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

• Kengo Matsumoto ^[1]
  1. [1] Joetsu University of Education

     Joetsu University of Education

     Japón

     
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 123, Nº 1, 2018, págs. 91-100
• Idioma: inglés
• DOI: 10.7146/math.scand.a-102939
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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¯).