PreprintCC BY 4.0arXiv
The Cuntz semigroup of the graph C*-algebra of a finite graph
Abstract
We compute the Cuntz semigroup of a graph C*-algebra associated to a finite graph by combining Hong and Szymański's realisation of the entire ideal lattice of a graph C*-algebra, Ara, Moreno and Pardo's computation of the Murray-von Neumann semigroup of a unital graph C*-algebra and various Cuntz semigroup techniques. We also investigate certain properties of such Cuntz semigroups, and demonstrate that at the level of the Cuntz semigroup, there is no obstruction to the conjecture that the nuclear dimension of any graph C*-algebra is at most one.
Related
- The Cuntz semigroup of rings with stable rank one
- Certain Cuntz semigroup properties of extension C*-algebras
- Representations of the infinite Cuntz algebra
- The Cuntz-Pimsner algebra of the simplest Motzkin subproduct system is 2-subhomogeneous
- Asymptotic Behavior of Distance near the Origin Between Two Elements of the Semigroup in a Banach Algebra
BibTeX
@misc{chan2026cuntz,
title = {{The Cuntz semigroup of the graph C*-algebra of a finite graph}},
author = {Yao Ming Chan},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.01915},
eprint = {2610.01915},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.01915},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The Cuntz semigroup of the graph C*-algebra of a finite graph
AU - Yao Ming Chan
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.01915
UR - https://arxiv.org/abs/2610.01915
AB - We compute the Cuntz semigroup of a graph C*-algebra associated to a finite graph by combining Hong and Szymański's realisation of the entire ideal lattice of a graph C*-algebra, Ara, Moreno and Pardo's computation of the Murray-von Neumann semigroup of a unital graph C*-algebra and various Cuntz semigroup techniques. We also investigate certain properties of such Cuntz semigroups, and demonstrate that at the level of the Cuntz semigroup, there is no obstruction to the conjecture that the nuclear dimension of any graph C*-algebra is at most one.
ER -