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.

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Bibliographic Information

Book Title: Quantum Groups, Quantum Categories and Quantum Field Theory
Authors: Jürg Fröhlich, Thomas Kerler
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/BFb0084244
Publisher: Springer Berlin, Heidelberg
eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag Berlin Heidelberg 1993
Softcover ISBN: 978-3-540-56623-6Published: 12 May 1993
eBook ISBN: 978-3-540-47611-5Published: 15 November 2006
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: VIII, 432
Topics: K-Theory, Group Theory and Generalizations, Analysis, Quantum Information Technology, Spintronics, Quantum Physics

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Table of contents (8 chapters)

Front Matter

Back Matter

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