Ideals and simplicity of crossed products of graph C*-algebras by quasi-free actions

Let E be a row-finite directed graph without sinks, let G be a locally compact abelian group with dual group, and let ! be a labeling map, then, as defined by the second author in [16], one has the quasi-free action alpha(omega) of G on the graph C*-algebra C*(E). In this paper, we introduce the notion of E-class of subsets of, and using this, obtain a description of the gauge-invariant ideal structure and also a characterization of simplicity for the crossed product C*-algebra C* (E) x alpha(omega) G in the case of a row-finite directed graph E without sinks. Moreover, if the labeling map omega is in-phase and each loop in E has an exit, we prove that every ideal of the crossed product is gauge invariant.