A short note on Cuntz splice from a viewpoint of continuous orbit equivalence of topological Markov shifts
Keyword(s):
Let $A$ be an $N\times N$ irreducible matrix with entries in $\{0,1\}$. We present an easy way to find an $(N+3)\times (N+3)$ irreducible matrix $\bar {A}$ with entries in $\{0,1\}$ such that the associated Cuntz-Krieger algebras ${\mathcal {O}}_A$ and ${\mathcal {O}}_{\bar {A}}$ are isomorphic and $\det (1 -A) = - \det (1-\bar {A})$. As a consequence, we find that two Cuntz-Krieger algebras ${\mathcal {O}}_A$ and ${\mathcal {O}}_B$ are isomorphic if and only if the one-sided topological Markov shift $(X_A, \sigma _A)$ is continuously orbit equivalent to either $(X_B, \sigma _B)$ or $(X_{\bar {B}}, \sigma _{\bar {B}})$.
2015 ◽
Vol 37
(2)
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pp. 389-417
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2015 ◽
Vol 36
(5)
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pp. 1557-1581
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2017 ◽
Vol 165
(2)
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pp. 341-357
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1997 ◽
Vol 08
(03)
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pp. 357-374
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2013 ◽
Vol 34
(4)
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pp. 1103-1115
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2014 ◽
Vol 54
(4)
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pp. 863-877
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2016 ◽
Vol 285
(1-2)
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pp. 121-141
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1997 ◽
Vol 17
(5)
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pp. 1083-1129
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