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Catalogue Information
Field name	Details
Dewey Class	512.2
Title	Groups with the Haagerup Property ([EBook] :) : Gromov’s a-T-menability / / by Pierre-Alain Cherix, Paul Jolissaint, Alain Valette, Michael Cowling, Pierre Julg.
Author	Cherix, Pierre-Alain
Added Personal Name	Jolissaint, Paul author.
	Valette, Alain author.
	Cowling, Michael author.
	Julg, Pierre author.
Other name(s)	SpringerLink (Online service)
Publication	Basel : : Birkhäuser Basel : : Imprint: Birkhäuser, , 2001.
Physical Details	VII, 126 p. : online resource.
Series	Progress in mathematics 0743-1643 ; ; 197
ISBN	9783034882378
Summary Note	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.:
Contents note	1 Introduction -- 1.1 Basic definitions -- 1.2 Examples -- 1.3 What is the Haagerup property good for? -- 1.4 What this book is about -- 2 Dynamical Characterizations -- 2.1 Definitions and statements of results -- 2.2 Actions on measure spaces -- 2.3 Actions on factors -- 3 Simple Lie Groups of Rank One -- 3.1 The Busemann cocycle and theGromov scalar product -- 3.2 Construction of a quadratic form -- 3.3 Positivity -- 3.4 The link with complementary series -- 4 Classification of Lie Groups with the Haagerup Property -- 4.0 Introduction -- 4.1 Step one -- 4.2 Step two -- 5 The Radial Haagerup Property -- 5.0 Introduction -- 5.1 The geometry of harmonic NA groups -- 5.2 Harmonic analysis on H-type groups -- 5.3 Analysis on harmonic NA groups -- 5.4 Positive definite spherical functions -- 5.5 Appendix on special functions -- 6 Discrete Groups -- 6.1 Some hereditary results -- 6.2 Groups acting on trees -- 6.3 Group presentations -- 6.4 Appendix: Completely positive mapson amalgamated products,by Paul Jolissaint -- 7 Open Questions and Partial Results -- 7.1 Obstructions to the Haagerup property -- 7.2 Classes of groups -- 7.3 Group constructions -- 7.4 Geometric characterizations -- 7.5 Other dynamical characterizations.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-3-0348-8237-8
Links to Related Works	Subject References: Group theory . Group Theory and Generalizations . Lie groups . Mathematics . Topological groups . Topological groups, Lie groups . Authors: Cherix, Pierre-Alain . Cowling, Michael . Jolissaint, Paul . Julg, Pierre . Valette, Alain . Corporate Authors: SpringerLink (Online service) . Series: Progress in mathematics . Classification: 512.2 .

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

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