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

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

2007-09-08

arxiv.org/abs/0709.1185v1

Mathematics

Operator Algebras

22 pages

Scientific paper

A $\lambda$-graph system ${\frak L}$ is a generalization of a finite labeled graph and presents a subshift. We will prove that the topological dynamical systems $(X_{{\frak L}_1},\sigma_{{\frak L}_1})$ and $(X_{{\frak L}_2},\sigma_{{\frak L}_2})$ for $\lambda$-graph systems ${\frak L}_1$ and ${\frak L}_2$ are continuously orbit equivalent if and only if there exists 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 $X_{\Lambda_1}$ and $X_{\Lambda_2}$ are $\lambda$-continuously orbit equivalent if and only if there exists an isomorphism between the associated $C^*$-algebras ${\Cal O}_{\Lambda_1}$ and ${\Cal O}_{\Lambda_2}$ keeping their commutative $C^*$-subalgebras $C(X_{\Lambda_1})$ and $C(X_{\Lambda_2})$.

Affiliated with

Also associated with

No associations

Rating

Orbit equivalence of one-sided subshifts and the associated C^*-algebras does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Orbit equivalence of one-sided subshifts and the associated C^*-algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Orbit equivalence of one-sided subshifts and the associated C^*-algebras will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-44329