THE C-ALGEBRAS ASSOCIATED TO TIME-t AUTOMORPHISMS OF MAPPING TORI

We find the range of a trace on the K0-group of a crossed product by a time-t automorphism of a mapping torus. We also find a formula to compute the Voiculescu-Brown entropy for such an automorphism. By specializing to the commutative setting, we prove that the crossed products by minimal time-t hom...

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Bibliographic Details
Published in:Journal of operator theory 2006-09, Vol.56 (2), p.403-421
Main Author: ITZÁ-ORTIZ, BENJAMÍN A.
Format: Article
Language:English
Subjects:
Algebra
Automorphisms
Cantors theorem
Dynamical systems
Entropy
Ergodic theory
Homeomorphism
Mathematical theorems
Topological theorems
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Summary:We find the range of a trace on the K0-group of a crossed product by a time-t automorphism of a mapping torus. We also find a formula to compute the Voiculescu-Brown entropy for such an automorphism. By specializing to the commutative setting, we prove that the crossed products by minimal time-t homeomorphisms of suspensions built over strongly orbit equivalent Cantor minimal systems have isomorphic Elliott invariants. As an application of our results we give examples of dynamical systems on (compact metric) connected 1-dimensional spaces which are not flip conjugate (because of different entropy) yet their associated crossed products have isomorphic Elliott invariants.
ISSN:0379-4024
1841-7744