Crossed products by minimal homeomorphisms

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Let X be an infinite compact metric space with finite covering dimension and let h be a minimal homeomorphism of X. Let A be the associated crossed product C*-algebra. We show that A has tracial rank zero whenever the image of K_0 (A) in the affine functions on the tracial state space of A is dense. As a consequence, we show that these crossed product C*-algebras are in fact simple AH algebras with real rank zero. When X is connected and h is further assumed to be uniquely ergodic, then the above happens if and only if the rotation number associated to h has irrational values. By applying the classification theorem for nuclear simple C*-algebras with tracial rank zero, we show that two such dynamical systems have isomorphic crossed products if and only if they have isomorphic scaled ordered K-theory.
AMSLaTeX; 24 pages, no figures

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Operator Algebras, 46L55

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http://salesiana.dossiersoluciones.com/handle/123456789/72247

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0408291
 http://arxiv.org/abs/math/0408291

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arXiv