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 $C^{\ast }(\Lambda )$ for a finitely aligned $k$-graph $\Lambda$. We provide a condition on $\Lambda$ under which every ideal is gauge-invariant. We give conditions on $\Lambda$ under which $C^{\ast }(\Lambda )$ 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"