A modified E8 model puts the Standard Model inside the so(7,3) subalgebra with compact SU(3), and uses particle coordinates in four dimensions to compute several mixing angles and mass relations.
Division Algebras: 26 Dimensions; 3 Families
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The link of the Division Algebras to 10-dimensional spacetime and one leptoquark family is extended to 26-dimensional spacetime and three leptoquark families.
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Embeddings of the Standard Model in $E_8$
A modified E8 model puts the Standard Model inside the so(7,3) subalgebra with compact SU(3), and uses particle coordinates in four dimensions to compute several mixing angles and mass relations.