Locally compact groups with every isometric action bounded or proper

Romain Tessera; Alain Valette; Corina-Gabriela Ciobotaru

doi:10.1142/S1793525319500547

Locally compact groups with every isometric action bounded or proper

Romain Tessera, Alain Valette, Corina-Gabriela Ciobotaru

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avis › Tidsskriftartikel › Forskning › peer review

Abstract

A locally compact group G has property PL if every isometric G-action either has bounded orbits or is (metrically) proper. For p ≥ 1, say that G has property BP p if the same alternative holds for the smaller class of affine isometric actions on Lp-spaces. We explore properties PL and BP p and prove that they are equivalent for some interesting classes of groups: abelian groups, amenable almost connected Lie groups, amenable linear algebraic groups over a local field of characteristic 0. The appendix provides new examples of groups with property PL, including nonlinear ones.

Originalsprog	Engelsk
Tidsskrift	Journal of Topology and Analysis
Vol/bind	12
Nummer	2
Sider (fra-til)	267-292
Antal sider	26
ISSN	1793-5253
DOI	https://doi.org/10.1142/S1793525319500547
Status	Udgivet - 1 jun. 2020
Udgivet eksternt	Ja

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title = "Locally compact groups with every isometric action bounded or proper",

abstract = "A locally compact group G has property PL if every isometric G-action either has bounded orbits or is (metrically) proper. For p ≥ 1, say that G has property BP p if the same alternative holds for the smaller class of affine isometric actions on Lp-spaces. We explore properties PL and BP p and prove that they are equivalent for some interesting classes of groups: abelian groups, amenable almost connected Lie groups, amenable linear algebraic groups over a local field of characteristic 0. The appendix provides new examples of groups with property PL, including nonlinear ones.",

keywords = "bounded orbits, Howe-Moore property, L p -spaces, Metrically proper isometric actions",

author = "Romain Tessera and Alain Valette and Corina-Gabriela Ciobotaru",

note = "Funding Information: The second author would like to thank the Isaac Newton Institute for Mathematical Sciences, Cambridge for support and hospitality during the programme Non-Positive Curvature where work on this paper was finalized. This work was supported by EPSRC Grant No. EP/K032208/1. Publisher Copyright: {\textcopyright} 2020 World Scientific Publishing Company.",

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AU - Valette, Alain

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N1 - Funding Information: The second author would like to thank the Isaac Newton Institute for Mathematical Sciences, Cambridge for support and hospitality during the programme Non-Positive Curvature where work on this paper was finalized. This work was supported by EPSRC Grant No. EP/K032208/1. Publisher Copyright: © 2020 World Scientific Publishing Company.

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N2 - A locally compact group G has property PL if every isometric G-action either has bounded orbits or is (metrically) proper. For p ≥ 1, say that G has property BP p if the same alternative holds for the smaller class of affine isometric actions on Lp-spaces. We explore properties PL and BP p and prove that they are equivalent for some interesting classes of groups: abelian groups, amenable almost connected Lie groups, amenable linear algebraic groups over a local field of characteristic 0. The appendix provides new examples of groups with property PL, including nonlinear ones.

AB - A locally compact group G has property PL if every isometric G-action either has bounded orbits or is (metrically) proper. For p ≥ 1, say that G has property BP p if the same alternative holds for the smaller class of affine isometric actions on Lp-spaces. We explore properties PL and BP p and prove that they are equivalent for some interesting classes of groups: abelian groups, amenable almost connected Lie groups, amenable linear algebraic groups over a local field of characteristic 0. The appendix provides new examples of groups with property PL, including nonlinear ones.

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Locally compact groups with every isometric action bounded or proper

Abstract

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