On ergodicity of linear actions on $\mathbb{R}^n$ and factoriality of group von Neumann algebras

Abstract

We give some natural conditions on actions of discrete countable groups on abelian locally compact groups of Lie type that imply factoriality of the group von Neumann algebras of their semidirect products. This allows us to give a fairly large class of examples of locally compact groups whose group von Neumann algebras are factors.