The Elliott conjecture for Villadsen algebras of the first type
| dc.creator | Toms, Andrew S. | |
| dc.creator | Winter, Wilhelm | |
| dc.date | 2006-11-02 | |
| dc.date.accessioned | 2026-07-07T07:32:27Z | |
| dc.date.available | 2026-07-07T07:32:27Z | |
| dc.description | We study the class of simple C*-algebras introduced by Villadsen in his pioneering work on perforated ordered K-theory. We establish six equivalent characterisations of the proper subclass which satisfies the strong form of Elliott's classification conjecture: two C*-algebraic (Z-stability and approximate divisibility), one K-theoretic (strict comparison of positive elements), and three topological (finite decomposition rank, slow dimension growth, and bounded dimension growth). The equivalence of Z-stability and strict comparison constitutes a stably finite version of Kirchberg's characterisation of purely infinite C*-algebras. The other equivalences confirm, for Villadsen's algebras, heretofore conjectural relationships between various notions of good behaviour for nuclear C*-algebras. | |
| dc.description | 25 pages | |
| dc.identifier | https://arxiv.org/abs/math/0611059 | |
| dc.identifier | http://arxiv.org/abs/math/0611059 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/119120 | |
| dc.subject | Operator Algebras | |
| dc.subject | K-Theory and Homology | |
| dc.subject | 46L35; 46L80 | |
| dc.title | The Elliott conjecture for Villadsen algebras of the first type | |
| dc.type | text |