On the classification of simple Z-stable C*-algebras with real rank zero and finite decomposition rank

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We show that, if A is a separable simple unital C*-algebra which absorbs the Jiang-Su algebra Z tensorially and which has real rank zero and finite decomposition rank, then A is tracially AF in the sense of Lin, without any restriction on the tracial state space. As a consequence, the Elliott conjecture is true for the class of C*-algebras as above which, additionally, satisfy the Universal Coefficients Theorem. In particular, such algebras are completely determined by their ordered K-theory. They are approximately homogeneous of topological dimension less than or equal to 3, approximately subhomogeneous of topological dimension at most 2 and their decomposition rank also is no greater than 2.
16 pages, no figures. Final version; to appear in Journal of the LMS

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Operator Algebras, Functional Analysis, K-Theory and Homology, 46L85; 46L35

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http://salesiana.dossiersoluciones.com/handle/123456789/101070

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0502181
 http://arxiv.org/abs/math/0502181

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