Geodesic
On a class of $\mathrm{II}_1$ factors with at most one Cartan subalgebra
Narutaka Ozawa1 ; Sorin Popa2
1 University of California Los Angeles, Department of Mathematics, Los Angeles, CA 90095-1555, United States and Department of Mathematical Sciences, University of Tokyo, Komaba, 153-8914, Japan
2 University of California Los Angeles, Department of Mathematics, Los Angeles, CA 90095-1555, United States
Annals of mathematics, Tome 172 (2010) no. 1, pp. 713-749

Voir la notice de l'article provenant de la source Annals of Mathematics website

We prove that the normalizer of any diffuse amenable subalgebra of a free group factor $L(\mathbb{F}_r)$ generates an amenable von Neumann subalgebra. Moreover, any ${\rm II}_1$ factor of the form $Q \bar{\otimes} L(\mathbb{F}_r) $, with $Q$ an arbitrary subfactor of a tensor product of free group factors, has no Cartan subalgebras. We also prove that if a free ergodic measure-preserving action of a free group $\mathbb{F}_r$, $2\leq r \leq \infty$, on a probability space $(X,\mu)$ is profinite then the group measure space factor $L^\infty(X) \rtimes \mathbb{F}_r$ has unique Cartan subalgebra, up to unitary conjugacy.

DOI : 10.4007/annals.2010.172.713

Narutaka Ozawa 1 ; Sorin Popa 2

1 University of California Los Angeles, Department of Mathematics, Los Angeles, CA 90095-1555, United States and Department of Mathematical Sciences, University of Tokyo, Komaba, 153-8914, Japan
2 University of California Los Angeles, Department of Mathematics, Los Angeles, CA 90095-1555, United States 
@article{10_4007_annals_2010_172_713,
     author = {Narutaka Ozawa and Sorin Popa},
     title = {On a class of $\mathrm{II}_1$ factors with at most  one {Cartan} subalgebra},
     journal = {Annals of mathematics},
     pages = {713--749},
     publisher = {mathdoc},
     volume = {172},
     number = {1},
     year = {2010},
     doi = {10.4007/annals.2010.172.713},
     mrnumber = {2680430},
     zbl = {1201.46054},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4007/annals.2010.172.713/}
}
TY  - JOUR
AU  - Narutaka Ozawa
AU  - Sorin Popa
TI  - On a class of $\mathrm{II}_1$ factors with at most  one Cartan subalgebra
JO  - Annals of mathematics
PY  - 2010
SP  - 713
EP  - 749
VL  - 172
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4007/annals.2010.172.713/
DO  - 10.4007/annals.2010.172.713
LA  - en
ID  - 10_4007_annals_2010_172_713
ER  - 
%0 Journal Article
%A Narutaka Ozawa
%A Sorin Popa
%T On a class of $\mathrm{II}_1$ factors with at most  one Cartan subalgebra
%J Annals of mathematics
%D 2010
%P 713-749
%V 172
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4007/annals.2010.172.713/
%R 10.4007/annals.2010.172.713
%G en
%F 10_4007_annals_2010_172_713
Narutaka Ozawa; Sorin Popa. On a class of $\mathrm{II}_1$ factors with at most  one Cartan subalgebra. Annals of mathematics, Tome 172 (2010) no. 1, pp. 713-749. doi: 10.4007/annals.2010.172.713

Cité par Sources :