{
  "id": "1212.4349",
  "version": "v1",
  "published": "2012-12-18T13:44:02.000Z",
  "updated": "2012-12-18T13:44:02.000Z",
  "title": "Borel subalgebras of the Witt algebra $W_1$",
  "authors": [
    "Yu-Feng Yao",
    "Hao Chang"
  ],
  "comment": "13 pages; All comments are welcome!",
  "categories": [
    "math.RT",
    "math.RA"
  ],
  "abstract": "Let $\\mathbb{F}$ be an algebraically closed field of characteristic $p>3$, and $\\ggg$ the $p$-dimensional Witt algebra over $\\mathbb{F}$. Let $\\N$ be the nilpotent cone of $\\ggg$. Explicit description of $\\N$ is given, so that the conjugacy classes of Borel subalgebras of $\\ggg$ under the automorphism group are determined. In contrast with only one conjugacy class of Borel subalgebras in a classical simple Lie algebra, there are two conjugacy classes of Borel subalgebras in $\\ggg$. The representatives of conjugacy classes of Borel subalgebras, i.e., the so-called standard Borel subalgebras, are precisely given.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-12-18T13:44:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "conjugacy classes",
      "standard borel subalgebras",
      "dimensional witt algebra",
      "classical simple lie algebra",
      "nilpotent cone"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1212.4349Y"
    }
  }
}