Tensor Categories

Pavel Etingof · Shlomo Gelaki · Dmitri Nikshych · Victor Ostrik

2016년 8월 · Mathematical Surveys and Monographs 205권 · American Mathematical Soc.

eBook

344

페이지

검증되지 않은 평점과 리뷰입니다. 자세히 알아보기

eBook 정보

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.

저자 정보

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,
Victor Ostrik: University of Oregon, Eugene, OR