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

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dc.creatorWinter, Wilhelm
dc.date2005-02-09
dc.date2006-01-04
dc.date.accessioned2026-07-07T06:39:25Z
dc.date.available2026-07-07T06:39:25Z
dc.descriptionWe 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.
dc.description16 pages, no figures. Final version; to appear in Journal of the LMS
dc.identifierhttps://arxiv.org/abs/math/0502181
dc.identifierhttp://arxiv.org/abs/math/0502181
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/101070
dc.subjectOperator Algebras
dc.subjectFunctional Analysis
dc.subjectK-Theory and Homology
dc.subject46L85; 46L35
dc.titleOn the classification of simple Z-stable C*-algebras with real rank zero and finite decomposition rank
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