Groups with the Haagerup Property
Subtitle: Gromov's a-T-menability
By: by Pierre-Alain Cherix, Paul Jolissaint, Alain Valette, Michael Cowling, Pierre Julg
Contributors: Jolissaint, Paul; Valette, Alain; Cowling, Michael; Julg, Pierre
Series: Progress in Mathematics -- 197; Progress in Mathematics -- 197.
Publisher: Birkhäuser Basel; Imprint: Birkhäuser
Published: 2001
Place of publication: Basel
Language: eng
Format: [electronic resource] :
Number of pages: 126
ISBN-13: 9783034882378
Subjects: Group theory; Mathematics; Topological 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.