Gong, Guihua On inductive limits of matrix algebras over higher dimensional spaces. II. (English) Zbl 0901.46054 Math. Scand. 80, No. 1, 56-100 (1997). Summary: We will prove the following result. Suppose that \(A= \lim_{n\to\infty} \bigoplus_{i=1}^{k_n} M_{[n,i]} (C(X_{n,i}))\) is of real rank zero, where the spaces \(X_{n,i}\) are finite CW complexes with uniformly bounded dimension (or with slow dimension growth in a generalized sense for non simple \(C^*\)-algebras). Then \(A\) can be written as an inductive limit of finite direct sums of matrix algebras over 3-dimensional finite CW complexes. (Hence it can be classified by its graded ordered \(K\)-group, if one supposes further that \(A\) is simple.) [For part I see ibid. 80, No. 1, 41-55 (1997; review above)]. Cited in 2 ReviewsCited in 10 Documents MSC: 46L35 Classifications of \(C^*\)-algebras 46L80 \(K\)-theory and operator algebras (including cyclic theory) 46M40 Inductive and projective limits in functional analysis Keywords:real rank zero; finite CW complexes with uniformly bounded dimension; slow dimension growth; inductive limit of finite direct sums of matrix algebras over 3-dimensional finite CW complexes; graded ordered \(K\)-group Citations:Zbl 0901.46053 PDFBibTeX XMLCite \textit{G. Gong}, Math. Scand. 80, No. 1, 56--100 (1997; Zbl 0901.46054) Full Text: DOI EuDML