Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cuntz-Krieger algebras associated with Hilbert $C^*$-quad modules of
  commuting matrices   Let ${\cal O}_{{\cal H}^{A,B}_\kappa}$ be the $C^*$-algebra associated with
the Hilbert $C^*$-quad module arising from commuting matrices $A,B$ with
entries in $\{0,1\}$. We will show that if the associated tiling space
$X_{A,B}^\kappa$ is transitive, the $C^*$-algebra ${\cal O}_{{\cal
H}^{A,B}_\kappa}$ is simple and purely infinite. In particulr, for two positive
integers $N,M$, the $K$-groups of the simple purely infinite $C^*$-algebra
${\cal O}_{{\cal H}^{[N],[M]}_\kappa}$ are computed by using the Euclidean
algorithm.

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The categories of this paper are: patt-sol
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The categories of this paper are: alg-geom
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The categories of this paper are: solv-int
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The categories of this paper are: q-bio
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The categories of this paper are: funct-an
16
The categories of this paper are: stat
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The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: math-ph
1
The categories of this paper are: cs
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The categories of this paper are: plasm-ph
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The categories of this paper are: eess
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The categories of this paper are: adap-org
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The categories of this paper are: physics