{
  "id": "1710.02275",
  "version": "v1",
  "published": "2017-10-06T04:50:07.000Z",
  "updated": "2017-10-06T04:50:07.000Z",
  "title": "Universal two-parameter $\\mathcal{W}_{\\infty}$-algebra and vertex algebras of type $\\mathcal{W}(2,3,\\dots, N)$",
  "authors": [
    "Andrew R. Linshaw"
  ],
  "comment": "52 pages, preliminary version, all comments welcome",
  "categories": [
    "math.RT",
    "hep-th",
    "math.QA"
  ],
  "abstract": "We prove the longstanding physics conjecture that there exists a unique two-parameter $\\mathcal{W}_{\\infty}$-algebra which is freely generated of type $\\mathcal{W}(2,3,\\dots)$, and generated by the weights $2$ and $3$ fields. Subject to some mild constraints, all vertex algebras of type $\\mathcal{W}(2,3,\\dots, N)$ for some $N$ can be obtained as quotients of this universal algebra.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-06T04:50:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "vertex algebras",
      "universal two-parameter",
      "mild constraints",
      "longstanding physics conjecture",
      "unique two-parameter"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 52,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}