On the classification of simple Z-stable C*-algebras with real rank zero and finite decomposition rank

Details On the classification of simple Z-stable C*-algebras with real rank zero and finite decomposition rank On the classification of simple Z-stable C*-algebras with real rank zero and finite decomposition rank

2005-02-09

arxiv.org/abs/math/0502181v2

Mathematics

Operator Algebras

16 pages, no figures. Final version; to appear in Journal of the LMS

Scientific paper

We show that, if A is a separable simple unital C*-algebra which absorbs the Jiang-Su algebra Z tensorially and which has real rank zero and finite decomposition rank, then A is tracially AF in the sense of Lin, without any restriction on the tracial state space. As a consequence, the Elliott conjecture is true for the class of C*-algebras as above which, additionally, satisfy the Universal Coefficients Theorem. In particular, such algebras are completely determined by their ordered K-theory. They are approximately homogeneous of topological dimension less than or equal to 3, approximately subhomogeneous of topological dimension at most 2 and their decomposition rank also is no greater than 2.

Affiliated with

Also associated with

No associations

Rating

On the classification of simple Z-stable C*-algebras with real rank zero and finite decomposition rank 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 On the classification of simple Z-stable C*-algebras with real rank zero and finite decomposition rank, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the classification of simple Z-stable C*-algebras with real rank zero and finite decomposition rank will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-722169