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Abstract: A $\lambda$-graph system ${\frak L}$ is a generalization of a finite labeledgraph and presents a subshift. We will prove that the topological dynamicalsystems $X {{\frak L} 1},\sigma {{\frak L} 1}$ and $X {{\frakL} 2},\sigma {{\frak L} 2}$ for $\lambda$-graph systems ${\frak L} 1$ and${\frak L} 2$ are continuously orbit equivalent if and only if there exists anisomorphism between the associated $C^*$-algebras ${\Cal O} {{\frak L} 1}$ and${\Cal O} {{\frak L} 2}$ keeping their commutative $C^*$-subalgebras$CX {{\frak L} 1}$ and $CX {{\frak L} 2}$. It is also equivalent to thecondition that there exists a homeomorphism from $X {{\frak L} 1}$ to$X {{\frak L} 2}$ intertwining their topological full inverse semigroups. Inparticular, one-sided subshifts $X {\Lambda 1}$ and $X {\Lambda 2}$ are$\lambda$-continuously orbit equivalent if and only if there exists anisomorphism between the associated $C^*$-algebras ${\Cal O} {\Lambda 1}$ and${\Cal O} {\Lambda 2}$ keeping their commutative $C^*$-subalgebras$CX {\Lambda 1}$ and $CX {\Lambda 2}$.



Autor: Kengo Matsumoto

Fuente: https://arxiv.org/







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