A short note on Cuntz splice from a viewpoint of continuous orbit equivalence of topological Markov shifts
Let A be an N× N irreducible matrix with entries in {0,1}. We present an easy way to find an (N+3)× (N+3) irreducible matrix A with entries in {0,1} such that the associated Cuntz-Krieger algebras O _A and O _A are isomorphic and (1 -A) = - (1-A). As a consequence, we find that two Cuntz-Krieger algebras O _A and O _B are isomorphic if and only if the one-sided topological Markov shift (X_A, σ _A) is continuously orbit equivalent to either (X_B, σ _B) or (X_B , σ _B ). , number=1, journal=MATHEMATICA SCANDINAVICA, author=Matsumoto, Kengo, year=2018, month=Aug., pages=91–100