{
  "id": "1907.08989",
  "version": "v1",
  "published": "2019-07-21T15:32:57.000Z",
  "updated": "2019-07-21T15:32:57.000Z",
  "title": "Borel subalgebras of Cartan Type Lie Algebras",
  "authors": [
    "Ke Ou",
    "Bin Shu"
  ],
  "comment": "10 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "Let $ W(n) $ be Jacobson-Witt algebra over algebraic closed field $ \\mathbb{K} $ with positive characteristic $ p>2. $ It is difficult to classify all Borel subalgebras of $ W(n) $ or non-classical restricted simple Lie algebras. The present paper and \\cite{S7} study two kinds of subalgebras which are easily to understand and highly related to Borel subalgebras. In \\cite{S7}, the last author investigates a class of special Borel subalgebras of $W(n)$ which is called homogeneous Borel subalgebras. The present paper focuses on subalgebras of $ W(n) $ which are related to Borel subalgebras such that firstly, they could be trigonalizable; and secondly, they essentially belong to the ones investigated in \\cite{S7}. In this paper, the conjugation classes of these subalgebras and representative for each class will be determined. Then some properties such as filtration and dimension will be investigated.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-21T15:32:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cartan type lie algebras",
      "non-classical restricted simple lie algebras",
      "special borel subalgebras",
      "jacobson-witt algebra",
      "algebraic closed field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}