{
  "annotation_id": "d05db5f2-4eaa-4983-880f-931c0866def8",
  "date_created": "2026-03-02T18:01:25.147000Z",
  "date_modified": "2026-03-02T18:01:25.147000Z",
  "file_hash": "73d46f26d687174e42f1c25dbaf3c945ec9e5f74880131de2bf15059d5382f3e",
  "private": false,
  "record": {
    "abstract": "A key notion bridging the gap between {\\it quantum operator algebras}\n\\cite{LZ10} and {\\it vertex operator algebras} \\cite{Bor}\\cite{FLM} is the\ndefinition of the commutativity of a pair of quantum operators (see section 2\nbelow). This is not commutativity in any ordinary sense, but it is clearly the\ncorrect generalization to the quantum context. The main purpose of the current\npaper is to begin laying the foundations for a complete mathematical theory of\n{\\it commutative quantum operator algebras.} We give proofs of most of the\nrelevant results announced in \\cite{LZ10}, and we carry out some calculations\nwith sufficient detail to enable the interested reader to become proficient\nwith the algebra of commuting quantum operators.",
    "arxiv_id": "q-alg/9501014",
    "authors": [
      "Bong H. Lian",
      "Gregg J. Zuckerman"
    ],
    "categories": [
      "q-alg",
      "hep-th",
      "math.QA"
    ],
    "title": "Commutative Quantum Operator Algebras",
    "url": "https://arxiv.org/abs/q-alg/9501014"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "5db14ff7-3c7d-4a5b-b9bd-de97554ef5d9",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}