{
  "id": "1210.7094",
  "version": "v2",
  "published": "2012-10-26T10:52:47.000Z",
  "updated": "2013-02-12T12:07:57.000Z",
  "title": "Takiff superalgebras and Conformal Field Theory",
  "authors": [
    "A. Babichenko",
    "D. Ridout"
  ],
  "comment": "25 pages",
  "categories": [
    "math-ph",
    "hep-th",
    "math.MP"
  ],
  "abstract": "A class of non-semisimple extensions of Lie superalgebras is studied. They are obtained by adjoining to the superalgebra its adjoint representation as an abelian ideal. When the superalgebra is of affine Kac-Moody type, a generalisation of Sugawara's construction is shown to give rise to a copy of the Virasoro algebra and so, presumably, to a conformal field theory. Evidence for this is detailed for the extension of the affinisation of the superalgebra gl(1|1): Its highest weight irreducible modules are classified using spectral flow, the irreducible supercharacters are computed and a continuum version of the Verlinde formula is verified to give non-negative integer structure coefficients. Interpreting these coefficients as those of the Grothendieck ring of fusion, partial results on the true fusion ring and its indecomposable structures are deduced.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-02-12T12:07:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "conformal field theory",
      "takiff superalgebras",
      "affine kac-moody type",
      "highest weight irreducible modules",
      "non-negative integer structure coefficients"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1088/1751-8113/46/12/125204",
      "journal": "Journal of Physics A Mathematical General",
      "year": 2013,
      "month": "Mar",
      "volume": 46,
      "number": 12,
      "pages": 125204
    },
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1193796,
      "adsabs": "2013JPhA...46l5204B"
    }
  }
}