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