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Quantum Isometry Groups

  • Debashish Goswami
  • Jyotishman Bhowmick

Part of the Infosys Science Foundation Series book series (ISFS)

Also part of the Infosys Science Foundation Series in Mathematical Sciences book sub series (ISFM)

Table of contents

  1. Front Matter
    Pages i-xxviii
  2. Debashish Goswami, Jyotishman Bhowmick
    Pages 1-35
  3. Debashish Goswami, Jyotishman Bhowmick
    Pages 37-67
  4. Debashish Goswami, Jyotishman Bhowmick
    Pages 69-95
  5. Debashish Goswami, Jyotishman Bhowmick
    Pages 97-127
  6. Debashish Goswami, Jyotishman Bhowmick
    Pages 129-147
  7. Debashish Goswami, Jyotishman Bhowmick
    Pages 149-162
  8. Debashish Goswami, Jyotishman Bhowmick
    Pages 163-177
  9. Debashish Goswami, Jyotishman Bhowmick
    Pages 179-198
  10. Debashish Goswami, Jyotishman Bhowmick
    Pages 199-219
  11. Debashish Goswami, Jyotishman Bhowmick
    Pages 221-235

About this book

Introduction

This book offers an up-to-date overview of the recently proposed theory of quantum isometry groups. Written by the founders, it is the first book to present the research on the “quantum isometry group”, highlighting the interaction of noncommutative geometry and quantum groups, which is a noncommutative generalization of the notion of group of isometry of a classical Riemannian manifold. The motivation for this generalization is the importance of isometry groups in both mathematics and physics. The framework consists of Alain Connes’ “noncommutative geometry” and the operator-algebraic theory of “quantum groups”. The authors prove the existence of quantum isometry group for noncommutative manifolds given by spectral triples under mild conditions and discuss a number of methods for computing them. One of the most striking and profound findings is the non-existence of non-classical quantum isometry groups for arbitrary classical connected compact manifolds and, by using this, the authors explicitly describe quantum isometry groups of most of the noncommutative manifolds studied in the literature. Some physical motivations and possible applications are also discussed.

Keywords

Compact Quantum Group Equivariant Spectral Triples Hopf Algebra Noncommutative Geometry Quantum Isometry Group

Authors and affiliations

  • Debashish Goswami
    • 1
  • Jyotishman Bhowmick
    • 2
  1. 1.Statistics and Mathematics UnitIndian Statistical InstituteKolkataIndia
  2. 2.Statistics and Mathematics UnitIndian Statistical InstituteKolkataIndia

Bibliographic information

  • DOI https://doi.org/10.1007/978-81-322-3667-2
  • Copyright Information Springer (India) Pvt. Ltd 2016
  • Publisher Name Springer, New Delhi
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-81-322-3665-8
  • Online ISBN 978-81-322-3667-2
  • Series Print ISSN 2363-6149
  • Series Online ISSN 2363-6157
  • Buy this book on publisher's site