Journal of Geometry and Symmetry in Physics

Composition Algebras, Exceptional Jordan Algebra and Related Groups

Ivan Todorov and Svetla Drenska

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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 $\frak{J}$. The automorphism group $\rm{F}_4$ of $\frak{J}$ and its maximal Borel-de~Siebenthal subgroups $\frac{\rm SU(3)\times \rm SU(3)}{\mathbb{Z}_3}$ and ${\rm Spin}(9)$ are studied in some detail with an eye to possible applications to the fundamental fermions in the Standard Model of particle physics.

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J. Geom. Symmetry Phys., Volume 46 (2017), 59-93.

First available in Project Euclid: 14 February 2018

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Todorov, Ivan; Drenska, Svetla. Composition Algebras, Exceptional Jordan Algebra and Related Groups. J. Geom. Symmetry Phys. 46 (2017), 59--93. doi:10.7546/jgsp-46-2017-59-93.

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