Classification of \(C^*\)-algebras of real rank zero and unsuspended \(E\)-equivalence types (Q1381528)

In [Ann. Math., II. Ser. 144, No. 3, 497-610 (1996; Zbl 0867.46041)], the author and \textit{G. A. Elliott} proved that ordered scaled K-groups provide a complete invariant for the simple members of a certain class of inductive limit \(C^*\)-algebras. The present paper exhibits an example to show that these invariants no longer suffice when the simplicity restriction is lifted. An additional invariant is introduced to fill the gap. Classification of amenable \(C^*\)-algebras was surveyed by \textit{G. A. Elliott} in [Proceedings of the international congress of mathematicians, ICM '94, August 3-11, 1994, Zürich, Switzerland. Vol. II. Basel: Birkhäuser, 922-932 (1995)].