The simplicity of the C*-algebras associated to arbitrary labeled spaces

TL;DR

This paper investigates the conditions under which the C*-algebras derived from arbitrary labeled spaces are simple, providing a classification of ideals and criteria for minimality.

Contribution

It offers a comprehensive classification of gauge-invariant ideals and characterizes minimality, leading to new simplicity results for these C*-algebras.

Findings

Classification of all gauge-invariant ideals

Characterization of minimality in terms of ideal structure

Simplicity criteria for C*-algebras of labeled spaces

Abstract

In this paper, we consider the simplicity of the C*-algebra associated to an arbitrary weakly left-resolving labeled space (E, L, E), where E is the smallest non-degenerate accommodating set. We classify all gauge-invariant ideals of C*(E, L, E) and characterize minimality of (E, L, E) in terms of ideal structure of C*(E, L, E). Using these results, we prove simplicity results for C*-algebras associated to arbitrary labeled spaces.