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Relative Cuntz-Krieger algebras of finitely aligned higher-rank graphs
We define the relative Cuntz-Krieger algebras associated to finitely aligned
higher-rank graphs. We prove versions of the gauge-invariant uniqueness theorem
and the Cuntz-Krieger uniqueness theorem for relative Cuntz-Krieger algebras.Comment: 16 page
Do phantom Cuntz-Krieger algebras exist?
If phantom Cuntz-Krieger algebras do not exist, then real rank zero
Cuntz-Krieger algebras can be characterized by outer properties. In this survey
paper, a summary of the known results on non-existence of phantom Cuntz-Krieger
algebras is given.Comment: 8 page
The K-theoretical range of Cuntz-Krieger algebras
We augment Restorff's classification of purely infinite Cuntz-Krieger
algebras by describing the range of his invariant on purely infinite
Cuntz-Krieger algebras. We also describe its range on purely infinite graph
C*-algebras with finitely many ideals, and provide 'unital' range results for
purely infinite Cuntz-Krieger algebras and unital purely infinite graph
C*-algebras.Comment: 16 pages. This article contains material that was originally
contained arXiv:1301.7223v1. v2: minor changes, v3: minor changes, final
versio
The -algebras of finitely aligned higher-rank graphs
We generalise the theory of Cuntz-Krieger families and graph algebras to the
class of finitely aligned -graphs. This class contains in particular all
row-finite -graphs. The Cuntz-Krieger relations for non-row-finite
-graphs look significantly different from the usual ones, and this
substantially complicates the analysis of the graph algebra. We prove a
gauge-invariant uniqueness theorem and a Cuntz-Krieger uniqueness theorem for
the -algebras of finitely aligned -graphs.Comment: 27 page
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