TY - JOUR
AU - Kengo Matsumoto
PY - 2018/08/06
Y2 - 2019/01/21
TI - A short note on Cuntz splice from a viewpoint of continuous orbit equivalence of topological Markov shifts
JF - MATHEMATICA SCANDINAVICA
JA - MathScand
VL - 123
IS - 1
SE - Articles
DO - 10.7146/math.scand.a-102939
UR - https://www.mscand.dk/article/view/102939
AB - 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 $(X_{\bar {B}}, \sigma _{\bar {B}})$.
ER -