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

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.