Journal of Geometry and Symmetry in Physics

Composition Algebras, Exceptional Jordan Algebra and Related Groups

Ivan Todorov and 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 $\frak{J}$. 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.

Article information

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

Dates
First available in Project Euclid: 14 February 2018

Permanent link to this document
https://projecteuclid.org/euclid.jgsp/1518577294

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

Mathematical Reviews number (MathSciNet)
MR3791932

Citation

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. https://projecteuclid.org/euclid.jgsp/1518577294


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