Deducing the symmetry of the standard model from the automorphism and structure groups of the exceptional Jordan algebra

2018/06/17 by Ivan Todorov, Michel Dubois-Violette · 46 citations
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Algebra over a field #Algebraic and Geometric Analysis #Algebraic structures and combinatorial models #Automorphism #Graded Lie algebra #Jordan algebra #Lie algebra #Lie conformal algebra #Simple (philosophy) #Standard Model (mathematical formulation) #Symmetry (geometry) #Symmetry group #hep-th #math-ph #math.MP #math.QA

paper · pdf · doi:10.1142/s0217751x1850118x

published in International Journal of Modern Physics A 33(20), 1850118 (World Scientific) · 16 pages, 1 figure

arxiv created 2018/06/17 · openalex publication_date 2018/07/19 · arxiv updated 2018/08/15 · openalex created_date 2019/06/27 · openalex updated_date 2026/08/05

Abstract

We continue the study undertaken in Ref. 16 of the exceptional Jordan algebra [Formula: see text] as (part of) the finite-dimensional quantum algebra in an almost classical space–time approach to particle physics. Along with reviewing known properties of [Formula: see text] and of the associated exceptional Lie groups we argue that the symmetry of the model can be deduced from the Borel–de Siebenthal theory of maximal connected subgroups of simple compact Lie groups.

Citations

• On an Algebraic Generalization of the Quantum Mechanical Formalism
• The algebra of grand unified theories
• Exceptional quantum geometry and particle physics
• The octonions

Cited by

• Higgs and Yukawa Structure in a Clifford Algebra Model with Three Generations and S₃ Family Symmetry
• Electroweak Structure and Three Fermion Generations in Clifford Algebra with S3 Family Symmetry
• Octonions, complex structures and Standard Model fermions
• Three generations, two unbroken gauge symmetries, and one eight-dimensional algebra

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• The Standard Model Gauge Group from the Exceptional Jordan Algebra
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• Octonions, exceptional Jordan algebra and the role of the group F₄ in particle physics
• Exceptional quantum geometry and particle physics