Uniform Roe algebras of uniformly locally finite metric spaces are rigid

• 成果类型: Article
• 署名作者: Baudier, Florent P.; Braga, Bruno M.; Farah, Ilijas; Khukhro, Ana; Vignati, Alessandro; Willett, Rufus
• 署名单位: Texas A&M University System; Texas A&M University College Station; York University - Canada; University of Cambridge; Universite Paris Cite; Sorbonne Universite; University of Hawaii System; University of Hawaii Manoa
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-022-01140-x
• 发表日期: 2022
• 页码: 1071-1100
• 关键词: equivalence; exactness; THEOREM

摘要

We show that if X and Y are uniformly locally finite metric spaces whose uniform Roe algebras, C-u* (X) and C-u* (Y), are isomorphic as C*-algebras, then X and Y are coarsely equivalent metric spaces. Moreover, we show that coarse equivalence between X and Y is equivalent to Morita equivalence between C-u* (X) and C-u* (Y). As an application, we obtain that if Gamma and Lambda are finitely generated groups, then the crossed products l(infinity)(Gamma) (sic)(r) Gamma and l(infinity)(Lambda) (sic)(r) Lambda are isomorphic if and only if Gamma and Lambda are bi-Lipschitz equivalent.