Gauge-invariant ideals in the C*-algebras of finitely aligned higher-rank graphs

Abstract

We produce a complete descrption of the lattice of gauge-invariant ideals in $C^*(Λ)$ for a finitely aligned $k$-graph $Λ$. We provide a condition on $Λ$ under which every ideal is gauge-invariant. We give conditions on $Λ$ under which $C^*(Λ)$ satisfies the hypotheses of the Kirchberg-Phillips classification theorem.