Detecting ideals in reduced crossed product C*-algebras of topological dynamical systems

Abstract

We introduce the ℓ 1 -ideal intersection property for crossed product C * -algebras. It is implied by C * -simplicity as well as C * -uniqueness. We show that topological dynamical systems of arbitrary lattices in connected Lie groups, arbitrary linear groups over the integers in a number field and arbitrary virtually polycyclic groups have the ℓ 1 -ideal intersection property. On the way, we extend previous results on C * -uniqueness of L 1 -groupoid algebras to the general twisted setting.