Decomposition rank of subhomogeneous $C^*$-algebras

Details Decomposition rank of subhomogeneous $C^*$-algebras Decomposition rank of subhomogeneous $C^*$-algebras

2002-10-28

arxiv.org/abs/math/0210420v1

Mathematics

Operator Algebras

28 pages

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Decomposition rank of subhomogeneous $C^*$-algebras does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Decomposition rank of subhomogeneous $C^*$-algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Decomposition rank of subhomogeneous $C^*$-algebras will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-49838