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

2015/11/04 by Matsumoto, Kengo
#37B10 #46L35 #46L80 #FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1511.01193

Abstract

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 their Cuntz--Krieger algebras O_A and O_A are isomorphic and det(1 -A) = - det(1-A). As a consequence, we know 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 (X_B, σ_B) or (X_B, σ_B).

Related

• Orbit equivalence of topological Markov shifts and Cuntz-Krieger algebras
• Continuous orbit equivalence, flow equivalence of Markov shifts and circle actions on Cuntz--Krieger algebras
• Full groups of Cuntz-Krieger algebras and Higman-Thompson groups
• Uniformly continuous orbit equivalence of Markov shifts and gauge actions on Cuntz-Krieger algebras
• Strongly continuous orbit equivalence of one-sided topological Markov shifts