Comptes Rendus
no. 1-2
Group Theory/Functional Analysis
A Note on the von Neumann algebra of a Baumslag–Solitar group

Presented by: 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.

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.

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.

Received:
Accepted:
Published online:
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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