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


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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Ivan Todorov. Svetla Drenska. "Composition Algebras, Exceptional Jordan Algebra and Related Groups." J. Geom. Symmetry Phys. 46 59 - 93, 2017.


Published: 2017
First available in Project Euclid: 14 February 2018

MathSciNet: MR3791932
Digital Object Identifier: 10.7546/jgsp-46-2017-59-93

Rights: Copyright © 2017 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences

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