Jürg Fröhlich, Thomas Kerler (auth.)3540566236, 9783540566236, 0387566236
This book reviews recent results on low-dimensional quantum field theories and their connection with quantum group theory and the theory of braided, balanced tensor categories. It presents detailed, mathematically precise introductions to these subjects and then continues with new results. Among the main results are a detailed analysis of the representation theory of U (sl ), for q a primitive root of unity, and a semi-simple quotient thereof, a classfication of braided tensor categories generated by an object of q-dimension less than two, and an application of these results to the theory of sectors in algebraic quantum field theory. This clarifies the notion of “quantized symmetries” in quantum fieldtheory. The reader is expected to be familiar with basic notions and resultsin algebra. The book is intended for research mathematicians, mathematical physicists and graduate students. |
Table of contents :
Introduction and survey of results….Pages 1-16
Local quantum theory with braid group statistics….Pages 17-44
Superselection sectors and the structure of fusion rule algebras….Pages 45-101
Hopf algebras and quantum groups at roots of unity….Pages 102-118
Representation theory of U q red ( sℓ 2 )….Pages 119-140
Path representations of the braid groups for quantum groups at roots of unity….Pages 141-175
Duality theory for local quantum theories, dimensions and balancing in quantum categories….Pages 176-283
The quantum categories with a generator of dimension less than two….Pages 284-411 |
Reviews
There are no reviews yet.