Rigidity for von Neumann algebras
Operator Algebras
2017-12-04 v1 Dynamical Systems
Functional Analysis
Abstract
We survey some of the progress made recently in the classification of von Neumann algebras arising from countable groups and their measure preserving actions on probability spaces. We emphasize results which provide classes of (W-superrigid) actions that can be completely recovered from their von Neumann algebras and II factors that have a unique Cartan subalgebra. We also present cocycle superrigidity theorems and some of their applications to orbit equivalence. Finally, we discuss several recent rigidity results for von Neumann algebras associated to groups.
Cite
@article{arxiv.1712.00151,
title = {Rigidity for von Neumann algebras},
author = {Adrian Ioana},
journal= {arXiv preprint arXiv:1712.00151},
year = {2017}
}
Comments
submitted to Proc. of the ICM 2018