Complexification of the Exceptional Jordan Algebra and Its Application to Particle Physics

Abstract

Recent papers contributed revitalizing the study of the exceptional Jordan algebra h(3)(O) in its relations with the true Standard Model gauge group G(SM). The absence of complex representations of F-4 does not allow Aut (h(3)(O)) to be a candidate for any Grand Unified Theories, but the automorphisms of the complexification of this algebra, i.e., h(3)(C)(O), are isomorphic to the compact form of E-6 and similar constructions lead to the gauge group of the minimal left-right symmetric extension of the Standard Model.