A Convex Structure on Sofic Embeddings

2011/12/09 by Liviu Paunescu, Paunescu, Liviu · 1 citation
Mathematics · #37A15 #Dynamical Systems (math.DS) #FOS: Mathematics #Group Theory (math.GR) #math.DS #math.GR #msc:37A15

paper · pdf · doi:10.48550/arxiv.1112.2195

12 pages

arxiv created 2012/09/16 · arxiv updated 2012/09/18

Abstract

Nathanial Brown introduced a convex-like structure on the set of unitary equivalence classes of unital *-homomorphisms of a separable type II₁ factor into R^ω(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 ergodicaly on the Loeb measure space then that representation is an extreme point.

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