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On inductive limits of matrix algebras over higher dimensional spaces. II. (English) Zbl 0901.46054
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)].

46L35 Classifications of \(C^*\)-algebras
46L80 \(K\)-theory and operator algebras (including cyclic theory)
46M40 Inductive and projective limits in functional analysis
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