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    "paper_id": "34fac3d3-7f8c-40b5-b5c3-59163f46e8ad",
    "contributor_id": 3,
    "contributor_name": "ChenqiMeng",
    "base_hash": "ddca2d933f06b382b3f896da59bc7c16f1818edc860dfaf05f2736029f9c6af0",
    "title": "Introduction to Vertex Operator Algebras",
    "authors": "Chenqi Meng",
    "abstract": "Vertex operator algebra is a rigorous formulation of 2D chiral conformal field theory. This note reviews (will do!) its definition, construction, and properties. It in particular emphasizes the field (mathematics)-like properties of a VOA. A VOA can be viewed as a quantized field. We will eventually (hopefully) arrive at the quantum Galois theory of VOA.",
    "markdown_sha256": "5206be44ac3f641e3ef0d2fa2c7fb32da87fc0ba678f0becb894155a4fea9dc3",
    "explanation": "Expand the Virasoro covariance proof to show how the left-hand residues give the commutator, how the delta kernel produces the binomial expansion, and how the final residue selects n=j. The statement and the rest of the chapter are unchanged.",
    "submitted_at": "2026-10-28T08:25:57.286606+00:00",
    "primary_category": "math.QA",
    "secondary_categories": [],
    "license": "CC0-1.0",
    "agreement": {
      "version": "2026-10-19",
      "sha256": "12b437586e9f6a916c0b0d51430548ea47e644ef7d714f091056eb028088b106",
      "accepted_at": "2026-10-19T07:28:05.223110+00:00",
      "acceptance_id": 1
    },
    "chapters": [
      {
        "id": "about-this-note",
        "title": "About this note",
        "markdown_sha256": "a282a43eb783f5bc83de0faf631ac4e39c5bdccf82ea5833650b22c2cc2081c2"
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      {
        "id": "vertex-algebras",
        "title": "Vertex algebras: definitions and properties",
        "markdown_sha256": "cced358859fb48335d95d5c86362e2c1b94bd698b3805a612b196f644d032f92"
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      {
        "id": "vertex-operator-algebras",
        "title": "Vertex operator algebras",
        "markdown_sha256": "233e1c2fc1404892eaaa863191314eaeea246dc5af0a3fc56c7918a160bc4792"
      },
      {
        "id": "correlation-functions",
        "title": "Chiral correlation functions",
        "markdown_sha256": "915a637dc27b1a98d4f2ff519418227c5b3077d5ae8dfde50f72436f4df01159"
      },
      {
        "id": "modules",
        "title": "Modules and intertwining operators",
        "markdown_sha256": "871265dff96061879b1043ffa4a96caf4160999fd3b86790b402123fb2df09fb"
      },
      {
        "id": "tensor-categories",
        "title": "Vertex tensor categories",
        "markdown_sha256": "ea3cc4c149d8793faeb3cb3d4f1a6962aca839a2a123fc4b2ae2d65ad06c7aee"
      },
      {
        "id": "extensions",
        "title": "Extensions and quantum Galois theory",
        "markdown_sha256": "38c2ebc58642fa3cc00c09863fa0adde86ecb045c75f39ffc967589e3ded3978"
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    ],
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    "code": "CC0-1.0",
    "label": "CC0 1.0",
    "url": "https://creativecommons.org/publicdomain/zero/1.0/",
    "description": "Dedicate the work to the public domain to the extent legally possible. Reuse does not require attribution under CC0.",
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