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

Wilhelm Winter

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

Wilhelm Winter

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Abstract

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.

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Wilhelm Winter. 2006-01-04. On the classification of simple Z-stable C*-algebras with real rank zero and finite decomposition rank. https://arxiv.org/abs/math/0502181

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