{
  "id": "1808.04019",
  "version": "v1",
  "published": "2018-08-12T23:24:28.000Z",
  "updated": "2018-08-12T23:24:28.000Z",
  "title": "Stability for biparabolic subalgebras of simple Lie algebras",
  "authors": [
    "Kais Ammari"
  ],
  "comment": "in French. arXiv admin note: text overlap with arXiv:1305.1518; text overlap with arXiv:math/0503019 by other authors",
  "categories": [
    "math.RT"
  ],
  "abstract": "Let K be an algebraically closed field of characteristic 0. It is well known that any quasi-reductive Lie algebra is stable. However, there are stable Lie algebras which are not quasi-reductive. This raises the question, if for some particular class of non-reductive Lie algebras, there is equivalence between stability and quasi-reductivity. In particular, it was conjectured by Panyushev that these two notions are equivalent for biparabolic subalgebras of a reductive Lie algebra. In this paper, we give a positive answer to this conjecture.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-08-12T23:24:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "simple lie algebras",
      "biparabolic subalgebras",
      "stable lie algebras",
      "non-reductive lie algebras",
      "quasi-reductive lie algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "fr",
      "license": "arXiv",
      "status": "editable"
    }
  }
}