Tensor categories

by Etingof, P. I., (Pavel I.) Gelaki, Shlomo Nikshych, Dmitri Ostrik, Victor

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Title Statements

Full title :Tensor categories / Pavel Etingof, Shlomo Gelaki, Dmitri Nikshych, Victor Ostrik.

Summary

"Is there a vector space whose dimension is not 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"--Back cover.

Edition Statements

Publication Date:©2015

Publication Statements

Publisher(s):American mathematical Society
Place of Publication:Providence, Rhode Island
Language:eng
Publication Date:©2015

The Physical Object

Description:xvi, 343 pages ; : 27 cm.

Edition Identifiers

ISBN:9781470420246, 1470420244, 9781470434410, 1470434415
oclc:ocn904144361
LC Classification:QA612
Dewey Decimal:512/.57

Abelian categories -- Monoidal categories -- Z₊-rings -- Tensor categories -- Repreentation categories of Hopf algebras -- Finite tensor categories -- Module categories -- Braided categories -- Fusion categories.

Subjects

$K$-theory -- Higher algebraic $K$-theo… Algebraic topology Algèbres de Hopf Associative rings and algebras -- Hopf … Category theory; homological algebra --… Champs tensoriels Group theory and generalizations -- Lin… Hopf algebras Nonassociative rings and algebras -- Li… Tensor fields Topologie algébrique