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

2002/08/11 by N. Christopher Phillips, Phillips, N. Christopher · 1 citation
Mathematics · #Advanced Operator Algebra Research #Mathematical Dynamics and Fractals #Spectral Theory in Mathematical Physics #math.OA #msc:19A13 #msc:19B10 #msc:19K14 #msc:22A22 #msc:46L55 #msc:46L80 #msc:54H15 #msc:57S99

paper · pdf · doi:10.48550/arxiv.math/0208085

41 pages, AMSLaTeX

arxiv created 2002/08/11 · arxiv updated 2009/11/30

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 K₀ (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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