Minimal Dynamics and K-theoretic Rigidity: Elliott's Conjecture

Details Minimal Dynamics and K-theoretic Rigidity: Elliott's Conjecture Minimal Dynamics and K-theoretic Rigidity: Elliott's Conjecture

2009-03-24

arxiv.org/abs/0903.4133v1

Mathematics

Operator Algebras

19 pages

Scientific paper

Let X be an infinite, compact, metrizable space of finite covering dimension and h a minimal homeomorphism of X. We prove that the crossed product of C(X) by h 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.

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