Deducing the symmetry of the standard model from the automorphism and structure groups of the exceptional Jordan algebra

TL;DR

This paper explores how the symmetry of the Standard Model can be derived from the automorphism and structure groups of the exceptional Jordan algebra, linking algebraic structures to particle physics symmetries.

Contribution

It demonstrates that the symmetry of the Standard Model can be deduced using Borel-de Siebenthal theory applied to the automorphism groups of the exceptional Jordan algebra.

Findings

The automorphism group of the exceptional Jordan algebra relates to Standard Model symmetries.

Borel-de Siebenthal theory helps identify maximal subgroups relevant to particle physics.

The approach connects algebraic structures with physical symmetry groups.

Abstract

We continue the study undertaken in \cite{DV} of the exceptional Jordan algebra $J = J_3^8$ as (part of) the finite-dimensional quantum algebra in an almost classical space-time approach to particle physics. Along with reviewing known properties of $J$ and of the associated exceptional Lie groups we argue that the symmetry of the model can be deduced from the Borel-de Siebenthal theory of maximal connected subgroups of simple compact Lie groups.