{
  "id": "0708.0363",
  "version": "v2",
  "published": "2007-08-02T15:23:00.000Z",
  "updated": "2008-08-27T09:39:11.000Z",
  "title": "Cohomology and deformations of the infinite dimensional filiform Lie algebra m_2",
  "authors": [
    "Alice Fialowski",
    "Friedrich Wagemann"
  ],
  "comment": "17 pages",
  "journal": "Journal of Algebra 319 (2008), 5125-5143",
  "categories": [
    "math.RT",
    "math.RA"
  ],
  "abstract": "Denote $\\fm_2$ the infinite dimensional $\\N$-graded Lie algebra defined by the basis $e_i$ for $i\\geq 1$ and by relations $[e_1,e_i]=e_{i+1}$ for all $i\\geq 2$, $[e_2,e_j]=e_{j+2}$ for all $j\\geq 3$. We compute in this article the bracket structure on $H^1(\\fm_2,\\fm_2)$, $H^2(\\fm_2,\\fm_2)$ and in relation to this, we establish that there are only finitely many true deformations of $\\fm_2$ in each weight by constructing them explicitely. It turns out that in weight 0 one gets as non-trivial deformation only one formal non-converging deformation.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-08-27T09:39:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B65",
      "17B56",
      "58H15"
    ],
    "keywords": [
      "infinite dimensional filiform lie algebra",
      "cohomology",
      "graded lie algebra",
      "formal non-converging deformation",
      "non-trivial deformation"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0708.0363F"
    }
  }
}