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

2023/09/20 by Yasuhiko Sato, Sato, Yasuhiko · 1 citation
Mathematics · #46L06 #46L35 #46L51 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.2309.11068

openalex publication_date 2023/09/20 · openalex created_date 2023/09/22 · openalex updated_date 2026/07/28

Abstract

We construct an endomorphism of the Jiang-Su algebra 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 Z-absorbing C*-algebra is non-transportable in the Cuntz algebra O₂.

Cited by

• Ergodic automorphisms on Kirchberg algebras

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