Inner amenability, property Gamma, McDuff II_1 factors and stable equivalence relations
Operator Algebras
2018-09-17 v2 Dynamical Systems
Group Theory
Abstract
We say that a countable group is McDuff if it admits a free ergodic probability measure preserving action such that the crossed product is a McDuff II_1 factor. Similarly, is said to be stable if it admits such an action with the orbit equivalence relation being stable. The McDuff property, stability, inner amenability and property Gamma are subtly related and several implications and non implications were obtained in [Ef73,JS85,Va09,Ki12a,Ki12b]. We complete the picture with the remaining implications and counterexamples.
Keywords
Cite
@article{arxiv.1604.02911,
title = {Inner amenability, property Gamma, McDuff II_1 factors and stable equivalence relations},
author = {Tobe Deprez and Stefaan Vaes},
journal= {arXiv preprint arXiv:1604.02911},
year = {2018}
}
Comments
v2: minor changes, final version to appear in Ergodic Theory and Dynamical Systems