{
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  "authors": [
    {
      "affiliations": [
        {
          "country": "China", 
          "value": "Department of Mathematical Sciences, Xi\u2019an Jiaotong-Liverpool University, 111 Ren\u2019ai Road, Suzhou HET, Jiangsu, 215123, China", 
          "organization": "Xi\u2019an Jiaotong-Liverpool University"
        }
      ], 
      "surname": "Gillard", 
      "given_names": "Adam", 
      "full_name": "Gillard, Adam"
    }, 
    {
      "affiliations": [
        {
          "country": "China", 
          "value": "Department of Mathematical Sciences, Xi\u2019an Jiaotong-Liverpool University, 111 Ren\u2019ai Road, Suzhou HET, Jiangsu, 215123, China", 
          "organization": "Xi\u2019an Jiaotong-Liverpool University"
        }
      ], 
      "surname": "Gresnigt", 
      "email": "niels.gresnigt@xjtlu.edu.cn", 
      "full_name": "Gresnigt, Niels", 
      "given_names": "Niels"
    }
  ], 
  "titles": [
    {
      "source": "Springer", 
      "title": "Three fermion generations with two unbroken gauge symmetries from the complex sedenions"
    }
  ], 
  "dois": [
    {
      "value": "10.1140/epjc/s10052-019-6967-1"
    }
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  "publication_info": [
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      "page_end": "11", 
      "journal_title": "European Physical Journal C", 
      "material": "article", 
      "journal_volume": "79", 
      "artid": "s10052-019-6967-1", 
      "year": 2019, 
      "page_start": "1", 
      "journal_issue": "5"
    }
  ], 
  "$schema": "http://repo.scoap3.org/schemas/hep.json", 
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    "date": "2019-06-10T02:39:47.008054", 
    "source": "Springer", 
    "method": "Springer", 
    "submission_number": "e19961dc8b1611e9a46302163e01809a"
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  "page_nr": [
    11
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  "license": [
    {
      "url": "https://creativecommons.org/licenses//by/4.0", 
      "license": "CC-BY-4.0"
    }
  ], 
  "copyright": [
    {
      "holder": "The Author(s)", 
      "year": "2019"
    }
  ], 
  "control_number": "47531", 
  "record_creation_date": "2019-05-27T20:30:19.341856", 
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  "collections": [
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      "primary": "European Physical Journal C"
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  ], 
  "abstracts": [
    {
      "source": "Springer", 
      "value": "We show that three generations of leptons and quarks with unbroken Standard Model gauge symmetry $$SU(3)_c\\times U(1)_{em}$$ <math><mrow><mi>S</mi><mi>U</mi><msub><mrow><mo>(</mo><mn>3</mn><mo>)</mo></mrow><mi>c</mi></msub><mo>\u00d7</mo><mi>U</mi><msub><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow><mrow><mi>em</mi></mrow></msub></mrow></math>  can be described using the algebra of complexified sedenions $${\\mathbb {C}}\\otimes {\\mathbb {S}}$$ <math><mrow><mi>C</mi><mo>\u2297</mo><mi>S</mi></mrow></math> . A primitive idempotent is constructed by selecting a special direction, and the action of this projector on the basis of $${\\mathbb {C}}\\otimes {\\mathbb {S}}$$ <math><mrow><mi>C</mi><mo>\u2297</mo><mi>S</mi></mrow></math>  can be used to uniquely split the algebra into three complex octonion subalgebras $${\\mathbb {C}}\\otimes {\\mathbb {O}}$$ <math><mrow><mi>C</mi><mo>\u2297</mo><mi>O</mi></mrow></math> . These subalgebras all share a common quaternionic subalgebra. The left adjoint actions of the 8 $${\\mathbb {C}}$$ <math><mi>C</mi></math> -dimensional $${\\mathbb {C}}\\otimes {\\mathbb {O}}$$ <math><mrow><mi>C</mi><mo>\u2297</mo><mi>O</mi></mrow></math>  subalgebras on themselves generates three copies of the Clifford algebra $${\\mathbb {C}}\\ell (6)$$ <math><mrow><mi>C</mi><mi>\u2113</mi><mo>(</mo><mn>6</mn><mo>)</mo></mrow></math> . It was previously shown that the minimal left ideals of $${\\mathbb {C}}\\ell (6)$$ <math><mrow><mi>C</mi><mi>\u2113</mi><mo>(</mo><mn>6</mn><mo>)</mo></mrow></math>  describe a single generation of fermions with unbroken $$SU(3)_c\\times U(1)_{em}$$ <math><mrow><mi>S</mi><mi>U</mi><msub><mrow><mo>(</mo><mn>3</mn><mo>)</mo></mrow><mi>c</mi></msub><mo>\u00d7</mo><mi>U</mi><msub><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow><mrow><mi>em</mi></mrow></msub></mrow></math>  gauge symmetry. Extending this construction from $${\\mathbb {C}}\\otimes {\\mathbb {O}}$$ <math><mrow><mi>C</mi><mo>\u2297</mo><mi>O</mi></mrow></math>  to $${\\mathbb {C}}\\otimes {\\mathbb {S}}$$ <math><mrow><mi>C</mi><mo>\u2297</mo><mi>S</mi></mrow></math>  naturally leads to a description of exactly three generations."
    }
  ], 
  "imprints": [
    {
      "date": "2019-05-27", 
      "publisher": "Springer"
    }
  ]
}