{
  "id": "1102.5187",
  "version": "v1",
  "published": "2011-02-25T08:16:59.000Z",
  "updated": "2011-02-25T08:16:59.000Z",
  "title": "Quasifinite representations of a class of Block type Lie algebras $\\BB$",
  "authors": [
    "Yucai Su",
    "Chunguang Xia",
    "Ying Xu"
  ],
  "comment": "LaTeX, 22 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "Intrigued by a well-known theorem of Mathieu's on Harish-Chandra modules over the Virasoro algebra, we give an analogous result for a class of Block type Lie algebras $\\BB$, where the parameter $q$ is a nonzero complex number. We also classify quasifinite irreducible highest weight $\\BB$-modules and irreducible $\\BB$-modules of the intermediate series. In particular, we obtain that an irreducible $\\BB$-module of the intermediate series may be a nontrivial extension of a $\\Vir$-module of the intermediate series if $q$ is half of a negative integer, where $\\Vir$ is a subalgebra of $\\BB$ isomorphic to the Virasoro algebra.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-02-25T08:16:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "block type lie algebras",
      "quasifinite representations",
      "intermediate series",
      "virasoro algebra",
      "nonzero complex number"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1102.5187S"
    }
  }
}