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The Nuclear Dimension of Extensions and Graph $C^*$-Algebras

Year: 2026

Type: preprint

Abstract: We prove that the nuclear dimension of any graph $C^*$-algebra is at most two, and we compute the exact value of the nuclear dimension for a large class of graph $C^*$-algebras. In particular, this class covers all graphs with Condition (K). Our methods --- based on Szabó's recent $KK$-uniqueness theorem --- provide a unified approach to computing the nuclear dimension of various extensions. This includes the nuclear dimension of the Toeplitz algebra (first computed by Brake--Winter) and that of the Cuntz--Toeplitz algebras (first computed by Easo et al).

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2611.03082

Authors: Evington, Samuel, Faurot, Gregory, Schafhauser, Christopher

Language: English

Topic: Advanced Operator Algebra Research

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7225205774

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