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Vertex Operator Algebras and Related Areas
Edited by: Maarten Bergvelt, University of Illinois at Urbana-Champaign, IL, and Gaywalee Yamskulna and Wenhua Zhao, Illinois State University, Normal, IL
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Contemporary Mathematics
2009; 227 pp; softcover
Volume: 497
ISBN-10: 0-8218-4840-2
ISBN-13: 978-0-8218-4840-1
List Price: US$79
Member Price: US$63.20
Order Code: CONM/497
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Vertex operator algebras were introduced to mathematics in the work of Richard Borcherds, Igor Frenkel, James Lepowsky and Arne Meurman as a mathematically rigorous formulation of chiral algebras of two-dimensional conformal field theory. The aim was to use vertex operator algebras to explain and prove the remarkable Monstrous Moonshine conjectures in group theory. The theory of vertex operator algebras has now grown into a major research area in mathematics.

These proceedings contain expository lectures and research papers presented during the international conference on Vertex Operator Algebras and Related Areas, held at Illinois State University in Normal, IL, from July 7 to July 11, 2008.

The main aspects of this conference were connections and interactions of vertex operator algebras with the following areas: conformal field theories, quantum field theories, Hopf algebra, infinite dimensional Lie algebras, and modular forms. This book will be useful for researchers as well as for graduate students in mathematics and physics. Its purpose is not only to give an up-to-date overview of the fields covered by the conference but also to stimulate new directions and discoveries by experts in the areas.

Readership

Graduate students and research mathematicians interested in vertex operator algebras and its relations to infinite-dimensional Lie algebra, quantum field theory, and modular forms.

Table of Contents

  • D. Adamović and A. Milas -- An analogue of modular BPZ-equation in logarithmic (super)conformal field theory
  • P. Bantay -- Vector-valued modular forms
  • K. Barron -- Alternate notions of N=1 superconformality and deformations of N=1 vertex superalgebras
  • A. J. Feingold, A. Kleinschmidt, and H. Nicolai -- Hyperbolic Weyl groups and the four normed division algebras
  • M. R. Gaberdiel and T. Gannon -- Zhu's algebra, the \(C_2\) algebra, and twisted modules
  • C. Goff -- Fusion algebras for vertex operator algebras and finite groups
  • M. E. Hoffman -- Rooted trees and symmetric functions: Zhao's homomorphism and the commutative hexagon
  • Y.-Z. Huang -- Representations of vertex operator algebras and braided finite tensor categories
  • M. Jerković -- Recurrences and characters of Feigin-Stoyanovsky's type subspaces
  • C. H. Lam and H. Yamauchi -- The FLM conjecture and framed VOA
  • H. Li -- On quantum vertex algebras and their modules
  • A. R. Linshaw -- Introduction to invariant chiral differential operators
  • F. Patras -- Dynkin operators and renormalization group actions in pQFT
  • T. J. Robinson -- New perspectives on exponentiated derivations, the formal Taylor theorem, and Faà di Bruno's formula
  • G. Trupčević -- Combinatorial bases of Feigin-Stoyanovsky's type subspaces for \(\tilde{\mathfrak{sl}}_{\ell+1}(\mathbb C)\)
  • M. P. Tuite -- Exceptional vertex operator algebras and the Virasoro algebra
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