# Vertex Operator Algebras and Related Areas

Share this page *Edited by *
*Maarten Bergvelt; Gaywalee Yamskulna; Wenhua Zhao*

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

## Vertex Operator Algebras and Related Areas

- Contents v6 free
- Preface vii8 free
- Biography of Geoffrey Mason ix10 free
- List of Ph.D. Students Advised by Geoffrey Mason xi12 free
- List of Talks xiii14 free
- List of Participants xv16 free
- An Analogue of Modular BPZ-Equation in Logarithmic (Super)Conformal Field Theory 120 free
- Vector-Valued Modular Forms 1938
- Alternate Notions of N=1 Superconformality and Deformations of N=1 Vertex Superalgebras 3352
- Hyperbolic Weyl Groups and the Four Normed Division Algebras 5372
- Zhu's Algebra, the C2 Algebra, and Twisted Modules 6584
- Fusion Algebras for Vertex Operator Algebras and Finite Groups 7998
- Rooted Trees and Symmetric Functions: Zhao's Homomorphism and the Commutative Hexagon 85104
- Representations of Vertex Operator Algebras and Braided Finite Tensor Categories 97116
- Recurrences and Characters of Feigin-Stoyanovsky's Type Subspaces 113132
- The FLM Conjecture and Framed VOA 125144
- On Quantum Vertex Algebras and Their Modules 139158
- Introduction to Invariant Chiral Differential Operators 157176
- Dynkin Operators and Renormalization Group Actions in pQFT 169188
- New Perspectives on Exponentiated Derivations, the Formal Taylor Theorem, and Faà Di Bruno's Formula 185204
- Combinatorial Bases of Feigin-Stoyanovsky’s Type Subspaces for sll+1(C) 199218
- Exceptional Vertex Operator Algebras and the Virasoro Algebra 213232