Geometric classification of simple graph algebras (Q2842234)

A graph algebra is a \(C^\ast\)-algebra associated to a directed graph in a prescribed manner. The paper is concerned with the classification of simple unital graph algebras. The author presents a list of five allowed moves on graphs that keep the associated \(C^\ast\)-algebras in the same stable isomorphism class. Moreover, if two simple unital graph algebras are stably isomorphic, their graphs can be transformed into each other using only the moves from their list. An inspiration for the method was the classification of irreducible shifts of finite type presented in [\textit{J. Franks}, Ergodic Theory Dyn. Syst. 4, 53--66 (1984; Zbl 0555.54026)]. The paper starts with a very nice informative introduction on the subject.