{
  "id": "0708.1711",
  "version": "v2",
  "published": "2007-08-13T13:57:25.000Z",
  "updated": "2008-07-14T13:54:32.000Z",
  "title": "Generators of simple Lie algebras in arbitrary characteristics",
  "authors": [
    "Jean-Marie Bois"
  ],
  "comment": "26 pages, final version, to appear in Math. Z. Main improvements and corrections in Section 4.3",
  "doi": "10.1007/s00209-008-0397-3",
  "categories": [
    "math.RT",
    "math.AG",
    "math.RA"
  ],
  "abstract": "In this paper we study the minimal number of generators for simple Lie algebras in characteristic 0 or p > 3. We show that any such algebra can be generated by 2 elements. We also examine the 'one and a half generation' property, i.e. when every non-zero element can be completed to a generating pair. We show that classical simple algebras have this property, and that the only simple Cartan type algebras of type W which have this property are the Zassenhaus algebras.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-07-14T13:54:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B50",
      "17B45"
    ],
    "keywords": [
      "simple lie algebras",
      "arbitrary characteristics",
      "generators",
      "simple cartan type algebras",
      "classical simple algebras"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0708.1711B"
    }
  }
}