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Tensor Categories

By: Pavel Etingof,Shlomo Gelaki,Dmitri Nikshych,Victor Ostrik

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Tensor Categories

By: Pavel Etingof,Shlomo Gelaki,Dmitri Nikshych,Victor Ostrik

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.

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Page Count

362

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470434415

ISBN 13

9781470434410

Tensor Categories

By: Pavel Etingof,Shlomo Gelaki,Dmitri Nikshych,Victor Ostrik

Write a review Read reviews Take a Quiz Solve Book Puzzle

Tensor Categories

By: Pavel Etingof,Shlomo Gelaki,Dmitri Nikshych,Victor Ostrik

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.

Average ratings

N/A

5

0%

4

0%

3

0%

2

0%

1

0%

Solve jigsaw puzzle

Age

Page Count

362

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470434415

ISBN 13

9781470434410