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    "contributor_id": 3,
    "contributor_name": "ChenqiMeng",
    "base_hash": "4d9a882000816d49a6295fd33fad7663cdf8a5badc831cc3ead45ce6ceb37a20",
    "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": "437a70f8fdf9d30e99e43f658a6b5f58adaf2dd3f862a78fa91d58a619ed6a34",
    "explanation": "Revise the constructions chapter as Basic structure of VOAs. Use field notation for definitions, leave routine verifications as exercises, and add ideals, simplicity, quotient VOAs, kernels, and the unique simple quotient for CFT type. Remove the orbifold and coset placeholders from this chapter; their separate chapters are reserved for a later submission.",
    "submitted_at": "2026-10-28T13:19:36.883649+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": "e129af1e12b564976535a6cf671334e2e26059aee4ac1266bbf90fe779b57d4b"
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      {
        "id": "vertex-algebras",
        "title": "Vertex algebras",
        "markdown_sha256": "d551a16fd743f5a7f52975fe24ecb5692606de9ee4d23840970a6ee56209eaf4"
      },
      {
        "id": "vertex-operator-algebras",
        "title": "Vertex operator algebras",
        "markdown_sha256": "4dc3385252cd28ce8faa47aa712d67a8711875f8db8248e573f702e64c5190f0"
      },
      {
        "id": "constructions",
        "title": "Basic structure of VOAs",
        "markdown_sha256": "9f9702bc76754b368be0657ce7fbf7f83457d8845c68c0ce892acde5c736095b"
      },
      {
        "id": "examples",
        "title": "Examples of VOAs",
        "markdown_sha256": "1041c5031ebc9fe9a068b27eac02a6e06aa5eca7c47949f79f5c12521e9129ab"
      },
      {
        "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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    "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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}