Nuclear dimension of graph C${}^{\ast }$-algebras with Condition~(K)

Abstract

We prove that for any countable directed graph $E$ with Condition~(K), the associated graph $C^{\ast }$-algebra $C^{\ast }(E)$ has nuclear dimension at most $2$. Furthermore, we provide a sufficient condition producing an upper bound of $1$.

14 pages; corrected some errors and improved clarity in the proof of Lemmas 4.2 and 4.3. Appeared in Proc. Amer. Math. Soc