eBook ISBN:  9780821881767 
Product Code:  CONM/497.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
eBook ISBN:  9780821881767 
Product Code:  CONM/497.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 

Book DetailsContemporary MathematicsVolume: 497; 2009; 227 ppMSC: Primary 17; 05; 11; 81; 16
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 twodimensional 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 uptodate overview of the fields covered by the conference but also to stimulate new directions and discoveries by experts in the areas.
ReadershipGraduate students and research mathematicians interested in vertex operator algebras and its relations to infinitedimensional Lie algebra, quantum field theory, and modular forms.

Table of Contents

Articles

Dražen Adamović and Antun Milas — An analogue of modular BPZequation in logarithmic (super)conformal field theory [ MR 2568395 ]

P. Bantay — Vectorvalued modular forms [ MR 2568396 ]

Katrina Barron — Alternate notions of $N=1$ superconformality and deformations of $N=1$ vertex superalgebras [ MR 2568397 ]

Alex J. Feingold, Axel Kleinschmidt and Hermann Nicolai — Hyperbolic Weyl groups and the four normed division algebras [ MR 2568398 ]

Matthias R. Gaberdiel and Terry Gannon — Zhu’s algebra, the $C_2$ algebra, and twisted modules [ MR 2568399 ]

Christopher Goff — Fusion algebras for vertex operator algebras and finite groups [ MR 2568400 ]

Michael E. Hoffman — Rooted trees and symmetric functions: Zhao’s homomorphism and the commutative hexagon [ MR 2568401 ]

YiZhi Huang — Representations of vertex operator algebras and braided finite tensor categories [ MR 2568402 ]

Miroslav Jerković — Recurrences and characters of FeiginStoyanovsky’s type subspaces [ MR 2568403 ]

Ching Hung Lam and Hiroshi Yamauchi — The FLM conjecture and framed VOA [ MR 2568404 ]

Haisheng Li — On quantum vertex algebras and their modules [ MR 2568405 ]

Andrew R. Linshaw — Introduction to invariant chiral differential operators [ MR 2568406 ]

Frédéric Patras — Dynkin operators and renormalization group actions in pQFT [ MR 2568407 ]

Thomas J. Robinson — New perspectives on exponentiated derivations, the formal Taylor theorem, and Faà di Bruno’s formula [ MR 2568408 ]

Goran Trupčević — Combinatorial bases of FeiginStoyanovsky’s type subspaces for $\tilde {\mathfrak {sl}}_{l+1}(\Bbb C)$ [ MR 2568409 ]

Michael P. Tuite — Exceptional vertex operator algebras and the Virasoro algebra [ MR 2568410 ]


Additional Material

RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
 Book Details
 Table of Contents
 Additional Material
 Requests
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 twodimensional 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 uptodate overview of the fields covered by the conference but also to stimulate new directions and discoveries by experts in the areas.
Graduate students and research mathematicians interested in vertex operator algebras and its relations to infinitedimensional Lie algebra, quantum field theory, and modular forms.

Articles

Dražen Adamović and Antun Milas — An analogue of modular BPZequation in logarithmic (super)conformal field theory [ MR 2568395 ]

P. Bantay — Vectorvalued modular forms [ MR 2568396 ]

Katrina Barron — Alternate notions of $N=1$ superconformality and deformations of $N=1$ vertex superalgebras [ MR 2568397 ]

Alex J. Feingold, Axel Kleinschmidt and Hermann Nicolai — Hyperbolic Weyl groups and the four normed division algebras [ MR 2568398 ]

Matthias R. Gaberdiel and Terry Gannon — Zhu’s algebra, the $C_2$ algebra, and twisted modules [ MR 2568399 ]

Christopher Goff — Fusion algebras for vertex operator algebras and finite groups [ MR 2568400 ]

Michael E. Hoffman — Rooted trees and symmetric functions: Zhao’s homomorphism and the commutative hexagon [ MR 2568401 ]

YiZhi Huang — Representations of vertex operator algebras and braided finite tensor categories [ MR 2568402 ]

Miroslav Jerković — Recurrences and characters of FeiginStoyanovsky’s type subspaces [ MR 2568403 ]

Ching Hung Lam and Hiroshi Yamauchi — The FLM conjecture and framed VOA [ MR 2568404 ]

Haisheng Li — On quantum vertex algebras and their modules [ MR 2568405 ]

Andrew R. Linshaw — Introduction to invariant chiral differential operators [ MR 2568406 ]

Frédéric Patras — Dynkin operators and renormalization group actions in pQFT [ MR 2568407 ]

Thomas J. Robinson — New perspectives on exponentiated derivations, the formal Taylor theorem, and Faà di Bruno’s formula [ MR 2568408 ]

Goran Trupčević — Combinatorial bases of FeiginStoyanovsky’s type subspaces for $\tilde {\mathfrak {sl}}_{l+1}(\Bbb C)$ [ MR 2568409 ]

Michael P. Tuite — Exceptional vertex operator algebras and the Virasoro algebra [ MR 2568410 ]