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    "paper_id": "34fac3d3-7f8c-40b5-b5c3-59163f46e8ad",
    "contributor_id": 3,
    "contributor_name": "ChenqiMeng",
    "base_hash": "ccad06b5be9428916434470a51eab47f915f24e5bf6edb0ff7cabdab52cea822",
    "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": "3c575e635e8b0bd7aa9a806f1d2a1f18932061144378f76a0be3abd526d45105",
    "explanation": "Add the G-orbifolds chapter after Basic structure of VOAs. Define fixed-point VOAs, record their inherited conformal structure, and develop averaging, simplicity, and fixed points in stages. Leave routine verifications as exercises and cite the cyclicity result used in the simplicity proof. Defer characters and module-theoretic topics.",
    "submitted_at": "2026-10-28T13:57:38.560740+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": "orbifolds",
        "title": "G-orbifolds",
        "markdown_sha256": "05f532514873e6c50c9d8cac3c3242f271adb484aebb0b02c22c3ef925144b6b"
      },
      {
        "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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    "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.",
    "declaration": null
  }
}