2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71719We 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.19 pages. Additional references added in Section 8. Title of Section 6 changed from "The lattice structure" to "The lattice order"Operator Algebras46L05text