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      the complexification of the exceptional Jordan algebra and applications to particle physics

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      Octonions, Jordan Algebras, Lie groups, Particle physics

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          Abstract

          Abstract Recent papers of Todorov and Dubois-Violette[4] and Krasnov[7] contributed revitalizing the study of the exceptional Jordan algebra h3(O) in its relations with the true Standard Model gauge group GSM. The absence of complex representations of F4 does not allow Aut (h3 (O)) to be a candidate for any Grand Unified Theories, but the group of automorphisms of the complexification of this algebra isisomorphic to the compact form of E6. Following Boyle in [12], it is then easy to show that the gauge group of the minimal left-right symmetric extension of the Standard Model is isomorphic to a proper subgroup of Aut(C⊗h3(O))

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          ScienceOpen Preprints
          ScienceOpen
          10 September 2021
          Affiliations
          [1 ] Universidade do Algarve
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          Article
          10.14293/S2199-1006.1.SOR-.PPETDJ5.v1

          This work has been published open access under Creative Commons Attribution License CC BY 4.0 , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Conditions, terms of use and publishing policy can be found at www.scienceopen.com .

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          Mathematical physics

          Octonions, Jordan Algebras, Lie groups, Particle physics

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