-Stable ASH Algebras

Abstract

AbstractThe Jiang–Su algebra has come to prominence in the classification program for nuclear C*-algebras of late, due primarily to the fact that Elliott’s classification conjecture in its strongest form predicts that all simple, separable, and nuclear C*-algebras with unperforated K-theory will absorb tensorially, i.e., will be -stable. There exist counterexamples which suggest that the conjecture will only hold for simple, nuclear, separable and -stable C*-algebras. We prove that virtually all classes of nuclear C*-algebras for which the Elliott conjecture has been confirmed so far consist of -stable C*-algebras. This follows in large part from the following result, also proved herein: separable and approximately divisible C*-algebras are -stable.