Resumen de A short note on Cuntz splice from a viewpoint of continuous orbit equivalence of topological Markov shifts

Kengo Matsumoto

• 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 OA and OA¯ are isomorphic and det(1−A)=−det(1−A¯). As a consequence, we find that two Cuntz-Krieger algebras OA and OB are isomorphic if and only if the one-sided topological Markov shift (XA,σA) is continuously orbit equivalent to either (XB,σB) or (XB¯,σB¯).