Inductive limits of projective C*-algebras

Details Inductive limits of projective C*-algebras Inductive limits of projective C*-algebras

2011-05-10

arxiv.org/abs/1105.1979v1

Mathematics

Operator Algebras

24 pages

Scientific paper

We show that a C*-algebra is an inductive limits of projective C*-algebras if and only if it has trivial shape, i.e., is shape equivalent to the zero C*-algebra. In particular, every contractible C*-algebra is an inductive limit of projectives, and one may assume that the connecting morphisms are surjective. Interestingly, an example of Dadarlat shows that trivial shape does not pass to full hereditary sub-C*-algebra. It then follows that the same fails for projectivity. To obtain these results, we develop criteria for inductive limit decompositions, and we discuss the relation with different concepts of approximation. As main application of our findings we show that a C*-algebra is (weakly) projective if and only if it is (weakly) semiprojective and has trivial shape. It follows that a C*-algebra is projective if and only if it is contractible and semiprojective. This confirms a conjecture of Loring.

Affiliated with

Also associated with

No associations

Rating

Inductive limits of projective 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 Inductive limits of projective C*-algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Inductive limits of projective C*-algebras will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-280547