The simplicity of the C*-algebras associated to arbitrary 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.