Orbit equivalence of one-sided subshifts and the associated C^*-algebras

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dc.creatorMatsumoto, Kengo
dc.date2007-09-08
dc.date.accessioned2026-07-07T08:28:23Z
dc.date.available2026-07-07T08:28:23Z
dc.descriptionA $λ$-graph system ${\frak L}$ is a generalization of a finite labeled graph and presents a subshift. We will prove that the topological dynamical systems $(X_{{\frak L}_1},σ_{{\frak L}_1})$ and $(X_{{\frak L}_2},σ_{{\frak L}_2})$ for $λ$-graph systems ${\frak L}_1$ and ${\frak L}_2$ are continuously orbit equivalent if and only if there exists an isomorphism between the associated $C^*$-algebras ${\Cal O}_{{\frak L}_1}$ and ${\Cal O}_{{\frak L}_2}$ keeping their commutative $C^*$-subalgebras $C(X_{{\frak L}_1})$ and $C(X_{{\frak L}_2})$. It is also equivalent to the condition that there exists a homeomorphism from $X_{{\frak L}_1}$ to $X_{{\frak L}_2}$ intertwining their topological full inverse semigroups. In particular, one-sided subshifts $X_{Λ_1}$ and $X_{Λ_2}$ are $λ$-continuously orbit equivalent if and only if there exists an isomorphism between the associated $C^*$-algebras ${\Cal O}_{Λ_1}$ and ${\Cal O}_{Λ_2}$ keeping their commutative $C^*$-subalgebras $C(X_{Λ_1})$ and $C(X_{Λ_2})$.
dc.description22 pages
dc.identifierhttps://arxiv.org/abs/0709.1185
dc.identifierhttp://arxiv.org/abs/0709.1185
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/137597
dc.subjectOperator Algebras
dc.subjectDynamical Systems
dc.subject46L55
dc.titleOrbit equivalence of one-sided subshifts and the associated C^*-algebras
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