An example of a solid von Neumann algebra

TL;DR

This paper proves that the group-measure-space von Neumann algebra associated with the action of SL(2,Z) on the 2-torus is solid, using topological amenability of the group action on the Higson corona.

Contribution

It demonstrates the solidity of a specific von Neumann algebra using novel topological and group action techniques.

Findings

The von Neumann algebra $L^ abla(T^2) times SL(2,Z)$ is solid.

The proof leverages topological amenability of the SL(2,Z) action.

The approach connects group actions on the Higson corona to operator algebra properties.

Abstract

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