Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Topological conjugacy of topological Markov shifts and Cuntz-Krieger
  algebras   For an irreducible non-permutation matrix $A$, the triplet
$({{\mathcal{O}}_A},{{\mathcal{D}}_A},\rho^A)$ for the Cuntz-Krieger algebra
${{\mathcal{O}}_A}$, its canonical maximal abelian $C^*$-subalgebra
${{\mathcal{D}}_A}$, and its gauge action $\rho^A$ is called the Cuntz-Krieger
triplet. We introduce a notion of strong Morita equivalence in the
Cuntz-Krieger triplets, and prove that two Cuntz-Krieger triplets
$({{\mathcal{O}}_A},{{\mathcal{D}}_A},\rho^A)$ and
$({{\mathcal{O}}_B},{{\mathcal{D}}_B},\rho^B)$ are strong Morita equivalent if
and only if $A$ and $B$ are strong shift equivalent.
  We also show that the generalized gauge actions on the stabilized
Cuntz-Krieger algebras are cocycle conjugate if the underlying matrices are
strong shift equivalent. By clarifying K-theoretic behavior of the cocycle
conjugacy, we investigate a relationship between cocycle conjugacy of the gauge
actions on the stabilized Cuntz-Krieger algebras and topological conjugacy of
the underlying topological Markov shifts.

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The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
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The categories of this paper are: nucl-ex
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The categories of this paper are: physics
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The categories of this paper are: cs
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The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
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The categories of this paper are: math-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: eess
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The categories of this paper are: hep-lat
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The categories of this paper are: supr-con
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The categories of this paper are: chao-dyn