{
  "id": "2006.05285",
  "version": "v1",
  "published": "2020-06-09T14:24:40.000Z",
  "updated": "2020-06-09T14:24:40.000Z",
  "title": "A geometric characterisation of subvarieties of the standard E_6-variety related to the ternions, degenerate split quaternions and sextonions over arbitrary fields",
  "authors": [
    "Anneleen De Schepper"
  ],
  "comment": "54 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "The main achievement of this paper is a geometric characterisation of certain subvarieties of the Cartan variety (the standard projective variety associated to the split exceptional group of Lie type E_6) over an arbitrary field K. The characterised varieties arise as Veronese representations of certain ring projective planes over quadratic subalgebras of the split octonions over K (among which the sextonions, a 6-dimensional non-associative algebra). We describe how these varieties are linked to the Freudenthal-Tits magic square, and discuss how they would even fit in, when also allowing the sextonions and other \"degenerate composition algebras\" as the algebras used to construct the square.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-09T14:24:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14N05",
      "51A45",
      "51B25",
      "51C05",
      "51E24"
    ],
    "keywords": [
      "degenerate split quaternions",
      "arbitrary field",
      "geometric characterisation",
      "sextonions",
      "subvarieties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 54,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}