An example of a non-amenable dynamical system which is boundary amenable

Abstract

It is shown that the action of $\mathrm{SL}(3,\mathbb{Z})$ on the Stone-uCech boundary of $\mathrm{SL}(3,\mathbb{Z})/\mathrm{SL}(2,\mathbb{Z})$ is amenable. This confirms a prediction by Bekka and Kalantar.

Title changed; other minor changes, mainly in the exposition. The results are unchanged. Final version, to appear in Proc. Amer. Math. Soc