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

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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Content:
Front Matter....Pages i-vii
Introduction....Pages 1-13
Dynamical Characterizations....Pages 15-32
Simple Lie Groups of Rank One....Pages 33-39
Classification of Lie Groups with the Haagerup Property....Pages 41-61
The Radial Haagerup Property....Pages 63-84
Discrete Groups....Pages 85-104
Open Questions and Partial Results....Pages 105-114
Back Matter....Pages 115-126

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Content:
Front Matter....Pages i-vii
Introduction....Pages 1-13
Dynamical Characterizations....Pages 15-32
Simple Lie Groups of Rank One....Pages 33-39
Classification of Lie Groups with the Haagerup Property....Pages 41-61
The Radial Haagerup Property....Pages 63-84
Discrete Groups....Pages 85-104
Open Questions and Partial Results....Pages 105-114
Back Matter....Pages 115-126
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