ENGLISH

Groups with the Haagerup Property: Gromov’s a-T-menability

By Alain Valette , Michael Cowling , Pierre-Alain Cherix , Paul Jolissaint , Pierre Julg (auth.)

Book information

Publisher
Birkhäuser Basel
Year
2001
ISBN
978-3-0348-9486-9, 978-3-0348-8237-8
DOI
10.1007/978-3-0348-8237-8
Language
english
Format
PDF
Filesize
4 MB (3767725 bytes)
Series
Progress in Mathematics 197
Edition
1
Pages
126\129
Orientation
yes
Scanned
yes
Time added
2013-08-01 04:00:00
Group Theory and Generalizations; Topological GrouLie Groups

Description

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.

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