Decomposition Rank of Subhomogeneous C*-Algebras

• Autores: Wilhelm Winter
• Localización: Proceedings of the London Mathematical Society, ISSN 0024-6115, Vol. 89, Nº 2, 2004, págs. 427-456
• Idioma: inglés
• DOI: 10.1112/s0024611504014716
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• Resumen

  • 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.