Lectures on Tensor Categories and Modular Functors

ISBN-13: 9780821826867 / Angielski / Miękka / 2001 / 222 str.

Bojko Bakalov; Alexander Kirillov

Opis

This title gives an exposition of the relations among the following three topics: monoidal tensor categories (such as a category of representations of a quantum group), 3-dimensional topological quantum field theory, and 2-dimensional modular functors (which naturally arise in 2-dimensional conformal field theory). The following examples are discussed in detail: the category of representations of a quantum group at a root of unity and the Wess-Zumino-Witten modular functor. The idea that these topics are related first appeared in the physics literature in the study of quantum field theory. The works of Witten and Moore-Seiberg triggered many papers, both physical and mathematical, exploring various aspects of these relations. Upon preparing to lecture on the topic at MIT, however, the authors discovered that the existing literature was difficult and incomplete. This text gathers results, fills existing gaps, and simplifies some proofs.