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Lectures on Tensor Categories and Modular Functors
 
Bojko Bakalov University of California, Berkeley, Berkeley, CA
Alexander Kirillov, Jr. SUNY at Stony Brook, Stony Brook, NY
Lectures on Tensor Categories and Modular Functors
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
Lectures on Tensor Categories and Modular Functors
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Lectures on Tensor Categories and Modular Functors
Bojko Bakalov University of California, Berkeley, Berkeley, CA
Alexander Kirillov, Jr. SUNY at Stony Brook, Stony Brook, NY
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 Details
     
     
    University Lecture Series
    Volume: 212001; 221 pp
    MSC: 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.

    Readership

    Graduate 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
     
     
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 212001; 221 pp
MSC: 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.

Readership

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
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.