Comptes Rendus
no. 1-2
Group Theory/Functional Analysis
A Note on the von Neumann algebra of a Baumslag–Solitar group
[Une Note sur l'algèbre de von Neumann d'un groupe de Baumslag–Solitar]

Présenté par : the Editorial Board

Pierre Fima1
1 Institut mathématiques de Jussieu, université Paris Diderot, 175, rue de Chevaleret, 75013 Paris, France
Comptes Rendus. Mathématique, Volume 349 (2011) no. 1-2, pp. 25-27.

Nous étudions des propriétés qualitatives de l'algèbre de von Neumann d'un groupe de Baumslag–Solitar. À savoir, nous démontrons que, dans le cas non-moyennable et C.C.I., le facteur II1 associé est premier, n'est pas solide, et n'a pas de sous-algèbre de Cartan.

We study qualitative properties of the von Neumann algebra of a Baumslag–Solitar group. Namely, we prove that, in the non-amenable and ICC case, the associated II1 factor is prime, not solid, and does not have any Cartan subalgebra.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2010.12.008
Pierre Fima 1

1 Institut mathématiques de Jussieu, université Paris Diderot, 175, rue de Chevaleret, 75013 Paris, France 
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Pierre Fima. A Note on the von Neumann algebra of a Baumslag–Solitar group. Comptes Rendus. Mathématique, Volume 349 (2011) no. 1-2, pp. 25-27. doi : 10.1016/j.crma.2010.12.008. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.12.008/

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