Introduction to Vertex Operator Algebras

AcceptedSubmitted by ChenqiMeng · via CLI27 Oct 2026, 12:45 UTC

Accepted 27 Oct 2026, 12:46 UTC

math.QA — Quantum Algebra · Primary

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Snapshot 261027.d00baeb1d1a3 — Changed abstract and the introduction.

Changed abstract and the introduction.

Submission hash: d00baeb1d1a3f6b8c5fe5802a6d059fea30e99167bf61bcc161fba349ec93145
Base version: 261022.e59efb3016b7

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Abstract

− These developing notes introduce vertex operator algebras, assuming familiarity with formal calculus. The current substantive chapter derives creation, translation, skew-symmetry, product and iterate expansions, weak associativity, and the Jacobi identity from the locality axioms of a vertex algebra. The remaining chapters outline conformal structures, chiral correlation functions, modules and intertwining operators, vertex tensor categories, extensions, and quantum Galois theory.

+ 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.

--- Base version+++ Proposed version@@ -2,4 +2,4 @@  - Scope: foundations of vertex operator algebras and their applications. - Prerequisites: formal calculus.-- Roadmap: VA axioms and properties → conformal structure → chiral correlation functions → modules → tensor categories → extensions and quantum Galois theory.+- Roadmap: VA axioms and properties → conformal structure → chiral correlation functions → orbifold and coset constructions → modules → tensor categories → extensions and quantum Galois theory.

Accepted by ChenqiMeng on 27 Oct 2026, 12:46 UTC. The submitted snapshot is preserved.

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