Lectures on Tensor Categories and Modular Functors by Bojko B... - 9780821826867

Lectures on Tensor Categories and Modular FunctorsAuthor(s): Bojko Bakalov, Alexander A. Kirillov, Jr.\nFormat: Paperback\nPublisher: American Mathematical Society, United States\nImprint: American Mathematical Society\nISBN-13: 9780821826867, 978-0821826867\nSynopsis\nThis book 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. Pioneering works of Witten and Moore-Seiberg triggered an avalanche of papers, both physical and mathematical, exploring various aspe.