The Elliott conjecture for Villadsen algebras of the first type

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We study the class of simple C*-algebras introduced by Villadsen in his pioneering work on perforated ordered K-theory. We establish six equivalent characterisations of the proper subclass which satisfies the strong form of Elliott's classification conjecture: two C*-algebraic (Z-stability and approximate divisibility), one K-theoretic (strict comparison of positive elements), and three topological (finite decomposition rank, slow dimension growth, and bounded dimension growth). The equivalence of Z-stability and strict comparison constitutes a stably finite version of Kirchberg's characterisation of purely infinite C*-algebras. The other equivalences confirm, for Villadsen's algebras, heretofore conjectural relationships between various notions of good behaviour for nuclear C*-algebras.
25 pages

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Operator Algebras, K-Theory and Homology, 46L35; 46L80

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http://salesiana.dossiersoluciones.com/handle/123456789/119120

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0611059
 http://arxiv.org/abs/math/0611059

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arXiv