https://doi.org/10.1140/epjc/s10052-019-6967-1
Regular Article - Theoretical Physics
Three fermion generations with two unbroken gauge symmetries from the complex sedenions
Department of Mathematical Sciences, Xi’an Jiaotong-Liverpool University, 111 Ren’ai Road, Suzhou HET, Jiangsu, 215123, China
* e-mail: niels.gresnigt@xjtlu.edu.cn
Received:
24
April
2019
Accepted:
17
May
2019
Published online:
27
May
2019
We show that three generations of leptons and quarks with unbroken Standard Model gauge symmetry 
can be described using the algebra of complexified sedenions 
. A primitive idempotent is constructed by selecting a special direction, and the action of this projector on the basis of can be used to uniquely split the algebra into three complex octonion subalgebras 
. These subalgebras all share a common quaternionic subalgebra. The left adjoint actions of the 8 
-dimensional subalgebras on themselves generates three copies of the Clifford algebra 
. It was previously shown that the minimal left ideals of describe a single generation of fermions with unbroken gauge symmetry. Extending this construction from to naturally leads to a description of exactly three generations.
© The Author(s), 2019
