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An existence result for simple inductive limits of interval algebras. (English) Zbl 0902.46036
The paper gives an abstract characterization of the so-called Elliot triples. Let \(G\) be a simple noncyclic dimension group, such that the extreme boundary of the state space is compact and totally disconnected. Let also \(\Delta\) be a metrizable Choquet simplex and \(f:\Delta\to S(G)\) be an affine continuous map with the property \(f(\partial_e\Delta)= \partial_eS(G)\). It is shown that \((G,\Delta, f)\) is the Elliot triple of some simple unital \(C^*\)-algebra which is the inductive limit of finite direct sums of matrix algebras over \(C([0, 1])\).

46L05 General theory of \(C^*\)-algebras
46M40 Inductive and projective limits in functional analysis
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