2023/04/16 by Shirly Geffen, Geffen, Shirly, Dan Ursu +1
Mathematics · #46L55 #47L65 #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.2304.07852
openalex publication_date 2023/04/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/02
In this paper, we give a complete, two-way characterization, of when a noncommutative crossed product A \rtimesλG is simple, in the case of G being an FC-hypercentral group. This is a large class of amenable groups that contains all virtually nilpotent groups, and in the finitely-generated setting, coincides with the set of groups which have polynomial growth. We further completely characterize the ideal intersection property under the assumption that the group is FC, meaning that every element has a finite conjugacy class. Finally, for minimal actions of arbitrary discrete groups on unital C*-algebras, we are able to characterize when the crossed product A \rtimesλG is prime.