{
  "annotation_id": "91f69187-4f86-4af9-8607-45a8edb408c9",
  "date_created": "2026-03-02T18:01:28.014000Z",
  "date_modified": "2026-03-02T18:01:28.014000Z",
  "file_hash": "41faddcc5f28988f047f5f2fdd90f2eb6a8b03d726ff79b2b8ba05eec32953da",
  "private": false,
  "record": {
    "abstract": "We prove a generalized rationality property and a new identity that we call\nthe ``Jacobi identity\u0027\u0027 for intertwining operator algebras. Most of the main\nproperties of genus-zero conformal field theories, including the main\nproperties of vertex operator algebras, modules, intertwining operators,\nVerlinde algebras, and fusing and braiding matrices, are incorporated into this\nidentity. Together with associativity and commutativity for intertwining\noperators proved by the author in \\cite{H2} and \\cite{H3}, the results of the\npresent paper solve completely the problem of finding a natural purely\nalgebraic structure on the direct sum of all inequivalent irreducible modules\nfor a suitable vertex operator algebra. Two equivalent definitions of\nintertwining operator algebra in terms of this Jacobi identity are given.",
    "arxiv_id": "q-alg/9704008",
    "authors": [
      "Yi-Zhi Huang"
    ],
    "categories": [
      "q-alg",
      "hep-th",
      "math.QA"
    ],
    "title": "Generalized Rationality and a \"Jacobi Identity\" for Intertwining   Operator Algebras",
    "url": "https://arxiv.org/abs/q-alg/9704008"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "9a6cc90f-d581-4401-9c71-ecef07ffc370",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}