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Mathematics
Vertex Algebras
1. Foundations and Motivation
2. Mathematical Preliminaries
3. Basic Structure of Vertex Algebras
4. Axioms and Fundamental Properties
5. Core Operations and Concepts
6. Fundamental Examples
7. Affine Vertex Algebras
8. Virasoro and Conformal Structure
9. Module Theory and Representations
10. Advanced Constructions
11. Intertwining Operators and Fusion
12. Zhu's Theory
13. Vertex Operator Superalgebras
14. Rationality and Finiteness
15. Moonshine and Connections
16. Computational Aspects
17. Applications and Related Areas
Zhu's Theory
Zhu's Algebra A(V)
Construction and Definition
Multiplication Formula
Unit Element
Examples and Calculations
Module Correspondence
Functor to A(V)-modules
Irreducible Module Classification
Character Theory
Finiteness Conditions
Higher Zhu Algebras
A_n(V) Constructions
C_2-Algebra
Applications to Rationality
Modular Invariance
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11. Intertwining Operators and Fusion
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13. Vertex Operator Superalgebras