Parafermions, ternary algebras and their associated superspace

TL;DR

This paper demonstrates that parafermions of order two serve as essential tools for constructing ternary superspaces, which are related to cubic extensions of the Poincaré algebra, expanding the algebraic framework of supersymmetry.

Contribution

It introduces the use of parafermions of order two to develop ternary superspaces linked to cubic Poincaré algebra extensions, a novel approach in algebraic structures.

Findings

Parafermions of order two are fundamental for ternary superspace construction.

Ternary superspaces are related to cubic extensions of the Poincaré algebra.

New algebraic framework for supersymmetry involving ternary structures.

Abstract

Parafermions of order two are shown to be the fundamental tool to construct ternary superspaces related to cubic extensions of the Poincar\'e algebra