Tensor categories

著者

• Etingof, P. I. (Pavel I.)
• Gelaki, Shlomo
• Nikshych, Dmitri
• Ostrik, Viktor Valentinovich

書誌事項

Tensor categories

Pavel Etingof ... [et al.]

（Mathematical surveys and monographs, v. 205）

American Mathematical Society, c2015

• : softcover

注記

Other authors: Shlomo Gelaki, Dmitri Nikshych, Victor Ostrik

Includes bibliographical references (p. 325-337) and index

内容説明・目次

巻冊次

ISBN 9781470420246

内容説明

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.

目次

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

巻冊次

: softcover ISBN 9781470434410

内容説明

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.

目次

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

「Nielsen BookData」 より

詳細情報

• NII書誌ID(NCID): BB19193476
• ISBN:
  • 9781470420246
  • 9781470434410
• LCCN: 2015006773
• 出版国コード: us
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Providence, R.I.
• ページ数/冊数: xvi, 343 p.
• 大きさ: 27 cm
• 分類:
  • LCC : QA612
  • DC23 : 512/.57
• 件名:
  • LCSH : Algebraic topology
  • LCSH : Tensor fields
  • LCSH : Hopf algebras
• 親書誌ID:
  • BA00134419