Crossed products of the Cantor set by free minimal actions of Zd
Abstract
Let d be a positive integer, let X be the Cantor set, and let Zd act freely and minimally on X. We prove that the crossed product C* (Zd, X) has stable rank one, real rank zero, and cancellation of projections, and that the order on K0 (C* (Zd, X)) is determined by traces. We obtain the same conclusion for the C*-algebras of various kinds of aperiodic tilings.
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