An example of a solid von Neumann algebra

Abstract

We prove that the group-measure-space von Neumann algebra $L^\infty(\mathbb T^2) \rtimes \mathrm{SL}(2,\mathbb Z)$ is solid. The proof uses topological amenability of the action of $\mathrm{SL}L(2,\mathbb Z)$ on the Higson corona of $\mathbb Z^2$.