C_0(X)-algebras, stability and strongly self-absorbing C*-algebras
| dc.creator | Hirshberg, Ilan | |
| dc.creator | Rordam, Mikael | |
| dc.creator | Winter, Wilhelm | |
| dc.date | 2006-10-10 | |
| dc.date.accessioned | 2026-07-07T07:28:55Z | |
| dc.date.available | 2026-07-07T07:28:55Z | |
| dc.description | 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. | |
| dc.description | 33 pages | |
| dc.identifier | https://arxiv.org/abs/math/0610344 | |
| dc.identifier | http://arxiv.org/abs/math/0610344 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/117913 | |
| dc.subject | Operator Algebras | |
| dc.subject | 46L05 | |
| dc.title | C_0(X)-algebras, stability and strongly self-absorbing C*-algebras | |
| dc.type | text |