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Vertex Algebras and Algebraic Curves, Second edition
About this Title
Edward Frenkel, University of California, Berkeley, CA and David Ben-Zvi, University of Chicago, Chicago, IL
Publication: Mathematical Surveys and Monographs
Publication Year:
2001; Volume 88
ISBNs: 978-0-8218-3674-3 (print); 978-1-4704-1315-6 (online)
DOI: https://doi.org/10.1090/surv/088
MathSciNet review: MR2082709
MSC: Primary 17B69; Secondary 14D21, 14H81, 17B67, 17B68, 81R10, 81T40
Table of Contents
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Front/Back Matter
Chapters
- 1. Definition of vertex algebras
- 2. Vertex algebras associated to Lie algebras
- 3. Associativity and operator product expansion
- 4. Applications of the operator product expansion
- 5. Modules over vertex algebras and more examples
- 6. Vertex algebra bundles
- 7. Action of internal symmetries
- 8. Vertex algebra bundles: Examples
- 9. Conformal blocks I
- 10. Conformal blocks II
- 11. Free field realization I
- 12. Free field realization II
- 13. The Knizhnik–Zamolodchikov equations
- 14. Solving the KZ equations
- 15. Quantum Drinfeld–Sokolov reduction and $\mathcal {W}$–algebras
- 16. Vertex Lie algebras and classical limits
- 17. Vertex algebras and moduli spaces I
- 18. Vertex algebras and moduli spaces II
- 19. Chiral algebras
- 20. Factorization