2018/03/16 by Eusebio Gardella, Martino Lupini, Gardella, Eusebio +1
Mathematics · Medicine · Physics and Astronomy · #Advanced Operator Algebra Research #FOS: Mathematics #Functional Analysis (math.FA) #Neurological and metabolic disorders #Noncommutative and Quantum Gravity Theories #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.1803.06308
openalex publication_date 2018/03/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study strongly outer actions of discrete groups on C*-algebras in relation to (non)amenability. In contrast to related results for amenable groups, where uniqueness of strongly outer actions on the Jiang-Su algebra is expected, we show that uniqueness fails for all nonamenable groups, and that the failure is drastic. Our main result implies that if G contains a copy of the free group, then there exist uncountable many, non-cocycle conjugate strongly outer actions of G on any Jiang-Su stable tracial C*-algebra. Similar conclusions apply for outer actions on McDuff tracial von Neumann algebras. We moreover show that G is amenable if and only if the Bernoulli shift on a finite strongly self-absorbing C*-algebra absorbs the trivial action on the Jiang-Su algebra. Our methods consist in a careful study of weak containments of the Koopman representations of different Bernoulli-type actions.