Softcover ISBN:  9780821826867 
Product Code:  ULECT/21 
221 pp 
List Price:  $39.00 
MAA Member Price:  $35.10 
AMS Member Price:  $31.20 
Electronic ISBN:  9781470421687 
Product Code:  ULECT/21.E 
221 pp 
List Price:  $36.00 
MAA Member Price:  $32.40 
AMS Member Price:  $28.80 

Book DetailsUniversity Lecture SeriesVolume: 21; 2001MSC: Primary 18; 81; 57; Secondary 17;
This book gives an exposition of the relations among the following three topics: monoidal tensor categories (such as a category of representations of a quantum group), 3dimensional topological quantum field theory, and 2dimensional modular functors (which naturally arise in 2dimensional conformal field theory). The following examples are discussed in detail: the category of representations of a quantum group at a root of unity and the WessZuminoWitten modular functor.
The idea that these topics are related first appeared in the physics literature in the study of quantum field theory. Pioneering works of Witten and MooreSeiberg triggered an avalanche of papers, both physical and mathematical, exploring various aspects of these relations. Upon preparing to lecture on the topic at MIT, however, the authors discovered that the existing literature was difficult and that there were gaps to fill.
The text is wholly expository and finely succinct. It gathers results, fills existing gaps, and simplifies some proofs. The book makes an important addition to the existing literature on the topic. It would be suitable as a course text at the advancedgraduate level.ReadershipGraduate students and research mathematicians interested in representation theory and mathematical physics

Table of Contents

Chapters

Introduction

Chapter 1. Braided tensor categories

Chapter 2. Ribbon categories

Chapter 3. Modular tensor categories

Chapter 4. 3dimensional topological quantum field theory

Chapter 5. Modular functors

Chapter 6. Moduli spaces and complex modular functors

Chapter 7. WessZuminoWitten model


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This book gives an exposition of the relations among the following three topics: monoidal tensor categories (such as a category of representations of a quantum group), 3dimensional topological quantum field theory, and 2dimensional modular functors (which naturally arise in 2dimensional conformal field theory). The following examples are discussed in detail: the category of representations of a quantum group at a root of unity and the WessZuminoWitten modular functor.
The idea that these topics are related first appeared in the physics literature in the study of quantum field theory. Pioneering works of Witten and MooreSeiberg triggered an avalanche of papers, both physical and mathematical, exploring various aspects of these relations. Upon preparing to lecture on the topic at MIT, however, the authors discovered that the existing literature was difficult and that there were gaps to fill.
The text is wholly expository and finely succinct. It gathers results, fills existing gaps, and simplifies some proofs. The book makes an important addition to the existing literature on the topic. It would be suitable as a course text at the advancedgraduate level.
Graduate students and research mathematicians interested in representation theory and mathematical physics

Chapters

Introduction

Chapter 1. Braided tensor categories

Chapter 2. Ribbon categories

Chapter 3. Modular tensor categories

Chapter 4. 3dimensional topological quantum field theory

Chapter 5. Modular functors

Chapter 6. Moduli spaces and complex modular functors

Chapter 7. WessZuminoWitten model