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INNER AMENABLE GROUPOIDS AND CENTRAL SEQUENCES

Part of: Measure-theoretic ergodic theory Selfadjoint operator algebras Ergodic theory

Published online by Cambridge University Press:  26 May 2020

YOSHIKATA KIDA Open the ORCID record for YOSHIKATA KIDA [Opens in a new window]  and
ROBIN TUCKER-DROB
YOSHIKATA KIDA
Affiliation:
Graduate School of Mathematical Sciences, The University of Tokyo, Komaba,Tokyo153-8914, Japan; kida@ms.u-tokyo.ac.jp
ROBIN TUCKER-DROB
Affiliation:
Department of Mathematics, Texas A&M University, College Station, TX 77843, USA; rtuckerd@math.tamu.edu

Abstract

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We introduce inner amenability for discrete probability-measure-preserving (p.m.p.) groupoids and investigate its basic properties, examples, and the connection with central sequences in the full group of the groupoid or central sequences in the von Neumann algebra associated with the groupoid. Among other things, we show that every free ergodic p.m.p. compact action of an inner amenable group gives rise to an inner amenable orbit equivalence relation. We also obtain an analogous result for compact extensions of equivalence relations that either are stable or have a nontrivial central sequence in their full group.

MSC classification

Primary: 37A20: Orbit equivalence, cocycles, ergodic equivalence relations
Secondary: 28D15: General groups of measure-preserving transformations 46L10: General theory of von Neumann algebras
Type
Analysis
Information
Forum of Mathematics, Sigma , Volume 8 , 2020 , e29
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s) 2020

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