{
  "id": "math/0703383",
  "version": "v2",
  "published": "2007-03-13T15:59:28.000Z",
  "updated": "2007-08-30T20:54:00.000Z",
  "title": "Cohomology and deformations of the infinite dimensional filiform Lie algebra m_0",
  "authors": [
    "Alice Fialowski",
    "Friedrich Wagemann"
  ],
  "comment": "25 pages",
  "categories": [
    "math.RT",
    "math.RA"
  ],
  "abstract": "Denote m_0 the infinite dimensional N-graded Lie algebra defined by basis e_i, i>= 1 and relations [e_1,e_i] = e_(i+1) for all i>=2. We compute in this article the bracket structure on H1(m_0,m_0), H2(m_0,m_0) and in relation to this, we establish that there are only finitely many true deformations of m_0 in each nonpositive weight, by constructing them explicitely. It turns out that in weight 0 one gets exactly the other two filiform Lie algebras.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-08-30T20:54:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B65",
      "58H15"
    ],
    "keywords": [
      "infinite dimensional filiform lie algebra",
      "deformations",
      "infinite dimensional n-graded lie algebra",
      "cohomology"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......3383F"
    }
  }
}