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

http://dx.doi.org/10.4153/CJM-2006-045-2
Canad. J. Math. 58(2006), 1268-1290

  Published:2006-12-01
 Printed: Dec 2006

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.