Minimal dynamics and the classification of C~*-algebras

摘要

Let X be an infinite, compact, metrizable space of finite covering dimension and α:X→X a minimal homeomorphism. We prove that the crossed product C(X) x_α Z absorbs the Jiang-Su algebra tensorially and has finite nuclear dimension. As a consequence, these algebras are determined up to isomorphism by their graded ordered K-theory under the necessary condition that their projections separate traces. This result applies, in particular, to those crossed products arising from uniquely ergodic homeomorphisms.