Unique Cartan decomposition for II_1 factors arising from arbitrary actions of hyperbolic groups
Operator Algebras
2014-09-15 v3 Dynamical Systems
Group Theory
Abstract
We prove that for any free ergodic probability measure preserving action of a non-elementary hyperbolic group, or a lattice in a rank one simple Lie group, the associated group measure space II_1 factor has L^\infty(X) as its unique Cartan subalgebra, up to unitary conjugacy.
Keywords
Cite
@article{arxiv.1201.2824,
title = {Unique Cartan decomposition for II_1 factors arising from arbitrary actions of hyperbolic groups},
author = {Sorin Popa and Stefaan Vaes},
journal= {arXiv preprint arXiv:1201.2824},
year = {2014}
}
Comments
v3: Considerably simplified proof of the main result. v2: Improved exposition; new result proving uniqueness of Cartan for crossed products by irreducible lattices in products of rank one Lie groups