A Convex Structure on Sofic Embeddings

Details A Convex Structure on Sofic Embeddings A Convex Structure on Sofic Embeddings

2011-12-09

arxiv.org/abs/1112.2195v1

Mathematics

Dynamical Systems

11 pages

Scientific paper

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.

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