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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
10.
Advanced Constructions
10.1.
Orbifold Theory
10.1.1.
Automorphism Groups
10.1.2.
Fixed Point Subalgebras
10.1.3.
Twisted Sectors
10.1.4.
Orbifold Models
10.1.5.
G-Twisted Modules
10.2.
Coset Construction
10.2.1.
GKO Construction
10.2.2.
Branching Rules
10.2.3.
Coset Conformal Vectors
10.2.4.
Minimal Models
10.2.5.
Parafermion Algebras
10.3.
Extension Theory
10.3.1.
Simple Current Extensions
10.3.2.
Abelian Extensions
10.3.3.
Non-Abelian Extensions
10.3.4.
Classification Problems
10.4.
Tensor Product Theory
10.4.1.
Fusion Products
10.4.2.
Intertwining Operators
10.4.3.
Braiding and Associativity
10.4.4.
Modular Tensor Categories
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9. Module Theory and Representations
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11. Intertwining Operators and Fusion