Localizing the Elliott conjecture at strongly self-absorbing C*-algebras

Details Localizing the Elliott conjecture at strongly self-absorbing C*-algebras Localizing the Elliott conjecture at strongly self-absorbing C*-algebras

2007-08-02

arxiv.org/abs/0708.0283v3

Mathematics

Operator Algebras

The previous version contained a mistake (pointed out by Huaxin Lin) in the proof of Theorem 3.4, which affected the main Coro

Scientific paper

We formally introduce the concept of localizing the Elliott conjecture at a given strongly self-absorbing C*-algebra $D$; we also explain how the known classification theorems for nuclear C*-algebras fit into this concept. As a new result in this direction, we employ recent results of Lin to show that (under a mild K-theoretic condition) the class of separable, unital, simple C*-algebras with locally finite decomposition rank and UCT, and for which projections separate traces, satisfies the Elliott conjecture localized at the Jiang-Su algebra Z. Our main result is formulated in a more general way; this allows us to outline a strategy to possibly remove the trace space condition as well as the K-theory restriction entirely. When regarding both our result and the recent classification theorem of Elliott, Gong and Li as generalizations of the real rank zero case, the two approaches are perpendicular in a certain sense. The strategy to attack the general case aims at combining these two approaches. Our classification theorem covers simple ASH algebras for which projections separate traces (and the K-groups of which have finitely generated torsion part); it does, however, not at all depend on an inductive limit structure. Also, in the monotracial case it does not rely on the existence or absence of projections in any way. In fact, it is the first such result which, in a natural way, covers all known unital, separable, simple, nuclear and stably finite C*-algebras of real rank zero (the K-groups of which have finitely generated torsion part) as well as the (projectionless) Jiang-Su algebra itself.

Affiliated with

Also associated with

No associations

Rating

Localizing the Elliott conjecture at strongly self-absorbing 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 Localizing the Elliott conjecture at strongly self-absorbing C*-algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Localizing the Elliott conjecture at strongly self-absorbing C*-algebras will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-244575