Andrew Toms
On the Independence of K-Theory and Stable Rank for Simple C*-Algebras
Jiang and Su and (independently) Elliott discovered a simple, nuclear, infinite-dimensional C*-algebra ?? having the same Elliott invariant as the complex numbers. For a nuclear C*-algebra A with weakly unperforated K*-group the Elliott invariant of A ? ?? is isomorphic to that of A. Thus, any simple nuclear C*-algebra A having a weakly unperforated K*-group which does not absorb ?? provides a counterexample to Elliott's conjecture that the simple nuclear C*-algebras will be classified by the Elliott invariant. In the sequel we exhibit a separable, infinite-dimensional, stably finite instance of such a non-??-absorbing algebra A, and so provide a counterexample to the Elliott conjecture for the class of simple, nuclear, infinite-dimensional, stably finite, separable C*-algebras.
Journal fur die reine und angewandte Mathematik (Crelles Journal), Walter de Gruyter
Print ISSN: 0075-4102
Volume: 2005, 01/2005
Pages: 185 - 199
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