On Labeled Graph $C^{\ast }$-algebras

Abstract

Given a directed graph $E$ and a labeling $\mathcal{L}$, one forms the labeled graph $C^{\ast }$-algebra by taking a weakly left--resolving labeled space $(E,\mathcal{L},\mathcal{B})$ and considering a universal generating family of partial isometries and projections. In this paper, we work on ideals for a labeled graph $C^{\ast }$-algebra when the graph contains sinks. Using some of the tools we build, we compute $C^{\ast }(E,\mathcal{L},\mathcal{B})$ when $E$ is a finite graph.

The Rocky Mountain Journal of Mathematics, to appear. arXiv admin note: text overlap with arXiv:1907.06164