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# Gauge-Invariant Ideals in the $C^*$-Algebras of Finitely Aligned Higher-Rank Graphs

Published:2006-12-01
Printed: Dec 2006
• Aidan Sims
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## Abstract

We produce a complete description of the lattice of gauge-invariant ideals in $C^*(\Lambda)$ 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 $C^*(\Lambda)$ satisfies the hypotheses of the Kirchberg--Phillips classification theorem.
 Keywords: Graphs as categories, graph algebra, $C^*$-algebra
 MSC Classifications: 46L05 - General theory of $C^*$-algebras