Normalizers inside amalgamated free product von Neumann algebras
type: Item
instance of: scholarly article
title: Normalizers inside amalgamated free product von Neumann algebras
zbMATH Open document ID: 1315.46067
DOI: 10.4171/PRIMS/147
author: Stefaan Vaes
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 2014-11-28T00:00:00Z
full work available at URL: https://arxiv.org/abs/1305.3225
review text: Summary: Recently, \textit{A. Ioana} [Ann. Sci. Éc. Norm. Supér. (4) 48, No. 1, 71--130 (2015; Zbl 1351.46058)] proved that all crossed products \(L^\infty(X) \rtimes (\Gamma_1*\Gamma_2)\) 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 [loc. cit.] deduced this result from a more general dichotomy theorem on the normalizer \(\mathcal N_M(A)^{''}\) 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 \(L^\infty(X) \rtimes (\Gamma_1*\Gamma_2)\).
Mathematics Subject Classification ID: 46L36
Mathematics Subject Classification ID: 46L54
Mathematics Subject Classification ID: 37A40
zbMATH DE Number: 6374910
zbMATH Keywords: amalgamated free products
zbMATH Keywords: Cartan subalgebras
zbMATH Keywords: deformation/rigidity theory
zbMATH Keywords: nonsingular group actions
MaRDI profile type: Publication
arXiv ID: 1305.3225
cites work: Amalgamated free product type III factors with at most one Cartan subalgebra
cites work: Bass-Serre rigidity results in von Neumann algebras
cites work: On the structural theory of $\rm II_1$ factors of negatively curved groups
cites work: On the structural theory of \(\mathrm{II}_1\) factors of negatively curved groups. II: Actions by product groups
cites work: Unbounded derivations, free dilations, and indecomposability results for II\(_1\) factors
cites work: Construction of type II1 factors with prescribed countable fundamental group
cites work: Strongly solid group factors which are not interpolated free group factors
cites work: A class of groups for which every action is W\(^\ast\)-superrigid
cites work: Type III factors with unique Cartan decomposition
cites work: Rigidity results for wreath product \(\mathrm{II}_1\) factors
cites work: Subequivalence relations and positive-definite functions
cites work: Amalgamated free products of weakly rigid factors and calculation of their symmetry groups
cites work: II1 FACTORS AND EQUIVALENCE RELATIONS WITH DISTINCT FUNDAMENTAL GROUPS
cites work: Incompressible transformations
cites work: On a class of II\(_1\) factors with at most one Cartan subalgebra
cites work: On a class of II1 factors with at most one Cartan subalgebra, II
cites work: Q3756753
cites work: On a class of type \(\text{II}_1\) factors with Betti numbers invariants
cites work: Strong rigidity of \(\text{II}_1\) factors arising from malleable actions of \(w\)-rigid groups. I
cites work: On the superrigidity of malleable actions with spectral gap
cites work: Cocycle and orbit superrigidity for lattices in SL\((n,\mathbb R)\) acting on homogeneous spaces
cites work: Group measure space decomposition of \(\text{II}_{1}\) factors and \(\text W^{*}\)-superrigidity
cites work: Unique Cartan decomposition for \(\mathrm{II}_1\) factors arising from arbitrary actions of free groups
cites work: Asymptotic Properties of Unitary Representations and Mixing
cites work: Remarks on HNN extensions in operator algebras
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