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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, and Victor Ostrik, University of Oregon, Eugene, OR
Mathematical Surveys and Monographs
2015; approx. 350 pp; hardcover
Volume: 205
ISBN-10: 1-4704-2024-4
ISBN-13: 978-1-4704-2024-6
List Price: US$110
Member Price: US$88
Order Code: SURV/205
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Not yet published.
Expected publication date is July 16, 2015.
See also:

Introduction to Representation Theory - Pavel Etingof, Oleg Golberg, Sebastian Hensel, Tiankai Liu, Alex Schwendner, Dmitry Vaintrob and Elena Yudovina

Hopf Algebras and Their Actions on Rings - Susan Montgomery

Lectures on Tensor Categories and Modular Functors - Bojko Bakalov and Alexander Kirillov, Jr

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.

Table of Contents

  • Abelian categories
  • Monoidal categories
  • \(\mathbb{Z}_+\)-rings
  • Tensor categories
  • Representation categories of Hopf algebras
  • Finite tensor categories
  • Module categories
  • Braided categories
  • Fusion categories
  • Bibliography
  • Index
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