On the rigidity of uniform Roe algebras over uniformly locally finite coarse spaces

Braga, B.; Farah, I.

doi:10.1090/tran/8180

On the rigidity of uniform Roe algebras over uniformly locally finite coarse spaces

Authors: B. M. Braga and I. Farah
Journal: Trans. Amer. Math. Soc. 374 (2021), 1007-1040
MSC (2010): Primary 46L80, 46L85, 51K05
DOI: https://doi.org/10.1090/tran/8180
Published electronically: November 3, 2020
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Abstract: Given a coarse space $(X,\mathcal {E})$ , one can define a $\mathrm {C}^{*}$ -algebra $\mathrm {C}^{*}_{u}(X)$ called the uniform Roe algebra of $(X,\mathcal {E})$ . It has been proved by J. Špakula and R. Willett that if the uniform Roe algebras of two uniformly locally finite metric spaces with property A are isomorphic, then the metric spaces are coarsely equivalent to each other. In this paper, we look at the problem of generalizing this result for general coarse spaces and on weakening the hypothesis of the spaces having property A.

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