{"title":"Complexification of the Exceptional Jordan Algebra and Its Application to Particle Physics","authors":"Daniele Corradetti","doi":"10.7546/jgsp-61-2021-1-16","DOIUrl":null,"url":null,"abstract":"Recent papers contributed revitalizing the study of the exceptional Jordan algebra $\\mathfrak{h}_{3}(\\mathbb{O})$ in its relations with the true Standard Model gauge group $\\mathrm{G}_{SM}$. The absence of complex representations of $\\mathrm{F}_{4}$ does not allow $\\Aut\\left(\\mathfrak{h}_{3}(\\mathbb{O})\\right)$ to be a candidate for any Grand Unified Theories, but the automorphisms of the complexification of this algebra, i.e., $\\mathfrak{h}_{3}^{\\mathbb{C}}(\\mathbb{O})$, are isomorphic to the compact form of $\\mathrm{E}_{6}$ and similar constructions lead to the gauge group of the minimal left-right symmetric extension of the Standard Model.","PeriodicalId":43078,"journal":{"name":"Journal of Geometry and Symmetry in Physics","volume":" ","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2021-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Geometry and Symmetry in Physics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.7546/jgsp-61-2021-1-16","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 2
Abstract
Recent papers contributed revitalizing the study of the exceptional Jordan algebra $\mathfrak{h}_{3}(\mathbb{O})$ in its relations with the true Standard Model gauge group $\mathrm{G}_{SM}$. The absence of complex representations of $\mathrm{F}_{4}$ does not allow $\Aut\left(\mathfrak{h}_{3}(\mathbb{O})\right)$ to be a candidate for any Grand Unified Theories, but the automorphisms of the complexification of this algebra, i.e., $\mathfrak{h}_{3}^{\mathbb{C}}(\mathbb{O})$, are isomorphic to the compact form of $\mathrm{E}_{6}$ and similar constructions lead to the gauge group of the minimal left-right symmetric extension of the Standard Model.
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The Journal of Geometry and Symmetry in Physics is a fully-refereed, independent international journal. It aims to facilitate the rapid dissemination, at low cost, of original research articles reporting interesting and potentially important ideas, and invited review articles providing background, perspectives, and useful sources of reference material. In addition to such contributions, the journal welcomes extended versions of talks in the area of geometry of classical and quantum systems delivered at the annual conferences on Geometry, Integrability and Quantization in Bulgaria. An overall idea is to provide a forum for an exchange of information, ideas and inspiration and further development of the international collaboration. The potential authors are kindly invited to submit their papers for consideraion in this Journal either to one of the Associate Editors listed below or to someone of the Editors of the Proceedings series whose expertise covers the research topic, and with whom the author can communicate effectively, or directly to the JGSP Editorial Office at the address given below. More details regarding submission of papers can be found by clicking on "Notes for Authors" button above. The publication program foresees four quarterly issues per year of approximately 128 pages each.
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