Octonionic Realizations of 1-dimensional Extended Supersymmetries. A Classification

TL;DR

This paper classifies non-associative octonionic realizations of one-dimensional extended supersymmetries, linking them to associative representations and providing examples of invariant dynamical systems with potential applications in superstring and M-theory.

Contribution

It introduces a classification of octonionic realizations of 1D extended supersymmetries and connects them to known associative representations, expanding the understanding of supersymmetric structures.

Findings

Classified octonionic realizations of 1D supersymmetries.

Provided examples like octonionic spinning particles and N=8 KdV.

Discussed potential applications in superstring and M-theory.

Abstract

The classification of the octonionic realizations of the one-dimensional extended supersymmetries is here furnished. These are non-associative realizations which, albeit inequivalent, are put in correspondence with a subclass of the already classified associative representations for 1D extended supersymmetries. Examples of dynamical systems invariant under octonionic realizations of the extended supersymmetries are given. We cite among the others the octonionic spinning particles, the N=8 KdV, etc. Possible applications to supersymmetric systems arising from dimensional reduction of the octonionic superstring and M-theory are mentioned.