Primitive Ideals of Labelled Graph $C^*$-algebras

TL;DR

This paper characterizes the primitive ideals of labelled graph $C^*$-algebras, expanding understanding of their structure through the analysis of weakly left-resolving labelled spaces.

Contribution

It provides a new characterization of primitive ideals specifically for labelled graph $C^*$-algebras, a topic not thoroughly explored before.

Findings

Characterization of primitive ideals in labelled graph $C^*$-algebras

Analysis of weakly left-resolving labelled spaces

Enhanced understanding of the ideal structure in these algebras

Abstract

Given a directed graph $E$ and a labeling $\mathcal{L}$, one forms the labelled graph $C^*$-algebra by taking a weakly left--resolving labelled space $(E, \mathcal{L}, \mathcal{B})$ and considering a universal generating family of partial isometries and projections. In this paper we provide characterization for primitive ideals of labelled graph $C^*$-algebras.