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 |
Show full item record
SCOPUSTM
Citations
5
checked on Sep 8, 2024
Page view(s)
2
checked on Sep 7, 2024
Google ScholarTM
Check
Altmetric
Altmetric
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.