Exceptional Lie Algebras, SU(3) and Jordan Pairs

TL;DR

This paper presents a unified perspective on exceptional Lie algebras through Jordan pairs, highlighting their structure and potential physical applications, emphasizing shared automorphisms and su(3) symmetry.

Contribution

It introduces a novel unifying framework connecting exceptional Lie algebras with Jordan pairs and su(3) symmetry, elucidating their internal structure.

Findings

Each algebra contains three Jordan pairs with shared automorphism Lie algebra.

The Jordan pair structure underpins the exceptional Lie algebras.

Potential physical applications and implications are discussed.

Abstract

A simple unifying view of the exceptional Lie algebras is presented. The underlying Jordan pair content and role are exhibited. Each algebra contains three Jordan pairs sharing the same Lie algebra of automorphisms and the same external su(3) symmetry. Eventual physical applications and implications of the theory are outlined.