The K-theory of maximal and reduced Roe algebras for Hecke pairs with equivariant coarse embeddings

2026/01/21 by Liang Guo, Hang Wang, Xiufeng Yao · 2 voices
Mathematics · #math.KT

paper · pdf · doi:10.1142/s1793525326500317

arxiv published 2026/01/21 · arxiv updated 2026/02/02

Abstract

In this paper, we generalize the Dirac-dual-Dirac method to Hecke pairs with equivariant coarse embeddings and establish the K-theoretic isomorphisms between the maximal and reduced equivariant Roe algebras. We also extend these results to prove the Baum--Connes conjecture in this context.

Citations

• Twisted Roe algebras and their K-theory
• The Novikov conjecture and extensions of coarsely embeddable groups
• A Differential Complex for CAT(0) Cubical Spaces
• La conjecture de Baum-Connes à coefficients pour les groupes hyperboliques
• Hecke C*-algebras, Schlichting completions, and Morita equivalence
• Groups acting properly on "bolic" spaces and the Novikov conjecture
• Groups acting properly on “bolic” spaces and the Novikov conjecture

Discussions

• Liang Guo, Hang Wang, Xiufeng Yao The K-theory of maximal and reduced Roe algebras for Hecke pairs with equivariant coarse embeddings https://arxiv.org/abs/2601.14682 [bsky, 0 points, 0 comments]
• Liang Guo, Hang Wang, Xiufeng Yao: The K-theory of maximal and reduced Roe algebras for Hecke pairs with equivariant coarse embeddings https://arxiv.org/abs/2601.14682 https://arxiv.org/pdf/2601.14682 [bsky, 0 points, 0 comments]

Related

• Maximal and reduced Roe algebras of coarsely embeddable spaces
• K-theory for the maximal Roe algebra of certain expanders
• K-theory of the maximal and reduced Roe algebras of metric spaces with A-by-CE coarse fibrations
• Twisted Roe algebras and their K-theory
• Fibring structures of ideals in Roe algebras and their K-theories