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Groups with the Haagerup Property

Gromov’s a-T-menability

  • Pierre-Alain Cherix
  • Paul Jolissaint
  • Alain Valette
  • Michael Cowling
  • Pierre Julg

Part of the Progress in Mathematics book series (PM, volume 197)

Table of contents

  1. Front Matter
    Pages i-vii
  2. Alain Valette
    Pages 1-13
  3. Paul Jolissaint
    Pages 15-32
  4. Pierre Julg
    Pages 33-39
  5. Pierre-Alain Cherix, Michael Cowling, Alain Valette
    Pages 41-61
  6. Michael Cowling
    Pages 63-84
  7. Paul Jolissaint, Pierre Julg, Alain Valette
    Pages 85-104
  8. Alain Valette
    Pages 105-114
  9. Back Matter
    Pages 115-126

About this book

Introduction

A locally compact group has the Haagerup property, or is a-T-menable in the sense of Gromov, if it admits a proper isometric action on some affine Hilbert space. As Gromov's pun is trying to indicate, this definition is designed as a strong negation to Kazhdan's property (T), characterized by the fact that every isometric action on some affine Hilbert space has a fixed point.

The aim of this book is to cover, for the first time in book form, various aspects of the Haagerup property. New characterizations are brought in, using ergodic theory or operator algebras. Several new examples are given, and new approaches to previously known examples are proposed. Connected Lie groups with the Haagerup property are completely characterized.

Keywords

Group theory algebra geometry harmonic analysis lie group locally compact group operator algebra quadratic form

Authors and affiliations

  • Pierre-Alain Cherix
    • 1
  • Paul Jolissaint
    • 2
  • Alain Valette
    • 2
  • Michael Cowling
    • 3
  • Pierre Julg
    • 4
  1. 1.Section de MathématiquesUniversité de GenèveGenève 24Switzerland
  2. 2.Institut de MathématiquesUniversité de NeuchâtelNeuchâtelSwitzerland
  3. 3.School of MathematicsUniversity of New South WalesSydneyAustralia
  4. 4.Département de MathématiquesUniversité d’OrléansOrléans Cedex 2France

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-0348-8237-8
  • Copyright Information Birkhäuser Verlag 2001
  • Publisher Name Birkhäuser, Basel
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-0348-9486-9
  • Online ISBN 978-3-0348-8237-8
  • Series Print ISSN 0743-1643
  • Series Online ISSN 2296-505X
  • Buy this book on publisher's site