A class of groups for which every action is W*-superrigid
Operator Algebras
2013-10-01 v3 Dynamical Systems
Group Theory
Abstract
We prove the uniqueness of the group measure space Cartan subalgebra in crossed products A \rtimes \Gamma covering certain cases where \Gamma is an amalgamated free product over a non-amenable subgroup. In combination with Kida's work we deduce that if \Sigma < SL(3,\Z) denotes the subgroup of matrices g with g_31 = g_32 = 0, then any free ergodic probability measure preserving action of \Gamma = SL(3,\Z) *_\Sigma SL(3,\Z) is stably W*-superrigid. In the second part we settle a technical issue about the unitary conjugacy of group measure space Cartan subalgebras.
Keywords
Cite
@article{arxiv.1010.5077,
title = {A class of groups for which every action is W*-superrigid},
author = {Cyril Houdayer and Sorin Popa and Stefaan Vaes},
journal= {arXiv preprint arXiv:1010.5077},
year = {2013}
}
Comments
v3: Minor changes; final version; to appear in Groups, Geometry, and Dynamics v2: We changed the title to make it more informative