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\(\mathcal{Z}\)-stability and finite-dimensional tracial boundaries. (English) Zbl 1335.46054

Summary: We show that a simple separable unital nuclear nonelementary \(C^\ast\)-algebra whose tracial state space has a compact extreme boundary with finite covering dimension admits uniformly tracially large order zero maps from matrix algebras into its central sequence algebra. As a consequence, strict comparison implies \(\mathcal{Z}\)-stability for these algebras.

MSC:

46L35 Classifications of \(C^*\)-algebras
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