dc.contributor |
Centre de Recerca Matemàtica |
dc.contributor.author |
Perera Domènech, Francesc |
dc.contributor.author |
Toms, Andrew S. |
dc.date.accessioned |
2006-02-03T12:42:02Z |
dc.date.available |
2006-02-03T12:42:02Z |
dc.date.issued |
2006-01 |
dc.identifier.uri |
http://hdl.handle.net/2072/1486 |
dc.format.extent |
326413 bytes |
dc.format.mimetype |
application/pdf |
dc.language.iso |
eng |
dc.publisher |
Centre de Recerca Matemàtica |
dc.relation.ispartofseries |
Prepublicacions del Centre de Recerca Matemàtica;662 |
dc.rights |
Aquest document està subjecte a una llicència d'ús de Creative Commons, amb la qual es permet copiar, distribuir i comunicar públicament l'obra sempre que se'n citin l'autor original, la universitat i el centre i no se'n faci cap ús comercial ni obra derivada, tal com queda estipulat en la llicència d'ús (http://creativecommons.org/licenses/by-nc-nd/2.5/es/) |
dc.subject |
C*-àlgebres |
dc.subject |
Invariants |
dc.title |
RECASTING THE ELLIOTT CONJECTURE |
dc.type |
info:eu-repo/semantics/preprint |
dc.description.abstract |
Let A be a simple, unital, finite, and exact C*-algebra which absorbs the Jiang-Su algebra Z tensorially. We prove that the Cuntz semigroup of A admits a complete order embedding into an ordered semigroup which is obtained from the Elliott invariant in a functorial manner. We conjecture that this embedding is an isomor
phism, and prove the conjecture in several cases. In these same cases - Z-stable algebras all - we prove that the Elliott conjecture in its strongest form is equivalent to a conjecture which appears much weaker. Outside the class of Z-stable C*-algebras, this weaker conjecture has no known counterexamples, and it is plausible that none
exist. Thus, we reconcile the still intact principle of Elliott's classification conjecture -that K-theoretic invariants will classify separable and nuclear C*-algebras- with the recent appearance of counterexamples to its strongest concrete form. |