2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66021To a directed graph $E$ is associated a $C^*$-algebra $C^* (E)$ called a graph $C^*$-algebra. There is a canonical action $γ$ of ${\bf T}$ on $C^* (E)$, called the gauge action. In this paper we present necessary and sufficient conditions for the fixed point algebra $C^* (E)^γ$ to be simple. Our results also yield some structure theorems for simple graph algebras.15 pages with one embedded diagram. To appear, Proc. OAMP conference, Constanta, 2001Operator Algebras46L55text