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On the classification of simple amenable $C*$-algebras with finite decomposition rank, II

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arxiv 1507.03437 v4 pith:RF47DCYD submitted 2015-07-13 math.OA

George A. Elliott , Guihua Gong , Huaxin Lin , Zhuang Niu This is my paper · ORCID
classification math.OA
keywords finiteamenableeveryranksimplealgebraalgebrasclassifiable
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abstract

We prove that every unital stably finite simple amenable $C^*$-algebra $A$ with finite nuclear dimension and with UCT such that every trace is quasi-diagonal has the property that $A\otimes Q$ has generalized tracial rank at most one, where $Q$ is the universal UHF-algebra. Consequently, $A$ is classifiable in the sense of Elliott.

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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. Non-amenable tight squeezes by Kirchberg algebras

    math.OA 2019-08 accept novelty 8.0 of 10

    Every Kirchberg algebra admits rigid, KK-equivalent, maximal embeddings into non-nuclear and non-exact simple C*-algebras, via perturbed free group crossed products.

  2. 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.

  3. Cuntz--Pimsner algebras of partial automorphisms twisted by vector bundles II: Nuclear dimension

    math.OA 2025-06 conditional novelty 6.0 of 10

    Minimal partial automorphisms twisted by vector bundles over compact infinite finite-dimensional base spaces produce Cuntz-Pimsner algebras that are classifiable by the Elliott invariant, with nuclear dimension at most one.

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