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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)].

##### MSC:
 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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