Strongly continuous orbit equivalence of one-sided topological Markov shifts

2014/08/20 by Kengo Matsumoto, Matsumoto, Kengo · 1 citation
Mathematics · Physics and Astronomy · #37B10 (Secondary) #46L35 #46L55 (Primary) #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Noncommutative and Quantum Gravity Theories #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.1408.4501

openalex publication_date 2014/08/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We will introduce a notion of strongly continuous orbit equivalence in one-sided topological Markov shifts. Strongly continuous orbit equivalence yields a topological conjugacy between their two-sided topological Markov shifts (X_A, σ_A) and (X_B, σ_B). We prove that one-sided topological Markov shifts (X_A, σ_A) and (X_B, σ_B) are strongly continuous orbit equivalent if and only if there exists an isomorphism bewteen the Cuntz-Krieger algebras O_A and 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.

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