Algebraic realisation of three fermion generations with $S_3$ family and unbroken gauge symmetry from $\mathbb{C}\ell (8)$

Liam Gourlay, Niels Gresnigt

Building on previous work, we extend an algebraic realisation of three fermion generations within the complex Clifford algebra $\mathbb{C}\ell (8)$ by incorporating a $U(1{)}_{em}$ ga…