Communications in Mathematical Physics

, Volume 256, Issue 1, pp 1–42

Crossed Products of the Cantor Set by Free Minimal Actions of ℤd


DOI: 10.1007/s00220-004-1171-y

Cite this article as:
Phillips, N. Commun. Math. Phys. (2005) 256: 1. doi:10.1007/s00220-004-1171-y


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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© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of OregonEugeneUSA