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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.17105 |
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| _version_ | 1866913958373359616 |
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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 |