Rokhlin dimension: Permanence properties and ideal separation

Abstract

We study the Rokhlin dimension for actions of residually finite groups on C*-algebras. We give a definition equivalent to the original one due to Szabó, Wu and Zacharias. We then prove a number of permanence properties and discuss actions on $C_0(X)$-algebras and commutative C*-algebras. Finally, we use a theorem of Sierakowski to show that, for an action with finite Rokhlin dimension, every ideal in the associated reduced crossed product C*-algebra arises from an invariant ideal of the underlying algebra.