Lectures on Tensor Categories and Modular Functors
Jr. Bojko Bakalov and Alexander Kirillov
This 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 aspects of these relations. Upon preparing to lecture on the topic at MIT, however, the authors discovered that the existing literature was difficult and that there were gaps to fill. The text is wholly expository and finely succinct. It gathers results, fills existing gaps, and simplifies some proofs. The book makes an important addition to the existing literature on the topic. It would be suitable as a course text at the advanced-graduate level
카테고리:
년:
2001
출판사:
American Mathematical Society
언어:
english
페이지:
206
ISBN 10:
0821826867
ISBN 13:
9780821826867
시리즈:
University Lecture Series
파일:
PDF, 1.59 MB
IPFS:
,
english, 2001