The range of the Elliott invariant of the simple \(AH\)-algebras with slow dimension growth (Q1273632)

The Elliott invariant consists of the ordered \(K_*\)-group and the space of tracial states together with a pairing between them. It is known that in the classification problem for some classes of \(C^*\)-algebras this invariant is complete. In particular it has been announced by \textit{G. Gong} that the Elliott invariant is complete for simple unital \(C^*\)-algebras which arise as limits of sequences of homogeneous \(C^*\)-algebras (\(AH\)-algebras) with slow dimension growth. In this paper the range of the Elliott invariant for this class of simple \(AH\)-algebras is determined.