Strongly Quasi-local algebras and their K-theories

2021/08/02 by Hengda Bao, Bao, Hengda, Xiaoman Chen +3 · 1 citation
Mathematics · Physics and Astronomy · #46H35 #46L80 #46M20 #51F30 #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #Noncommutative and Quantum Gravity Theories #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.2108.00642

openalex publication_date 2021/08/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we introduce a notion of strongly quasi-local algebras. They are defined for each discrete metric space with bounded geometry, and sit between the Roe algebra and the quasi-local algebra. We show that strongly quasi-local algebras are coarse invariants, hence encoding coarse geometric information of the underlying spaces. We prove that for a discrete metric space with bounded geometry which admits a coarse embedding into a Hilbert space, the inclusion of the Roe algebra into the strongly quasi-local algebra induces an isomorphism in K-theory.

Citations

• Quasi-local Algebras and Asymptotic Expanders

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• Asymptotic expansion for groupoids and Roe type algebras

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