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Main Authors: Wang, Zhijie, Fu, Benyin, Zhang, Jiawen
Format: Preprint
Published: 2025
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Online Access:https://arxiv.org/abs/2507.17105
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author Wang, Zhijie
Fu, Benyin
Zhang, Jiawen
author_facet Wang, Zhijie
Fu, Benyin
Zhang, Jiawen
contents In this paper, we investigate the ideal structure of Roe algebras for metric spaces beyond the scope of Yu's property A. Using the tool of rank distributions, we establish fibring structures for the lattice of ideals in Roe algebras and draw the border of each fibre by introducing the so-called ghostly ideals together with geometric ideals. We also provide coarse geometric criteria to ensure the coincidence of geometric and ghostly ideals and calculate their $K$-theories, which can be helpful to analyse obstructions to the coarse Baum-Connes conjecture on the level of ideals.
format Preprint
id arxiv_https___arxiv_org_abs_2507_17105
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Fibring structures of ideals in Roe algebras and their $K$-theories
Wang, Zhijie
Fu, Benyin
Zhang, Jiawen
Operator Algebras
47L20, 46L80, 51F30
In this paper, we investigate the ideal structure of Roe algebras for metric spaces beyond the scope of Yu's property A. Using the tool of rank distributions, we establish fibring structures for the lattice of ideals in Roe algebras and draw the border of each fibre by introducing the so-called ghostly ideals together with geometric ideals. We also provide coarse geometric criteria to ensure the coincidence of geometric and ghostly ideals and calculate their $K$-theories, which can be helpful to analyse obstructions to the coarse Baum-Connes conjecture on the level of ideals.
title Fibring structures of ideals in Roe algebras and their $K$-theories
topic Operator Algebras
47L20, 46L80, 51F30
url https://arxiv.org/abs/2507.17105