KK-rigidity of simple nuclear C*-algebras

2024/08/05 by Christopher Schafhauser, Schafhauser, Christopher · 1 citation
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.2408.02745

openalex publication_date 2024/08/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is shown that if A and B are unital separable simple nuclear \mathcal Z-stable C^*-algebras and there is a unital embedding A → B which is invertible on KK-theory and traces, then A ≅ B. In particular, two unital separable simple nuclear \mathcal Z-stable C^*-algebras which either have real rank zero or unique trace are isomorphic if and only if they are homotopy equivalent. It is further shown that two finite strongly self-absorbing C^*-algebras are isomorphic if and only if they are KK-equivalent in a unit-preserving way.

Cited by

• Centrally pure C*-algebras

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