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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
Vertex Operator Superalgebras
Super Vector Spaces
Z/2Z-Grading
Parity and Sign Rules
Super-Commutativity
Super-Lie Algebras
Superalgebra Axioms
Modified Locality
Super-Jacobi Identity
Parity Considerations
Sign Conventions
Neveu-Schwarz Algebra
Super-Virasoro Algebra
Ramond Algebra
Spectral Flow
Twisted Sectors
Fermionic Constructions
Free Fermion Algebra
Boson-Fermion Correspondence
Spin Representations
Clifford Algebra Relations
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12. Zhu's Theory
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14. Rationality and Finiteness