interpretation.

Findings

Fractional $Z_3$-superspace is isomorphic to the braided line at $q o e^{2 heta i/3}$.

$Z_3$-supersymmetry corresponds to translational invariance along the braided line.

The fractional translation generator arises as a limit of derivatives on the braided line.

Abstract

It is shown that fractional $Z_3$-superspace is isomorphic to the $q\to\exp(2\pi i/3)$ limit of the braided line. $Z_3$-supersymmetry is identified as translational invariance along this line. The fractional translation generator and its associated covariant derivative emerge as the $q\to\exp(2\pi i/3)$ limits of the left and right derivatives from the calculus on the braided line