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Decomposition Rank of Subhomogeneous C*-Algebras

Published online by Cambridge University Press:  08 September 2004

Wilhelm Winter
Wilhelm Winter
Affiliation:
Mathematisches Institut der Universität Münster, Einsteinstr. 62, D-48149 Münster, Germany. E-mail: wwinter@math.uni-muenster.de
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Abstract

We analyze the decomposition rank (a notion of covering dimension for nuclear C*-algebras introduced by E. Kirchberg and the author) of subhomogeneous C*-algebras. In particular, we show that a subhomogeneous C*-algebra has decomposition rank $n$ if and only if it is recursive subhomogeneous of topological dimension $n$, and that $n$ is determined by the primitive ideal space.

As an application, we use recent results of Q. Lin and N. C. Phillips to show the following. Let $A$ be the crossed product C*-algebra coming from a compact smooth manifold and a minimal diffeomorphism. Then the decomposition rank of $A$ is dominated by the covering dimension of the underlying manifold.

Keywords

C*-algebra bundlescovering dimensioncrossed productsminimal diffeomorphisms46L8546L35
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 89 , Issue 2 , September 2004 , pp. 427 - 456
Copyright
2004 London Mathematical Society

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Footnotes

This research was supported by EU-Network Quantum Spaces – Noncommutative Geometry (Contract No. HPRN-CT-2002-00280) and Deutsche Forschungsgemeinschaft (SFB 478).