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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
Advanced Constructions
Orbifold Theory
Automorphism Groups
Fixed Point Subalgebras
Twisted Sectors
Orbifold Models
G-Twisted Modules
Coset Construction
GKO Construction
Branching Rules
Coset Conformal Vectors
Minimal Models
Parafermion Algebras
Extension Theory
Simple Current Extensions
Abelian Extensions
Non-Abelian Extensions
Classification Problems
Tensor Product Theory
Fusion Products
Intertwining Operators
Braiding and Associativity
Modular Tensor Categories
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9. Module Theory and Representations
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11. Intertwining Operators and Fusion