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arxiv:2610.01915

The Cuntz semigroup of a unital graph C*-algebra

Published on Oct 1
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Abstract

The study computes Cuntz semigroups for unital graph C*-algebras via ideal lattice and Murray-von Neumann techniques, and relates them to nuclear dimension bounds.

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We compute the Cuntz semigroup of a unital graph C*-algebra 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.

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