{
  "id": "1910.00041",
  "version": "v1",
  "published": "2019-09-30T18:21:54.000Z",
  "updated": "2019-09-30T18:21:54.000Z",
  "title": "The matrix-extended $W_{1+\\infty}$ algebra",
  "authors": [
    "Lorenz Eberhardt",
    "Tomáš Procházka"
  ],
  "categories": [
    "hep-th",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We construct a quadratic basis of generators of matrix-extended $\\mathcal{W}_{1+\\infty}$ using a generalization of the Miura transformation. This makes it possible to conjecture a closed-form formula for the operator product expansions defining the algebra. We study truncations of the algebra. An explicit calculation at low levels shows that these are parametrized in a way consistent with the gluing description of the algebra. It is perhaps surprising that in spite of the fact that the algebras are rather complicated and non-linear, the structure of their truncations follows very simple gluing rules.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-09-30T18:21:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "miura transformation",
      "closed-form formula",
      "simple gluing rules",
      "operator product expansions defining",
      "quadratic basis"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}