A note on the von Neumann algebra of a Baumslag-Solitar group

preprint2010arXivOpen access

Abstract

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 II1{\rm II}_1 factor is prime, not solid, and does not have any Cartan subalgebra.

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