Simplicity of crossed products of 𝐶*-algebras

Abstract

Let ( A , G , α ) (A,G,\alpha ) be a C ∗ {C^{\ast }} -dynamical system and let G G be a discrete group. When G G is a cental shift in ( A , G , α ) (A,G,\alpha ) , we show that A A is G G -simple (resp. G G -prime) if and only if the C ∗ {C^{\ast }} -crossed product A × α G A \times {}_\alpha G is simple (resp. prime).