Tensor Categories

Pavel Etingof, Shlomo Gelaki, Dmitri Nikshych, Victor Ostrik (Autoren)

Buch | Hardcover

350 Seiten

2015
American Mathematical Society (Verlag)
978-1-4704-2024-6 (ISBN)

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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.

Pavel Etingof, Massachusetts Institute of Technology, Cambridge, MA, USA. Shlomo Gelaki, Technion - Israel Institute of Technology, Haifa, Israel. Dmitri Nikshych, University of New Hampshire, Durham, NH, USA. Victor Ostrik, University of Oregon, Eugene, OR, USA.

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

Erscheint lt. Verlag	30.8.2015
Reihe/Serie	Mathematical Surveys and Monographs
Verlagsort	Providence
Sprache	englisch
Maße	178 x 254 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
ISBN-10	1-4704-2024-4 / 1470420244
ISBN-13	978-1-4704-2024-6 / 9781470420246
Zustand	Neuware