Abstract
We interpret the elements of the exceptional Lie algebra e8(−24) as objects in the Standard Model, including lepton and quark spinors with the usual properties, the Standard Model Lie algebra su(3)⊕su(2)⊕u(1), and the Lorentz Lie algebra so(3,1). Our construction relies on identifying a complex structure on spinors and then working in the enveloping algebra. The resulting model naturally contains Grand Unified Theories based on SO(10) (Georgi), SU(5) (Georgi–Glashow), and SU(4) ×SU(2) ×SU(2) (Pati–Salam). We then briefly speculate on the role of the remaining elements of e8 and propose a mechanism leading to exactly three generations of particles.
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