Three generations of colored fermions with $S_3$ family symmetry from Cayley-Dickson sedenions

Niels G. Gresnigt, Liam Gourlay, Abhinav Varma

An algebraic representation of three generations of fermions with $SU(3{)}_C$ color symmetry based on the Cayley-Dickson algebra of sedenions $\mathbb{S}$ is constructed. Recent cons…