{
  "id": "1210.7132",
  "version": "v1",
  "published": "2012-10-26T13:08:18.000Z",
  "updated": "2012-10-26T13:08:18.000Z",
  "title": "Classification of quasifinite representations of a Lie algebra related to Block type",
  "authors": [
    "Yucai Su",
    "Chunguang Xia",
    "Ying Xu"
  ],
  "comment": "8 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "A well-known theorem of Mathieu's states that a Harish-chandra module over the Virasoro algebra is either a highest weight module, a lowest weight module or a module of the intermediate series. It is proved in this paper that an analogous result also holds for the Lie algebra $\\BB$ related to Block type, with basis {L_{\\a,i},C|a,i\\in\\Z, i\\ge0} and relations [L_{\\a,i},L_{\\b,j}]=((i+1)\\b-(j+1)\\a)L_{\\a+\\b,i+j}+\\d_{\\a+\\b,0}\\d_{i+j,0}\\frac{\\a^3-\\a}{6}C, [C,L_{\\a,i}]=0.Namely, an irreducible quasifinite $\\BB$-module is either a highest weight module, a lowest weight module or a module of the intermediate series.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-10-26T13:08:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B10",
      "17B65",
      "17B68"
    ],
    "keywords": [
      "lie algebra",
      "block type",
      "quasifinite representations",
      "lowest weight module",
      "highest weight module"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1210.7132S"
    }
  }
}