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Quantum Groups, Quantum Categories and Quantum Field Theory

  • Authors
  • Jürg Fröhlich
  • Thomas Kerler

Part of the Lecture Notes in Mathematics book series (LNM, volume 1542)

Table of contents

  1. Front Matter
    Pages I-VII
  2. Jürg Fröhlich, Thomas Kerler
    Pages 1-16
  3. Jürg Fröhlich, Thomas Kerler
    Pages 17-44
  4. Jürg Fröhlich, Thomas Kerler
    Pages 45-101
  5. Jürg Fröhlich, Thomas Kerler
    Pages 102-118
  6. Jürg Fröhlich, Thomas Kerler
    Pages 119-140
  7. Jürg Fröhlich, Thomas Kerler
    Pages 284-411
  8. Back Matter
    Pages 412-431

About this book

Introduction

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.

Keywords

Braid Groups Group theory Quantum Field Theory Quantum Groups Representation theory Tensor Categories algebra

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0084244
  • Copyright Information Springer-Verlag Berlin Heidelberg 1993
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-56623-6
  • Online ISBN 978-3-540-47611-5
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site