HNN extensions and unique group measure space decomposition of II_1 factors
Operator Algebras
2012-02-07 v2 Dynamical Systems
Group Theory
Abstract
We prove that for a fairly large family of HNN extensions \Gamma, the group measure space II_1 factor L^\infty(X) \rtimes \Gamma given by an arbitrary free ergodic probability measure preserving action of \Gamma, has a unique group measure space Cartan subalgebra up to unitary conjugacy. We deduce from this new examples of W^*-superrigid group actions, i.e. where the II_1 factor L^\infty(X) \rtimes \Gamma entirely remembers the group action that it was constructed from.
Keywords
Cite
@article{arxiv.1005.5002,
title = {HNN extensions and unique group measure space decomposition of II_1 factors},
author = {Pierre Fima and Stefaan Vaes},
journal= {arXiv preprint arXiv:1005.5002},
year = {2012}
}
Comments
Remarks added, final version, to appear in Trans. Amer. Math. Soc