When universal separated graph $C^*$-algebras are exact

Abstract

We consider when the universal C∗-algebras associated to separated graphs are exact. Specifically, for finite separated graphs we show that the universal C∗-algebra is exact if and only if the C∗-algebra is isomorphic to a graph C∗-algebra which occurs precisely when the universal and reduced C∗-algebras of the separated graph are isomorphic.