Vertex Algebras and Algebraic Curves

Edward Frenkel, David Ben-Zvi

348 pages, parution le 01/05/2001

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Résumé

Drawing on notes from courses Frankel has taught at Harvard and the University of California-Berkeley, he and Ben-Zvi introduce the theory of vertex algebras with a particular emphasis on their relationship with the geometry of algebraic curves. Assuming no more than standard college algebra, they strive to bridge the gap between the algebraic and geometric approaches. They do proceed to more advanced topics in later chapters, so readers experienced with the algebras might also find useful information.

Contents

Preface

Introduction

Ch. 1 Definition of Vertex Algebras
Ch. 2 Vertex Algebras Associated to Lie Algebras
Ch. 3 Associativity and Operator Product Expansion
Ch. 4 Rational Vertex Algebras
Ch. 5 Vertex Algebra Bundles
Ch. 6 Action of Internal Symmetries
Ch. 7 Vertex Algebra Bundles: Examples
Ch. 8 Conformal Blocks I
Ch. 9 Conformal Blocks II
Ch. 10 Free Field Realization I
Ch. 11 Free Field Realization II
Ch. 12 The Knizhnik-Zamolodchikov Equations
Ch. 13 Solving the KZ Equations
Ch. 14 Quantum Drinfeld-Sokolov Reduction and W-algebras
Ch. 15 Vertex Lie Algebras and Classical Limits
Ch. 16 Vertex Algebras and Moduli Spaces I
Ch. 17 Vertex Algebras and Moduli Spaces II
Ch. 18 Chiral Algebras

App. A.1 Discs, formal discs and ind-schemes
App. A.2 Connections
App. A.3 Lie algebroids and D-modules
App. A.4 Lie algebra cohomology

Bibliography

Index

List of Frequently Used Notation

L'auteur - Edward Frenkel

University of California, Berkeley

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L'auteur - David Ben-Zvi

University of Chicago, IL

Caractéristiques techniques

	PAPIER
Éditeur(s)	American Mathematical Society (AMS)
Auteur(s)	Edward Frenkel, David Ben-Zvi
Parution	01/05/2001
Nb. de pages	348
Format	18 x 26
Couverture	Relié
Poids	833g
Intérieur	Noir et Blanc
EAN13	9780821828946