TY  - BOOK
AU  - Edward Frenkel 
AU  - Ben-Zvi, David
TI  - Vertex algebras and algebraic curves
SN  - 9780821836743
AV  - QA326 
PY  - 2004///]
CY  - Rhode Island
PB  - American Mathematical Society
KW  - Mathematics
N1  - 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 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

N2  - This book is an introduction to the theory of vertex algebras with a particular emphasis on the relationship with the geometry of algebraic curves. The notion of a vertex algebra is introduced in a coordinate-independent way, so that vertex operators become well defined on arbitrary smooth algebraic curves, possibly equipped with additional data, such as a vector bundle. Vertex algebras then appear as the algebraic objects encoding the geometric structure of various moduli spaces associated with algebraic curves. Therefore they may be used to give a geometric interpretation of various questions of representation theory. --- summary provided by publisher
ER  -