Simple C*-algebras with locally finite decomposition rank
| dc.creator | Winter, Wilhelm | |
| dc.date | 2006-02-27 | |
| dc.date.accessioned | 2026-07-07T07:03:50Z | |
| dc.date.available | 2026-07-07T07:03:50Z | |
| dc.description | We introduce the notion of locally finite decomposition rank, a structural property shared by many stably finite nuclear C*-algebras. The concept is particularly relevant for Elliott's program to classify nuclear C*-algebras by K-theory data. We study some of its properties and show that a simple unital C*-algebra, which has locally finite decomposition rank, real rank zero and which absorbs the Jiang-Su algebra Z tensorially, has tracial rank zero in the sense of Lin. As a consequence, any such C*-algebra, if it additionally satisfies the Universal Coefficients Theorem, is approximately homogeneous of topological dimension at most 3. Our result in particular confirms the Elliott conjecture for the class of simple unital Z-stable ASH algebras with real rank zero. Moreover, it implies that simple unital Z-stable AH algebras with real rank zero not only have slow dimension growth in the ASH sense, but even in the AH sense. | |
| dc.description | 30 pages, no figures | |
| dc.identifier | https://arxiv.org/abs/math/0602617 | |
| dc.identifier | http://arxiv.org/abs/math/0602617 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/109130 | |
| dc.subject | Operator Algebras | |
| dc.subject | Functional Analysis | |
| dc.subject | K-Theory and Homology | |
| dc.subject | 46L85; 46L35 | |
| dc.title | Simple C*-algebras with locally finite decomposition rank | |
| dc.type | text |