Given a directed graph and a labeling , one forms the labeled graph -algebra by taking a weakly left-resolving labeled space and considering a universal generating family of partial isometries and projections. We work on ideals for a labeled graph -algebra when the graph contains sinks. Using some of the tools we build, we compute when is a finite graph.
"On labeled graph $C^*$-algebras." Rocky Mountain J. Math. 50 (3) 863 - 870, June 2020. https://doi.org/10.1216/rmj.2020.50.863