A NOTE ON THE VON NEUMANN ALGEBRA OF A BAUMSLAG-SOLITAR GROUP

Pierre Fima (1)

1 IMJ - Institut de Mathématiques de Jussieu

We study qualitative properties of the group von Neumann algebra of a Baumslag-Solitar group. Namely, we prove that, in the non-amenable and {ICC} case, the associated ${\rm II}_1$ factor is prime, not solid, and does not have any Cartan subalgebra.

Domaines: Algèbres d'opérateurs [math.OA]; Théorie des groupes [math.GR]

Pierre Fima. A NOTE ON THE VON NEUMANN ALGEBRA OF A BAUMSLAG-SOLITAR GROUP. 2010. ⟨hal-00535899⟩