# Journal of Operator Theory

Volume 74, Issue 2, Fall 2015  pp. 457-483.

Strongly continuous orbit equivalence of one-sided topological Markov shifts

Authors:  Kengo Matsumoto
Author institution: Department of Mathematics, Joetsu University of Education, Joetsu, 943-8512, Japan

Summary:  We prove that one-sided topological Markov shifts $(X_A, \sigma_A)$ and $(X_B, \sigma_B)$ are strongly continuous orbit equivalent if and only if there exists an isomorphism between the Cuntz--Krieger algebras ${\mathcal{O}}_A$ and ${\mathcal{O}}_B$ preserving their maximal commutative $C^*$-subalgebras $C(X_A)$ and $C(X_B)$ and giving cocycle conjugate gauge actions. An example of one-sided topological Markov shifts which are strongly continuous orbit equivalent but not one-sided topologically conjugate is presented.

DOI: http://dx.doi.org/10.7900/jot.2014aug19.2063
Keywords:  Cuntz-Krieger algebras, gauge action, topological Markov shifts, orbit equivalence