Geodesic
A class of superrigid group von Neumann algebras
Adrian Ioana1 ; Sorin Popa2 ; Stefaan Vaes3
1 Department of Mathematics, University of California, San Diego, La Jolla, CA 92093
2 Department of Mathematics, University of California at Los Angeles, Los Angeles, CA 90095-1555
3 Department of Mathematics, KU Leuven, Celestijnenlaan 200B, B-3001 Leuven<br/> Belgium
Annals of mathematics, Tome 178 (2013) no. 1, pp. 231-286.

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

We prove that for any group $G$ in a fairly large class of generalized wreath product groups, the associated von Neumann algebra $\mathrm{L} G$ completely “remembers” the group $G$. More precisely, if $\mathrm{L} G$ is isomorphic to the von Neumann algebra $\mathrm{L} \Lambda$ of an arbitrary countable group $\Lambda$, then $\Lambda$ must be isomorphic to $G$. This represents the first superrigidity result pertaining to group von Neumann algebras.
DOI : 10.4007/annals.2013.178.1.4

Adrian Ioana 1 ; Sorin Popa 2 ; Stefaan Vaes 3

1 Department of Mathematics, University of California, San Diego, La Jolla, CA 92093
2 Department of Mathematics, University of California at Los Angeles, Los Angeles, CA 90095-1555
3 Department of Mathematics, KU Leuven, Celestijnenlaan 200B, B-3001 Leuven<br/> Belgium 
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Adrian Ioana; Sorin Popa; Stefaan Vaes. A class of superrigid group von Neumann algebras. Annals of mathematics, Tome 178 (2013) no. 1, pp. 231-286. doi : 10.4007/annals.2013.178.1.4. http://geodesic.mathdoc.fr/articles/10.4007/annals.2013.178.1.4/

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