Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: When is the Cuntz-Krieger algebra of a higher-rank graph approximately
  finite-dimensional?   We investigate the question: when is a higher-rank graph C*-algebra
approximately finite dimensional? We prove that the absence of an appropriate
higher-rank analogue of a cycle is necessary. We show that it is not in general
sufficient, but that it is sufficient for higher-rank graphs with finitely many
vertices. We give a detailed description of the structure of the C*-algebra of
a row-finite locally convex higher-rank graph with finitely many vertices. Our
results are also sufficient to establish that if the C*-algebra of a
higher-rank graph is AF, then its every ideal must be gauge-invariant. We prove
that for a higher-rank graph C*-algebra to be AF it is necessary and sufficient
for all the corners determined by vertex projections to be AF. We close with a
number of examples which illustrate why our question is so much more difficult
for higher-rank graphs than for ordinary graphs.

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The categories of this paper are: gr-qc
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ph
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The categories of this paper are: q-alg
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The categories of this paper are: eess
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The categories of this paper are: quant-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: ao-sci
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The categories of this paper are: stat
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The categories of this paper are: hep-ex
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The categories of this paper are: adap-org
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The categories of this paper are: cmp-lg
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The categories of this paper are: bayes-an
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The categories of this paper are: physics
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-th