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On the classification of simple inductive limit \(C^{*}\)-algebras. II: The isomorphism theorem. (English) Zbl 1129.46051
It is shown that the Elliott invariant is a complete invariant for the class of unital simple \(C^*\)-algebras, which are inductive limits of sequences \(A_1\to A_2\to\dots\to A_n\to\dots\) with \(A_n=\bigoplus_{i=1}^{t_n}P_{n,i}M_{[n,i]}(C(X_{n,i}))P_{n,i}\), where the \(X_{n,i}\) are compact metric spaces of uniformly bounded finite dimension and the \(P_{n,i}\) are projections in the algebras \(M_{[n,i]}(C(X_{n,i}))\) of matrix-valued functions on \(X_{n,i}\).
[For Part I, see G. Gong, Doc. Math., J. DMV 7, 255–641 (2002; Zbl 1024.46018).]

MSC:
46L35 Classifications of \(C^*\)-algebras
19K56 Index theory
46L80 \(K\)-theory and operator algebras (including cyclic theory)
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