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A convex structure on sofic embeddings

Published online by Cambridge University Press:  14 March 2013

LIVIU PĂUNESCU
LIVIU PĂUNESCU*
Affiliation:
University of Vienna, Nordbergstrasse 15, 1090 Wien, Austria Institute of Mathematics ‘Simion Stoilow’, 21 Calea Grivitei Street, Bucharest, 010702, Romania email liviu.paunescu@imar.ro
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Abstract

Nathanial Brown [Topological dynamical systems associated to ${\mathit{II}}_{1} $-factors. Adv. Math. 227(4), 1665–1699] introduced a convex-like structure on the set of unitary equivalence classes of unital *-homomorphisms of a separable type ${\mathit{II}}_{1} $ factor into ${R}^{\omega } $ (ultrapower of the hyperfinite factor). The goal of this paper is to introduce such a structure on the set of sofic representations of groups. We prove that if the commutant of a representation acts ergodically on the Loeb measure space then that representation is an extreme point.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 34 , Issue 4 , August 2014 , pp. 1343 - 1352
Copyright
Copyright ©2013 Cambridge University Press 

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