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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
13.
Vertex Operator Superalgebras
13.1.
Super Vector Spaces
13.1.1.
Z/2Z-Grading
13.1.2.
Parity and Sign Rules
13.1.3.
Super-Commutativity
13.1.4.
Super-Lie Algebras
13.2.
Superalgebra Axioms
13.2.1.
Modified Locality
13.2.2.
Super-Jacobi Identity
13.2.3.
Parity Considerations
13.2.4.
Sign Conventions
13.3.
Neveu-Schwarz Algebra
13.3.1.
Super-Virasoro Algebra
13.3.2.
Ramond Algebra
13.3.3.
Spectral Flow
13.3.4.
Twisted Sectors
13.4.
Fermionic Constructions
13.4.1.
Free Fermion Algebra
13.4.2.
Boson-Fermion Correspondence
13.4.3.
Spin Representations
13.4.4.
Clifford Algebra Relations
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12. Zhu's Theory
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14. Rationality and Finiteness