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]
Comptes Rendus. Mathématique, Tome 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.

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

1 Institut mathématiques de Jussieu, université Paris Diderot, 175, rue de Chevaleret, 75013 Paris, France
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Fima, Pierre. A Note on the von Neumann algebra of a Baumslag–Solitar group. Comptes Rendus. Mathématique, Tome 349 (2011) no. 1-2, pp. 25-27. doi : 10.1016/j.crma.2010.12.008. http://www.numdam.org/articles/10.1016/j.crma.2010.12.008/

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