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    "submission_id": "5daec1df-51b4-4e9e-8c96-0614856b4f92",
    "paper_id": "34fac3d3-7f8c-40b5-b5c3-59163f46e8ad",
    "contributor_id": 3,
    "contributor_name": "ChenqiMeng",
    "base_hash": "9c52d363e410f87ebbc1d7dabba1525156a2aca556012813a4b7e8a39c70e76b",
    "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": "934d6b82857c5cb5842c53900f1e12b80de130a3373257d364dc0fa4444b00bd",
    "explanation": "Extend the weight-one discussion with the canonical invariant symmetric bilinear form and affine current algebra, including short proofs from skew-symmetry and Jacobi. Add inner automorphisms after the automorphism definitions, prove that weight-one zero-mode exponentials preserve the fields and conformal vector, and explain the integrated group action and its possible kernel. Distinguish invariance from nondegeneracy and include references. Changes are confined to the Vertex operator algebras and Basic structure of VOAs chapters.",
    "submitted_at": "2026-10-29T14:41:40.175925+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"
      },
      {
        "id": "vertex-algebras",
        "title": "Vertex algebras",
        "markdown_sha256": "d551a16fd743f5a7f52975fe24ecb5692606de9ee4d23840970a6ee56209eaf4"
      },
      {
        "id": "vertex-operator-algebras",
        "title": "Vertex operator algebras",
        "markdown_sha256": "b1999c78e5257dd32455b354d1db6008996b440fd7d4f3aabc0b9d42a2f14438"
      },
      {
        "id": "constructions",
        "title": "Basic structure of VOAs",
        "markdown_sha256": "692053fdeaa5cd76ac8e7f593b0a8352f85e1878c12888ede040a734775881a8"
      },
      {
        "id": "orbifolds",
        "title": "G-orbifolds",
        "markdown_sha256": "e155dd89c549102449aa82463e19aed200b56ffab8360b90c508414aa43b4313"
      },
      {
        "id": "cosets",
        "title": "Commutants and cosets",
        "markdown_sha256": "249f6c1af80e73888edf39614b16c3412a2d3b3201d1fd870120d405aad4412b"
      },
      {
        "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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  "licensing": {
    "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
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}