2019/12/16 by Kengo Matsumoto, Matsumoto, Kengo
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Dynamical Systems (math.DS) #FOS: Mathematics #Holomorphic and Operator Theory #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.1912.07216
openalex publication_date 2019/12/16 · openalex created_date 2019/12/26 · openalex updated_date 2026/07/28
A λ-graph bisystem L consists of two labeled Bratteli diagrams (L-,L+), that presents a two-sided subshift ΛL. We will construct a compact totally disconnected metric space with a shift homeomorphism consisting of two-dimensional configurations from a λ-graph bisystem. The configuration space has a certain étale AF-equivalence relation written RL with a natural shift homeomorphism σL coming from the shift homeomorphism σ_ΛL on the subshift ΛL. The equivalence relation RL yields an AF-algebra FL with an automorphism ρL on it. We will study invariance of the étale equivalence relation RL, the groupoid GL=RL\rtimes_σLℤ and the groupoid C^*-algebras C^*(RL), C^*(GL) under topological conjugacy of the presenting two-sided subshifts.