Full groups of one-sided topological Markov shifts

2012/05/07 by Kengo Matsumoto, Matsumoto, Kengo · 1 citation
Mathematics · #37B10 (Primary) 28D20 #37B40 #46L80 (Secondary) #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Finite Group Theory Research #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.1205.1320

openalex publication_date 2012/05/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let (X_A,σ_A) be the right one-sided topological Markov shift for an irreducible matrix with entries in \0,1\, and Γ_A the continuous full group of (X_A,σ_A). For two irreducible matrices A and B with entries in \0,1\, it will be proved that the continuous full groups Γ_A and Γ_B are isomorphic as abstract groups if and only if their one-sided topological Markov shifts (X_A,σ_A) and (X_B,σ_B) are continuously orbit equivalent.

Citations

• On Groups of Measure Preserving Transformations. I

Cited by

• Topological full groups of one-sided shifts of finite type

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