Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: All classifiable Kirchberg algebras are $C^{\ast}$-algebras of ample
  groupoids   In this note we show that every Kirchberg algebra in the UCT class is the
$C^{\ast}$-algebra of a Hausdorff, ample, amenable and locally contracting
groupoid. The non-unital case follows from Spielberg's graph-based models for
Kirchberg algebras. Our contribution is the unital case and our proof builds on
Spielberg's construction.

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The categories of this paper are: hep-lat
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The categories of this paper are: chem-ph
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The categories of this paper are: supr-con
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The categories of this paper are: cond-mat
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The categories of this paper are: nlin
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The categories of this paper are: cmp-lg
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The categories of this paper are: physics
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The categories of this paper are: funct-an
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The categories of this paper are: astro-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: patt-sol
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The categories of this paper are: q-alg
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The categories of this paper are: gr-qc
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The categories of this paper are: adap-org
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The categories of this paper are: eess
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The categories of this paper are: atom-ph