Decomposition rank of subhomogeneous $C^*$-algebras

Wilhelm Winter

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arXiv · math/0210420

Decomposition rank of subhomogeneous $C^*$-algebras

Wilhelm Winter

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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.

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BibTeX RIS

Wilhelm Winter. 2002-10-28. Decomposition rank of subhomogeneous $C^*$-algebras. https://arxiv.org/abs/math/0210420

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