{
  "id": "2211.04199",
  "version": "v1",
  "published": "2022-11-08T12:30:24.000Z",
  "updated": "2022-11-08T12:30:24.000Z",
  "title": "Fermion realisations of generalised Kac--Moody and Virasoro algebras associated to the two-sphere and the two-torus",
  "authors": [
    "Rutwig Campoamor-Stursberg",
    "Michel Rausch de Traubenberg"
  ],
  "comment": "10 pages",
  "categories": [
    "math-ph",
    "hep-th",
    "math.MP",
    "math.RT"
  ],
  "abstract": "Using the notion of extension of Kac-Moody algebras for higher dimensional compact manifolds recently introduced in [1], we show that for the two-torus $\\mathbb S^1 \\times \\mathbb S^1$ and the two-sphere $\\mathbb S^2$, these extensions, as well as extensions of the Virasoro algebra can be obtained naturally from the usual Kac-Moody and Virasoro algebras. Explicit fermionic realisations are proposed. In order to have well defined generators, beyond the usual normal ordering prescription, we introduce a regulator and regularise infinite sums by means of Riemann $\\zeta-$function.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-11-08T12:30:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "virasoro algebra",
      "fermion realisations",
      "generalised kac-moody",
      "two-sphere",
      "higher dimensional compact manifolds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}