Classification of equivariantly O₂-stable amenable actions on nuclear C^∗-algebras

2023/09/21 by Matteo Pagliero, Pagliero, Matteo, Gábor Szabó +1
Mathematics · Medicine · #46L35 #46L55 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Electroconvulsive Therapy Studies #FOS: Mathematics #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.2309.12472

openalex publication_date 2023/09/21 · openalex created_date 2023/09/26 · openalex updated_date 2026/07/28

Abstract

Given a second-countable, locally compact group G, we consider amenable G-actions on separable, stable, nuclear C^∗-algebras that are isometrically shift-absorbing and tensorially absorb the trivial action on the Cuntz algebra O₂. We show that such actions are classified up to cocycle conjugacy by the induced G-action on the primitive ideal space. In the special case when G is exact, we prove a unital version of our classification theorem. For compact groups, we obtain a classification up to conjugacy.

Related

• Continuous actions on primitive ideal spaces lift to C^∗-actions
• Strongly outer actions of amenable groups on Z-stable nuclear C^*-algebras
• Actions of amenable groups and crossed products of Z-absorbing C*-algebras
• Amenability and weak containment for actions of locally compact groups\n on C^*-algebras
• Actions on classifiable C*-algebras without equivariant property (SI)