Recasting the Elliott conjecture |
| |
Authors: | Francesc Perera Andrew S Toms |
| |
Institution: | (1) Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain;(2) Department of Mathematics, York University, 4700 Keele St, Toronto, ON, Canada, M3J 1P3 |
| |
Abstract: | Let A be a simple, unital, finite, and exact C*-algebra which absorbs the Jiang–Su algebra 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 isomorphism, and prove the conjecture in several cases. In these same cases— -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 -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 -theoretic invariants will classify separable and nuclear C*-algebras—with the recent appearance of counterexamples to its strongest concrete form.
Research supported by the DGI MEC-FEDER through Project MTM2005-00934, and the Comissionat per Universitats i Recerca de la
Generalitat de Catalunya. A. S. Toms was also supported in part by an NSERC Discovery Grant. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|