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$\mathcal Z$-stability and finite dimensional tracial boundaries (1209.3292v2)
Published 14 Sep 2012 in math.OA
Abstract: We show that a simple separable unital nuclear nonelementary $C*$-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 $\Z$-stability for these algebras.
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