Directed graph algebras have long been studied as tractable examples of C*-algebras, but they are limited by their inability to have torsion in their K_1 group. Graphs of groups, which are famed in geometric group theory because of their intimate connection with group actions on trees, are a more recent addition to the C*-algebra scene. In this talk, I will introduce the child of these two concepts – directed graphs of groups – and describe how their algebras inherit the best properties of its parents’, with a view to outlining how we can use these algebras to model a class of C*-algebras (stable UCT Kirchberg algebras) which is classified completely by K-theory.
