Fibring structures of ideals in Roe algebras and their K-theories

2025/07/23 by Zhijie Wang, Wang, Zhijie, Benyin Fu +3 · 2 citations
Mathematics · #46L80 #47L20 #51F30 #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #Operator Algebras (math.OA) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2507.17105

openalex publication_date 2025/07/23 · openalex created_date 2025/10/16 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Ghostly ideals in uniform Roe algebras
• Exact groupoids
• Ghostbusting and property A
• The maximal coarse Baum-Connes conjecture for spaces which admit a fibred coarse embedding into Hilbert space
• Higher index theory for certain expanders and Gromov monster groups I

Cited by

• K-theory of ghostly ideals for ℓ^p-coarsely embeddable spaces
• Ultracoarse Equilibria and Ordinal-Folding Dynamics in Operator-Algebraic Models of Infinite Multi-Agent Games

Related

• Ghostly ideals in uniform Roe algebras
• K-theory of ghostly ideals for ℓ^p-coarsely embeddable spaces
• Twisted Roe algebras and their K-theory
• K-theory of the maximal and reduced Roe algebras of metric spaces with A-by-CE coarse fibrations
• Ideal structures and rigidity of uniform Roe algebras