C_0(X)-algebras, stability and strongly self-absorbing C*-algebras

Details C_0(X)-algebras, stability and strongly self-absorbing C*-algebras C_0(X)-algebras, stability and strongly self-absorbing C*-algebras

2006-10-10

arxiv.org/abs/math/0610344v1

Mathematics

Operator Algebras

33 pages

Scientific paper

We study permanence properties of the classes of stable and so-called D-stable C*-algebras, respectively. More precisely, we show that a C_0(X)-algebra A is stable if all its fibres are, provided that the underlying compact metrizable space X has finite covering dimension or that the Cuntz semigroup of A is almost unperforated (a condition which is automatically satisfied for C*-algebras absorbing the Jiang--Su algebra Z tensorially). Furthermore, we prove that if D is a K_1-injective strongly self-absorbing C*-algebra, then A absorbs D tensorially if and only if all its fibres do, again provided that X is finite-dimensional. This latter statement generalizes results of Blanchard and Kirchberg. We also show that the condition on the dimension of X cannot be dropped. Along the way, we obtain a useful characterization of when a C*-algebra with weakly unperforated Cuntz semigroup is stable, which allows us to show that stability passes to extensions of Z-absorbing C*-algebras.

Affiliated with

Also associated with

No associations

Rating

C_0(X)-algebras, stability and 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 C_0(X)-algebras, stability and strongly self-absorbing C*-algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and C_0(X)-algebras, stability and strongly self-absorbing C*-algebras will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-579152