The Standard Model gauge group is characterized as a subgroup of Spin(10) via two suitably aligned commuting complex structures on R^10 encoded in orthogonal pure spinors whose sum is pure, described efficiently with octonions.
Deducing the symmetry of the standard model from the automorphism and structure groups of the exceptional Jordan algebra
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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.
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Octonions, complex structures and Standard Model fermions
The Standard Model gauge group is characterized as a subgroup of Spin(10) via two suitably aligned commuting complex structures on R^10 encoded in orthogonal pure spinors whose sum is pure, described efficiently with octonions.