Crossed products of the Cantor set by free minimal actions of Z^d

Abstract

Let d be a positive integer, let X be the Cantor set, and let Z^d act freely and minimally on X. We prove that the crossed product C* (Z^d, X) has stable rank one, real rank zero, and cancellation of projections, and that the order on K_0 (C* (Z^d, X)) is determined by traces. We obtain the same conclusion for the C*-algebras of various kinds of aperiodic tilings.

arXiv comment41 pages, AMSLaTeX

References in corpus (2)

• The Local Structure of Tilings and their Integer Group of Coinvariants
• A proof of the Gap Labeling Conjecture

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• Closed Convex Hulls of Unitary Orbits in C${}^{\ast }$-Algebras of Real Rank Zero
• On the $C^{\ast }$-algebra generated by the Koopman representation of a topological full group