Decomposition rank of subhomogeneous C*-algebras

الأصل · EN

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.