Endomorphisms of Z-absorbing C*-algebras without conditional expectations

Yasuhiko Sato

Endomorphisms of Z-absorbing C*-algebras without conditional expectations

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arxiv 2309.11068 v2 pith:6N4Q6EGD submitted 2023-09-20 math.OA math.FA

Yasuhiko Sato This is my paper · ORCID

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abstract

We construct an endomorphism of the Jiang-Su algebra $\mathcal{Z}$ which does not admit a conditional expectation. This answers a question in the testamentary homework by E. Kirchberg. As an application, it is shown that any unital separable nuclear $\mathcal{Z}$-absorbing C*-algebra is non-transportable in the Cuntz algebra $\mathcal{O}_2$.

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Ergodic automorphisms on Kirchberg algebras
math.OA 2025-05 conditional novelty 8.0 of 10

Every countable infinite discrete group admits an ergodic action on any unital Kirchberg algebra, and every aperiodic automorphism of such an algebra has a unitary perturbation that is ergodic.

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