A single Cl(10) Clifford algebra with embedded S3 symmetry realizes three fermion generations matching Standard Model quantum numbers without gauge boson replication.
OnC⊗H⊗O-Valued Gravity, Sedenions, Hermitian Matrix Geometry and Nonsymmetric Kaluza–Klein Theory.Advances in Applied Clifford Algebras, 29(3):1–16, 2019
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Electroweak Structure and Three Fermion Generations in Clifford Algebra with S3 Family Symmetry
A single Cl(10) Clifford algebra with embedded S3 symmetry realizes three fermion generations matching Standard Model quantum numbers without gauge boson replication.