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Trace spaces of simple nuclear C*-algebras with finite-dimensional extreme boundary

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arxiv 1209.3000 v1 pith:XHBUFJRO submitted 2012-09-13 math.OA

Yasuhiko Sato This is my paper · ORCID
classification math.OA
keywords algebratracealgebrasboundaryextremefinite-dimensionalnuclearsimple
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Let A be a unital separable simple infinite-dimensional nuclear C*-algebra with at least one tracial state. We prove that if the trace space of A has compact finite-dimensional extreme boundary then there exist unital embeddings of matrix algebras into a certain central sequence algebra of A which is determined by the uniform topology on the trace space. As an application, it is shown that if furthermore A has strict comparison then A absorbs the Jiang-Su algebra tensorially.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Extensions of pure C*-algebras

    math.OA 2025-06 conditional novelty 8.0 of 10

    Pureness of C*-algebras is preserved under extensions: an algebra is pure iff every closed ideal and its quotient are pure.

  2. The Cuntz semigroup and the radius of comparison of the crossed product by a finite group

    math.OA 2019-08 conditional novelty 8.0 of 10

    For finite group actions with the weak tracial Rokhlin property on simple stably finite C*-algebras, the fixed point algebra has radius of comparison at most that of A, and the crossed product at most one over the gro...

  3. 2-positive almost order zero maps and decomposition rank

    math.OA 2019-08 accept novelty 7.0 of 10

    Every 2-positive order zero map between C*-algebras is completely positive, and for unital separable C*-algebras finite decomposition rank can be characterized using 2-positive maps in place of completely positive ones.

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