C*-simplicity and the amenable radical

• 成果类型: Article
• 署名作者: Le Boudec, Adrien
• 署名单位: Universite Paris Saclay; Universite Catholique Louvain
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-016-0706-0
• 发表日期: 2017
• 页码: 159-174
• 关键词: hyperbolic groups; free-products; ALGEBRAS

摘要

A countable group is -simple if its reduced -algebra is simple. It is well-known that -simplicity implies that the amenable radical of the group must be trivial. We show that the converse does not hold by constructing explicit counter-examples. We additionally prove that every countable group embeds into a countable group with trivial amenable radical and that is not C*-simple.