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

Yasuhiko Sato

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

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

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

verification ladder T0 review T1 audit T2 compute T3 formal

0 comments

read the original abstract

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.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

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

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.

Pith tools