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arXiv · 1805.06739

Octonions, exceptional Jordan algebra and the role of the group F_4 in particle physics

Ivan Todorov·Svetla Drenska
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Abstract

Normed division rings are reviewed in the more general framework of composition algebras that include the split (indefinite metric) case. The Jordan - von Neumann - Wigner classification of finite dimensional Jordan algebras is outlined with special attention to the 27 dimensional exceptional Jordan algebra J. The automorphism group F_4 of J and its maximal Borel - de Siebenthal subgroups are studied in detail and applied to the classification of fundamental fermions and gauge bosons. Their intersection in F_4 is demonstrated to coincide with the gauge group of the Standard Model of particle physics. The first generation's fundamental fermions form a basis of primitive idempotents in the euclidean extension of the Jordan subalgebra JSpin_9 of J.

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Ivan Todorov, Svetla Drenska. 2018-09-27. Octonions, exceptional Jordan algebra and the role of the group F_4 in particle physics. https://doi.org/10.1007/s00006-018-0899-y

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