Softcover ISBN: | 978-0-8218-2686-7 |
Product Code: | ULECT/21 |
List Price: | $69.00 |
MAA Member Price: | $62.10 |
AMS Member Price: | $55.20 |
eBook ISBN: | 978-1-4704-2168-7 |
Product Code: | ULECT/21.E |
List Price: | $65.00 |
MAA Member Price: | $58.50 |
AMS Member Price: | $52.00 |
Softcover ISBN: | 978-0-8218-2686-7 |
eBook: ISBN: | 978-1-4704-2168-7 |
Product Code: | ULECT/21.B |
List Price: | $134.00 $101.50 |
MAA Member Price: | $120.60 $91.35 |
AMS Member Price: | $107.20 $81.20 |
Softcover ISBN: | 978-0-8218-2686-7 |
Product Code: | ULECT/21 |
List Price: | $69.00 |
MAA Member Price: | $62.10 |
AMS Member Price: | $55.20 |
eBook ISBN: | 978-1-4704-2168-7 |
Product Code: | ULECT/21.E |
List Price: | $65.00 |
MAA Member Price: | $58.50 |
AMS Member Price: | $52.00 |
Softcover ISBN: | 978-0-8218-2686-7 |
eBook ISBN: | 978-1-4704-2168-7 |
Product Code: | ULECT/21.B |
List Price: | $134.00 $101.50 |
MAA Member Price: | $120.60 $91.35 |
AMS Member Price: | $107.20 $81.20 |
-
Book DetailsUniversity Lecture SeriesVolume: 21; 2001; 221 ppMSC: 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), 3-dimensional topological quantum field theory, and 2-dimensional modular functors (which naturally arise in 2-dimensional 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 Wess-Zumino-Witten 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 Moore-Seiberg 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 advanced-graduate 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. 3-dimensional topological quantum field theory
-
Chapter 5. Modular functors
-
Chapter 6. Moduli spaces and complex modular functors
-
Chapter 7. Wess-Zumino-Witten model
-
-
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
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), 3-dimensional topological quantum field theory, and 2-dimensional modular functors (which naturally arise in 2-dimensional 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 Wess-Zumino-Witten 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 Moore-Seiberg 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 advanced-graduate 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. 3-dimensional topological quantum field theory
-
Chapter 5. Modular functors
-
Chapter 6. Moduli spaces and complex modular functors
-
Chapter 7. Wess-Zumino-Witten model