dc.contributor.author |
Perera Domènech, Francesc |
dc.contributor.author |
Toms, Andrew S. |
dc.contributor.author |
Universitat Autònoma de Barcelona. Centre de Recerca Matemàtica |
dc.date |
2006 |
dc.identifier |
https://ddd.uab.cat/record/44150 |
dc.identifier |
urn:oai:ddd.uab.cat:44150 |
dc.format |
application/pdf |
dc.language |
eng |
dc.publisher |
Centre de Recerca Matemàtica |
dc.relation |
Centre de Recerca Matemàtica. Prepublicacions ; |
dc.rights |
open access |
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 |
dc.rights |
https://creativecommons.org/licenses/by-nc-nd/2.5/ |
dc.subject |
C*-àlgebres |
dc.subject |
Invariants |
dc.title |
RECASTING THE ELLIOTT CONJECTURE |
dc.type |
Article |
dc.type |
Prepublicació |
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. |