dc.contributor |
Centre de Recerca Matemàtica |
dc.contributor.author |
Thiel, Hannes |
dc.contributor.author |
Winter, Wilhelm |
dc.date.accessioned |
2012-06-21T10:02:44Z |
dc.date.available |
2012-06-21T10:02:44Z |
dc.date.created |
2011 |
dc.date.issued |
2011 |
dc.identifier.uri |
http://hdl.handle.net/2072/196880 |
dc.format.extent |
18 p. |
dc.language.iso |
eng |
dc.publisher |
Centre de Recerca Matemàtica |
dc.relation.ispartofseries |
Prepublicacions del Centre de Recerca Matemàtica;1079 |
dc.rights |
info:eu-repo/semantics/openAccess |
dc.rights |
L'accés als continguts d'aquest document queda condicionat a l'acceptació de les condicions d'ús establertes per la següent llicència Creative Commons: http://creativecommons.org/licenses/by-nc-nd/3.0/es/ |
dc.source |
RECERCAT (Dipòsit de la Recerca de Catalunya) |
dc.subject.other |
C*-àlgebres |
dc.subject.other |
Grups, Teoria de -- Generadors |
dc.subject.other |
Estabilitat |
dc.title |
The generator problem for Z-stable C*-algebras |
dc.type |
info:eu-repo/semantics/preprint |
dc.subject.udc |
517 - Anàlisi |
dc.embargo.terms |
cap |
dc.description.abstract |
The generator problem was posed by Kadison in 1967, and it remains open until today. We provide a solution for the class of C*-algebras absorbing the Jiang-Su algebra Z tensorially. More precisely, we show that every unital, separable, Z-stable C*-algebra A is singly generated, which means that there exists an element x є A that is not contained in any proper sub-C*-
algebra of A. To give applications of our result, we observe that Z can be embedded into the reduced group C*-algebra of a discrete group that contains a non-cyclic, free subgroup. It follows that certain tensor products with reduced group C*-algebras are singly generated. In particular, C*r (F ∞) ⨂ C*r (F ∞) is singly generated. |