{
  "id": "1107.0702",
  "version": "v1",
  "published": "2011-07-04T18:38:56.000Z",
  "updated": "2011-07-04T18:38:56.000Z",
  "title": "A remarkable contraction of semisimple Lie algebras",
  "authors": [
    "Dmitri Panyushev",
    "Oksana Yakimova"
  ],
  "comment": "13 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "Recently, E.Feigin introduced a very interesting contraction $\\mathfrak q$ of a semisimple Lie algebra $\\mathfrak g$ (see arXiv:1007.0646 and arXiv:1101.1898). We prove that these non-reductive Lie algebras retain good invariant-theoretic properties of $\\mathfrak g$. For instance, the algebras of invariants of both adjoint and coadjoint representations of $\\mathfrak q$ are free, and also the enveloping algebra of $\\mathfrak q$ is a free module over its centre.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-07-04T18:38:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14L30",
      "17B20"
    ],
    "keywords": [
      "semisimple lie algebra",
      "non-reductive lie algebras retain",
      "invariant-theoretic properties",
      "coadjoint representations",
      "free module"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1107.0702P"
    }
  }
}