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

N. Christopher Phillips
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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.

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N. Christopher Phillips. 2002-08-11. Crossed products of the Cantor set by free minimal actions of Z^d. https://arxiv.org/abs/math/0208085

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