Pullbacks of graph C*-algebras from admissible pushouts of graphs

Abstract

We define an admissible decomposition of a graph $E$ into subgraphs $F_1$ and $F_2$, and consider the intersection graph $F_1\cap F_2$ as a subgraph of both $F_1$ and $F_2$. We prove that, if the graph $E$ is row finite and its decomposition into the subgraphs $F_1$ and $F_2$ is admissible, then the graph C*-algebra $C^{\ast }(E)$ of $E$ is the pullback C*-algebra of the canonical surjections from $C^{\ast }(F_1)$ and $C^{\ast }(F_2)$ onto $C^{\ast }(F_1\cap F_2)$.

10 pages; acknowledgments changed