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Journal of Operator Theory

Volume 70, Issue 1, Summer 2013  pp. 191-210.

The crossed-product structure of $C^*$-algebras arising from topological dynamical systems

Authors Cynthia Farthing (1), Nura Patani (2), and Paulette N. Willis (3)
Author institution: (1) Department of Mathematics, University of Iowa, Iowa City, 52242, U.S.A.
(2) School of Mathematical and Statistical Sciences, Arizona State University, Tempe, 85287, U.S.A.
(3) Department of Mathematics, University of Houston, Houston, 77204, U.S.A.

Summary:  We show that every topological $k$-graph constructed from a locally compact Hausdorff space $\Omega$ and a family of pairwise commuting local homeomorphisms on $\Omega$ satisfying a uniform boundedness condition on the cardinalities of inverse images may be realized as a semigroup crossed product in the sense of Larsen.

Keywords:  Crossed product, topological higher-rank graph, product system of $C^*$-correspondences, Cuntz-Pimsner algebra

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