Rigidity for geometric ideals in uniform Roe algebras
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| Titel: | Rigidity for geometric ideals in uniform Roe algebras |
|---|---|
| Autoren: | Jiang, Baojie, Zhang, Jiawen |
| Quelle: | Journal of Operator Theory. 94:35-64 |
| Publication Status: | Preprint |
| Verlagsinformationen: | Theta Foundation, 2025. |
| Publikationsjahr: | 2025 |
| Schlagwörter: | Mathematics - Operator Algebras, FOS: Mathematics, Operator Algebras (math.OA) |
| Beschreibung: | In this paper, we investigate the rigidity problems for geometric ideals in uniform Roe algebras associated to discrete metric spaces of bounded geometry. These ideals were introduced by Chen and Wang, and can be fully characterised in terms of ideals in the associated coarse structures. Our main result is that if two geometric ideals in uniform Roe algebras are stably isomorphic, then the coarse spaces associated to these ideals are coarsely equivalent. We also discuss the case of ghostly ideals and pose some open questions. |
| Publikationsart: | Article |
| ISSN: | 1841-7744 0379-4024 |
| DOI: | 10.7900/jot.2023aug18.2440 |
| DOI: | 10.48550/arxiv.2307.06525 |
| Zugangs-URL: | http://arxiv.org/abs/2307.06525 |
| Rights: | CC 0 |
| Dokumentencode: | edsair.doi.dedup.....2f62c30d3065cb2dddf515932eec55ff |
| Datenbank: | OpenAIRE |
Nájsť tento článok vo Web of Science | Abstract: | In this paper, we investigate the rigidity problems for geometric ideals in uniform Roe algebras associated to discrete metric spaces of bounded geometry. These ideals were introduced by Chen and Wang, and can be fully characterised in terms of ideals in the associated coarse structures. Our main result is that if two geometric ideals in uniform Roe algebras are stably isomorphic, then the coarse spaces associated to these ideals are coarsely equivalent. We also discuss the case of ghostly ideals and pose some open questions. |
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| ISSN: | 18417744 03794024 |
| DOI: | 10.7900/jot.2023aug18.2440 |