Villadsen, Jesper The range of the Elliott invariant of the simple \(AH\)-algebras with slow dimension growth. (English) Zbl 0916.19003 \(K\)-Theory 15, No. 1, 1-12 (1998). 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 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. Reviewer: V.M.Deundjak (Rostov-na-Donu) Cited in 1 ReviewCited in 16 Documents MSC: 19K14 \(K_0\) as an ordered group, traces 46L35 Classifications of \(C^*\)-algebras Keywords:simple \(C^*\)-algebras; operator \(K\)-theory; tracial states; Elliott invariant PDFBibTeX XMLCite \textit{J. Villadsen}, \(K\)-Theory 15, No. 1, 1--12 (1998; Zbl 0916.19003) Full Text: DOI