Equicontinuous actions of semisimple groups

Uri Bader; Tsachik Gelander

doi:https://doi.org/10.4171/GGD/420

Equicontinuous actions of semisimple groups

Uri Bader, Tsachik Gelander

Department of Mathematics

Weizmann Institute of Science

Research output: Contribution to journal › Article › peer-review

Abstract

We study equicontinuous actions of semisimple groups and some generalizations. We prove that any such action is universally closed, and in particular proper. We derive various applications, both old and new, including closedness of continuous homomorphisms, nonexistence of weaker topologies, metric ergodicity of transitive actions and vanishing of matrix coefficients for reflexive (more generally: WAP) representations.

Original language	English
Pages (from-to)	1003-1039
Number of pages	37
Journal	Groups Geometry And Dynamics
Volume	11
Issue number	3
DOIs	https://doi.org/10.4171/GGD/420
State	Published - 2017

Keywords

Howe-Moore Theorem
Mautner's phenomenon
Metric ergodicity
Uniform structures
WAP-representations

All Science Journal Classification (ASJC) codes

Discrete Mathematics and Combinatorics
Geometry and Topology

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https://doi.org/10.4171/GGD/420

Cite this

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abstract = "We study equicontinuous actions of semisimple groups and some generalizations. We prove that any such action is universally closed, and in particular proper. We derive various applications, both old and new, including closedness of continuous homomorphisms, nonexistence of weaker topologies, metric ergodicity of transitive actions and vanishing of matrix coefficients for reflexive (more generally: WAP) representations.",

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N2 - We study equicontinuous actions of semisimple groups and some generalizations. We prove that any such action is universally closed, and in particular proper. We derive various applications, both old and new, including closedness of continuous homomorphisms, nonexistence of weaker topologies, metric ergodicity of transitive actions and vanishing of matrix coefficients for reflexive (more generally: WAP) representations.

AB - We study equicontinuous actions of semisimple groups and some generalizations. We prove that any such action is universally closed, and in particular proper. We derive various applications, both old and new, including closedness of continuous homomorphisms, nonexistence of weaker topologies, metric ergodicity of transitive actions and vanishing of matrix coefficients for reflexive (more generally: WAP) representations.

KW - Howe-Moore Theorem

KW - Mautner's phenomenon

KW - Metric ergodicity

KW - Uniform structures

KW - WAP-representations

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DO - https://doi.org/10.4171/GGD/420

M3 - مقالة

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EP - 1039

JO - Groups Geometry And Dynamics

JF - Groups Geometry And Dynamics

IS - 3

ER -

Equicontinuous actions of semisimple groups

Abstract

Keywords

All Science Journal Classification (ASJC) codes

Access to Document

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