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PreprintarXiv licencearXiv

The Nuclear Dimension of Extensions and Graph C*-Algebras

  • Samuel Evington
  • Gregory Faurot
  • Christopher Schafhauser
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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).

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Cite

BibTeXRIS
BibTeX
@misc{evington2026nuclear,
  title = {{The Nuclear Dimension of Extensions and Graph $C^*$-Algebras}},
  author = {Samuel Evington and Gregory Faurot and Christopher Schafhauser},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.03082},
  eprint = {2611.03082},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.03082},
}
RIS
TY  - UNPB
TI  - The Nuclear Dimension of Extensions and Graph C^*-Algebras
AU  - Samuel Evington
AU  - Gregory Faurot
AU  - Christopher Schafhauser
PY  - 2026
DA  - 2026/11/02
PB  - arXiv
DO  - 10.48550/arxiv.2611.03082
UR  - https://arxiv.org/abs/2611.03082
AB  - 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).
ER  -