Gauge-invariant ideals in the C*-algebras of finitely aligned higher-rank graphs

Details Gauge-invariant ideals in the C*-algebras of finitely aligned higher-rank graphs Gauge-invariant ideals in the C*-algebras of finitely aligned higher-rank graphs

2004-06-29

arxiv.org/abs/math/0406592v2

Mathematics

Operator Algebras

19 pages. Additional references added in Section 8. Title of Section 6 changed from "The lattice structure" to "The lattice or

Scientific paper

We produce a complete descrption 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.

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