A Convex Structure on Sofic Embeddings
Dynamical Systems
2012-09-18 v2 Group Theory
Abstract
Nathanial Brown introduced a convex-like structure on the set of unitary equivalence classes of unital *-homomorphisms of a separable type 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 ergodicaly on the Loeb measure space then that representation is an extreme point.
Cite
@article{arxiv.1112.2195,
title = {A Convex Structure on Sofic Embeddings},
author = {Liviu Paunescu},
journal= {arXiv preprint arXiv:1112.2195},
year = {2012}
}
Comments
12 pages