On Hong and Szymanski's description of the primitive-ideal space of a graph algebra

TL;DR

This paper provides an explicit description of the ideal lattice of graph algebras for row-finite graphs with no sources, offering a simplified approach compared to previous work on primitive-ideal spaces.

Contribution

It introduces a new, simplified method for describing the ideal lattice of graph algebras in the specific context of row-finite, source-free graphs.

Findings

Explicit ideal lattice description for row-finite, source-free graph algebras

Simplified approach compared to Hong and Szymanski's primitive-ideal space analysis

Enhanced understanding of ideal structure in specific graph C*-algebras

Abstract

In 2004, Hong and Szymanski gave a complete description of the primitive-ideal space of the C*-algebra of a directed graph. This article details a slightly different approach, in the simpler context of row-finite graphs with no sources, obtaining an explicit description of the ideal lattice of a graph algebra.