{
  "abstract": "Starting from the Standard Model Lie algebra $\\mathfrak{g}_{\\mathrm{SM}} = \\mathfrak{sl}_3 \\oplus \\mathfrak{sl}_2 \\oplus \\mathbb{C}$ sitting inside the complex Lie algebra $\\mathfrak{e}_7$, we show how to decompose $\\mathfrak{e}_7$ into the direct sum of a Lie subalgebra containing $\\mathfrak{g}_{\\mathrm{SM}}$ and three 32-dimensional subspaces, each of which forms the same representation of $\\mathfrak{g}_{\\mathrm{SM}}$ as one generation of fermions and their antiparticles. The setting is due to Nasmith, and much of the mathematics is that underlying the $\\mathrm{E}_7$ generation unification of Kugo and Yanagida. New features include the derivation, in which as many results as possible rely only on the embedding $\\mathfrak{g}_{\\mathrm{SM}} \\subset \\mathfrak{e}_7$, and also the description of each 32-dimensional subspace as a copy of the exterior algebra $Λ\\mathbb{C}^5$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.06271",
  "author_total": 1,
  "authors": [
    {
      "name": "John C. Baez"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2y5397mdc6x1z.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.06271",
  "fulltext_url": null,
  "id": "2y5397mdc6x1z",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.06271",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "3106|Particle physics theoretical and experimental studies"
    ]
  ],
  "openalex": "W7201849729",
  "pdf_url": "https://arxiv.org/pdf/2608.06271",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2y5397mdc6x1z.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:19Z",
      "native_id": "2608.06271",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.06271"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Three Generations in E7",
  "title_text": "Three Generations in E7",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/2y5397mdc6x1z",
  "venue": "arXiv",
  "versions": []
}