{
  "id": "0812.4275",
  "version": "v2",
  "published": "2008-12-22T20:06:18.000Z",
  "updated": "2010-06-30T15:05:25.000Z",
  "title": "Quasi-reductive (bi)parabolic subalgebras in reductive Lie algebras",
  "authors": [
    "Karin Baur",
    "Anne Moreau"
  ],
  "comment": "20 pages",
  "journal": "Annales de l'Institut Fourier 61, 2 (2011) 417-451",
  "categories": [
    "math.RT"
  ],
  "abstract": "We say that a finite dimensional Lie algebra is quasi-reductive if it has a linear form whose stabilizer for the coadjoint representation, modulo the center, is a reductive Lie algebra with a center consisting of semisimple elements. Parabolic subalgebras of a semisimple Lie algebra are not always quasi-reductive (except in types A or C by work of Panyushev). The classification of quasi-reductive parabolic subalgebras in the classical case has been recently achieved in unpublished work of Duflo, Khalgui and Torasso. In this paper, we investigate the quasi-reductivity of biparabolic subalgebras of reductive Lie algebras. Biparabolic (or seaweed) subalgebras are the intersection of two parabolic subalgebras whose sum is the total Lie algebra. As a main result, we complete the classification of quasi-reductive parabolic subalgebras of reductive Lie algebras by considering the exceptional cases.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-06-30T15:05:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "reductive lie algebra",
      "quasi-reductive parabolic subalgebras",
      "finite dimensional lie algebra",
      "semisimple lie algebra",
      "total lie algebra"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0812.4275B"
    }
  }
}