Recasting the Elliott conjecture
| dc.creator | Perera, Francesc | |
| dc.creator | Toms, Andrew S. | |
| dc.date | 2006-01-19 | |
| dc.date | 2006-09-27 | |
| dc.date.accessioned | 2026-07-07T06:59:05Z | |
| dc.date.available | 2026-07-07T06:59:05Z | |
| dc.description | Let A be a simple, unital, exact, and finite 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 obtained from the Elliott invariant in a functorial manner. We conjecture that this embedding is an isomorphism, 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 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. | |
| dc.description | 28 pages; several typos corrected, Lemma 3.4 added; to appear in Math. Ann | |
| dc.identifier | https://arxiv.org/abs/math/0601478 | |
| dc.identifier | http://arxiv.org/abs/math/0601478 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/107620 | |
| dc.subject | Operator Algebras | |
| dc.subject | K-Theory and Homology | |
| dc.subject | 46L35, 46L80 | |
| dc.title | Recasting the Elliott conjecture | |
| dc.type | text |