Toms, Andrew S.; White, Stuart; Winter, Wilhelm \(\mathcal{Z}\)-stability and finite-dimensional tracial boundaries. (English) Zbl 1335.46054 Int. Math. Res. Not. 2015, No. 10, 2702-2727 (2015). 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. Cited in 1 ReviewCited in 26 Documents MSC: 46L35 Classifications of \(C^*\)-algebras Keywords:simple separable unital nuclear nonelementary \(C^\ast\)-algebra; \(\mathcal{Z}\)-stability PDFBibTeX XMLCite \textit{A. S. Toms} et al., Int. Math. Res. Not. 2015, No. 10, 2702--2727 (2015; Zbl 1335.46054) Full Text: DOI arXiv