Z-stability, finite dimensional tracial boundaries and continuous rank functions

Bhishan Jacelon

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arXiv · 1211.7044

Z-stability, finite dimensional tracial boundaries and continuous rank functions

Bhishan Jacelon

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Abstract

We observe that a recent theorem of Sato, Toms-White-Winter and Kirchberg-Rordam also holds for certain nonunital C*-algebras. Namely, we show that an algebraically simple, separable, nuclear, nonelementary C*-algebra with strict comparison, whose cone of densely finite traces has as a base a Choquet simplex with compact, finite dimensional extreme boundary, and which admits a continuous rank function, tensorially absorbs the Jiang-Su algebra Z.

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Bhishan Jacelon. 2013-07-03. Z-stability, finite dimensional tracial boundaries and continuous rank functions. https://arxiv.org/abs/1211.7044

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