Journal of Operator Theory

Volume 56, Issue 2, Fall 2006 pp. 403-421.

The $C^*$-algebras associated to time-${t}$ automorphisms of mapping tori

Authors: Benjamin A. Itza-Ortiz
Author institution: Department of Mathematics and Statistics, University of Ottawa, 585 King Edward Ave., Ottawa, K1N-6N5, Canada

Summary: We find the range of a trace on the $K_0$-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.

Keywords: Elliott invariant, Voiculescu-Brown entropy, mapping torus.

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