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Poly-$\mathbb{Z}$ group actions on Kirchberg algebras I

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arxiv 1810.05850 v2 pith:5N7UHCIX submitted 2018-10-13 math.OA

Masaki Izumi , Hiroki Matui This is my paper · ORCID
classification math.OA
keywords actionsalgebraskirchbergmathbbpoly-classificationgroupaddition
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abstract

Toward the complete classification of poly-$\mathbb{Z}$ group actions on Kirchberg algebras, we prove several fundamental theorems that are used in the classification. In addition, as an application of them, we classify outer actions of poly-$\mathbb{Z}$ groups of Hirsch length not greater than three on unital Kirchberg algebras up to $KK$-trivial cocycle conjugacy.

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  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.

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