{
  "id": "math/0509368",
  "version": "v2",
  "published": "2005-09-16T05:18:59.000Z",
  "updated": "2009-10-13T15:27:02.000Z",
  "title": "A category of modules for the full toroidal Lie algebra",
  "authors": [
    "Yuly Billig"
  ],
  "comment": "Missing factor of 2 inserted in the Sugawara formulas (3.20), (3.21) and Theorem 5.4. Proofs are not affected",
  "categories": [
    "math.RT"
  ],
  "abstract": "We introduce a category B of bounded modules for the toroidal Lie algebras and study irreducible modules in B. We show that one of the irreducible modules in this category, L(T_0), admits a structure of a vertex operator algebra. We prove that L(T_0) factors into a tensor product of a sub-VOA of a hyperbolic lattice VOA and a simple VOA associated with a twisted Virasoro-affine Lie algebra. Every irreducible module in category B is a VOA module for a slightly larger VOA V(T_0). Knowing the structure of V(T_0), we are able to give explicit realizations for all irreducible modules in category B and determine their characters.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-10-13T15:27:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B65",
      "17B69"
    ],
    "keywords": [
      "full toroidal lie algebra",
      "irreducible module",
      "hyperbolic lattice voa",
      "twisted virasoro-affine lie algebra",
      "vertex operator algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......9368B"
    }
  }
}