Authors: Baudier, Florent P.
Braga, Bruno M.
Farah, Ilijas 
Khukhro, Ana
Vignati, Alessandro
Willett, Rufus
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Uniform Roe algebras of uniformly locally finite metric spaces are rigid
Journal: Inventiones Mathematicae
Volume: 230
First page: 1071
Last page: 1100
Issue Date: 2022
Rank: ~M21a
ISSN: 0020-9910
DOI: 10.1007/s00222-022-01140-x
Abstract: 
We show that if X and Y are uniformly locally finite metric spaces whose uniform Roe algebras, Cu∗(X) and Cu∗(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 Cu∗(X) and Cu∗(Y). As an application, we obtain that if Γ and Λ are finitely generated groups, then the crossed products ℓ∞(Γ) ⋊ rΓ and ℓ∞(Λ) ⋊ rΛ are isomorphic if and only if Γ and Λ are bi-Lipschitz equivalent.
Publisher: Springer Link

Files in This Item:
File Description SizeFormat
s00222-022-01140-x.pdf410.3 kBAdobe PDFView/Open
Show full item record

SCOPUSTM   
Citations

2
checked on May 22, 2024

Page view(s)

32
checked on May 9, 2024

Download(s)

15
checked on May 9, 2024

Google ScholarTM

Check

Altmetric

Altmetric


This item is licensed under a Creative Commons License Creative Commons