Communications in Mathematical Physics

, Volume 256, Issue 1, pp 1-42

First online:

Crossed Products of the Cantor Set by Free Minimal Actions of ℤ d

  • N. Christopher PhillipsAffiliated withDepartment of Mathematics, University of Oregon Email author 

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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.