1. CJM 2006 (vol 58 pp. 1268)
|Gauge-Invariant Ideals in the $C^*$-Algebras of Finitely Aligned Higher-Rank Graphs |
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