Authors: Braga, Bruno M.
Farah, Ilijas 
Vignati, Alessandro
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: GENERAL UNIFORM ROE ALGEBRA RIGIDITY
Journal: Annales de l'Institut Fourier
Volume: 72
Issue: 1
First page: 301
Last page: 337
Issue Date: 1-Jul-2022
Rank: M22
ISSN: 0373-0956
DOI: 10.5802/aif.3461
Abstract: 
We generalize all known results on rigidity of uniform Roe algebras to the setting of arbitrary uniformly locally finite coarse spaces. For instance, we show that isomorphism between uniform Roe algebras of uniformly locally finite coarse spaces whose uniform Roe algebras contain only compact ghost projections implies that the base spaces are coarsely equivalent. Moreover, if one of the spaces has property A, then the base spaces are bijectively coarsely equivalent. We also provide a characterization for the existence of an embedding onto hereditary subalgebra in terms of the underlying spaces. As an application, we partially answer a question of White and Willett about Cartan subalgebras of uniform Roe algebras.
Keywords: Cartan subalgebra | coarse geometry | Uniform Roe algebras
Publisher: Association des Annales de l'Institut Fourier

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