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Tensor Categories

Pavel Etingof Massachusetts Institute of Technology, Cambridge, MA
Shlomo Gelaki Technion-Israel Institute of Technology, Haifa, Israel
Dmitri Nikshych University of New Hampshire, Durham, NH
Victor Ostrik University of Oregon, Eugene, OR
Available Formats:
Softcover ISBN: 978-1-4704-3441-0
Product Code: SURV/205.S
List Price: $69.00 MAA Member Price:$62.10
AMS Member Price: $55.20 Electronic ISBN: 978-1-4704-2349-0 Product Code: SURV/205.E List Price:$65.00
MAA Member Price: $58.50 AMS Member Price:$52.00
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List Price: $103.50 MAA Member Price:$93.15
AMS Member Price: $82.80 Click above image for expanded view Tensor Categories Pavel Etingof Massachusetts Institute of Technology, Cambridge, MA Shlomo Gelaki Technion-Israel Institute of Technology, Haifa, Israel Dmitri Nikshych University of New Hampshire, Durham, NH Victor Ostrik University of Oregon, Eugene, OR Available Formats:  Softcover ISBN: 978-1-4704-3441-0 Product Code: SURV/205.S  List Price:$69.00 MAA Member Price: $62.10 AMS Member Price:$55.20
 Electronic ISBN: 978-1-4704-2349-0 Product Code: SURV/205.E
 List Price: $65.00 MAA Member Price:$58.50 AMS Member Price: $52.00 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$103.50 MAA Member Price: $93.15 AMS Member Price:$82.80
• Book Details

Mathematical Surveys and Monographs
Volume: 2052015; 344 pp
MSC: Primary 17; 18; 19; 20;

Is there a vector space whose dimension is the golden ratio? Of course not—the golden ratio is not an integer! But this can happen for generalizations of vector spaces—objects of a tensor category. The theory of tensor categories is a relatively new field of mathematics that generalizes the theory of group representations. It has deep connections with many other fields, including representation theory, Hopf algebras, operator algebras, low-dimensional topology (in particular, knot theory), homotopy theory, quantum mechanics and field theory, quantum computation, theory of motives, etc. This book gives a systematic introduction to this theory and a review of its applications. While giving a detailed overview of general tensor categories, it focuses especially on the theory of finite tensor categories and fusion categories (in particular, braided and modular ones), and discusses the main results about them with proofs. In particular, it shows how the main properties of finite-dimensional Hopf algebras may be derived from the theory of tensor categories.

Many important results are presented as a sequence of exercises, which makes the book valuable for students and suitable for graduate courses. Many applications, connections to other areas, additional results, and references are discussed at the end of each chapter.

Graduate students and research mathematicians interested in category theory and Hopf algebras.

• Chapters
• Chapter 1. Abelian categories
• Chapter 2. Monoidal categories
• Chapter 3. $\mathbb {Z}_+$-rings
• Chapter 4. Tensor categories
• Chapter 5. Representation categories of Hopf algebras
• Chapter 6. Finite tensor categories
• Chapter 7. Module categories
• Chapter 8. Braided categories
• Chapter 9. Fusion categories

• Requests

Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Volume: 2052015; 344 pp
MSC: Primary 17; 18; 19; 20;

Is there a vector space whose dimension is the golden ratio? Of course not—the golden ratio is not an integer! But this can happen for generalizations of vector spaces—objects of a tensor category. The theory of tensor categories is a relatively new field of mathematics that generalizes the theory of group representations. It has deep connections with many other fields, including representation theory, Hopf algebras, operator algebras, low-dimensional topology (in particular, knot theory), homotopy theory, quantum mechanics and field theory, quantum computation, theory of motives, etc. This book gives a systematic introduction to this theory and a review of its applications. While giving a detailed overview of general tensor categories, it focuses especially on the theory of finite tensor categories and fusion categories (in particular, braided and modular ones), and discusses the main results about them with proofs. In particular, it shows how the main properties of finite-dimensional Hopf algebras may be derived from the theory of tensor categories.

Many important results are presented as a sequence of exercises, which makes the book valuable for students and suitable for graduate courses. Many applications, connections to other areas, additional results, and references are discussed at the end of each chapter.

Graduate students and research mathematicians interested in category theory and Hopf algebras.

• Chapters
• Chapter 1. Abelian categories
• Chapter 2. Monoidal categories
• Chapter 3. $\mathbb {Z}_+$-rings
• Chapter 4. Tensor categories
• Chapter 5. Representation categories of Hopf algebras
• Chapter 6. Finite tensor categories
• Chapter 7. Module categories
• Chapter 8. Braided categories
• Chapter 9. Fusion categories
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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