Division Algebras, Extended Supersymmetries and Applications

TL;DR

This paper explores the role of division algebras in classifying supersymmetric systems, introduces an N=8 Malcev superaffine algebra, and discusses potential applications in quantum mechanics and classical dynamics.

Contribution

It explicitly links division algebras to supersymmetry classifications and introduces a novel N=8 Malcev superaffine algebra with its relation to non-associative superconformal algebra.

Findings

Division algebras classify N=1,2,4,8 supersymmetric systems.

Introduction of N=8 Malcev superaffine algebra.

Discussion of applications in physics.

Abstract

I present here some new results which make explicit the role of the division algebras R,C,H,O in the construction and classification of, respectively, N=1,2,4,8 global supersymmetric quantum mechanical and classical dynamical systems. In particular an N=8 Malcev superaffine algebra is introduced and its relation to the non-associative N=8 SCA is discussed. A list of present and possible future applications is given.