On sofic groupoids and their full groups
type: Item
instance of: scholarly article
title: On sofic groupoids and their full groups
zbMATH Open document ID: 1439.20068
published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris
publication date: 2018-09-06T00:00:00Z
review text: In this work, the author proves that an aperiodic probability measure preserving (pmp) groupoid is sofic if and only if its full groupoid is metrically sofic, and he answers a question of \textit{C. T. Conley} et al. [Ergodic Theory Dyn. Syst. 33, No. 2, 334--374 (2013; Zbl 1268.05104)]. The author also invites us to answer the following question due to Vladimir Pestov: is a pmp equivalence relation sofic if and only if its full group is sofic? We must also remember that in [Proc. Am. Math. Soc. 143, No. 5, 1943--1950 (2015; Zbl 1362.20035).], \textit{G. Elek} proves that if a pmp equivalence relation is sofic then its full group is sofic.
Mathematics Subject Classification ID: 20L05
Mathematics Subject Classification ID: 37A05
Mathematics Subject Classification ID: 37A20
Mathematics Subject Classification ID: 20F65
zbMATH DE Number: 6933371
zbMATH Keywords: sofic groupoid
author: Luiz Gustavo Cordeiro
MaRDI profile type: Publication
full work available at URL: j.crma.2018.07.003
OpenAlex ID: W2884393190
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Wikidata QID: Q129498089
DOI: 10.1016/J.CRMA.2018.07.003
description: scientific article; zbMATH DE number 6933371