On Sofic Actions and Equivalence Relations

Details On Sofic Actions and Equivalence Relations On Sofic Actions and Equivalence Relations

2010-02-03

arxiv.org/abs/1002.0605v5

Mathematics

Operator Algebras

Improved version after remarks

Scientific paper

The notion of sofic equivalence relation was introduced by Gabor Elek and Gabor Lippner. Their technics employ some graph theory. Here we define this notion in a more operator algebraic context, starting from Connes' embedding problem, and prove the equivalence of this two definitions. We introduce a notion of sofic action for an arbitrary group and prove that amalgamated product of sofic actions over amenable groups is again sofic. We also prove that amalgamated product of sofic groups over an amenable subgroup is again sofic.

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