Normalizers inside amalgamated free product von Neumann algebras
Operator Algebras
2014-10-28 v1 Dynamical Systems
Group Theory
Abstract
Recently, Adrian Ioana proved that all crossed products by free ergodic probability measure preserving actions of a nontrivial free product group \Gamma_1 * \Gamma_2 have a unique Cartan subalgebra up to unitary conjugacy. Ioana deduced this result from a more general dichotomy theorem on the normalizer N_M(A)'' of an amenable subalgebra A of an amalgamated free product von Neumann algebra M = M_1 *_B M_2. We improve this dichotomy theorem by removing the spectral gap assumptions and obtain in particular a simpler proof for the uniqueness of the Cartan subalgebra in crossed products by \Gamma_1 * \Gamma_2.
Keywords
Cite
@article{arxiv.1305.3225,
title = {Normalizers inside amalgamated free product von Neumann algebras},
author = {Stefaan Vaes},
journal= {arXiv preprint arXiv:1305.3225},
year = {2014}
}