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Amenable purely infinite actions on the non-compact Cantor set

Part of: Selfadjoint operator algebras

Published online by Cambridge University Press:  20 November 2018

GÁBOR ELEK
GÁBOR ELEK*
Affiliation:
Department of Mathematics And Statistics, Fylde College, Lancaster University, Lancaster, LA1 4YF, UK email g.elek@lancaster.ac.uk
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Abstract

We prove that any countable non-amenable group $\unicode[STIX]{x1D6E4}$ admits a free, minimal, amenable, purely infinite action on the non-compact Cantor set. This answers a question of Kellerhals, Monod and Rørdam [Non-supramenable groups acting on locally compact spaces. Doc. Math.18 (2013), 1597–1626].

Keywords

Minimal actionsnon-compact Cantor settopological amenabilitypurely infinite actions

MSC classification

Primary: 46L55: Noncommutative dynamical systems
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 40 , Issue 6 , June 2020 , pp. 1619 - 1633
Copyright
© Cambridge University Press, 2018

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