Year: 2025
Type: article
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.
Source: Journal of Operator Theory
Authors: Baojie Jiang, Jiawen Zhang
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4414580974