We consider the simplicity of the -algebra associated to an arbitrary weakly left-resolving labeled space , where is the smallest nondegenerate accommodating set. We classify all gauge-invariant ideals of and characterize minimality of in terms of ideal structure of . Using these results, we prove that is simple if and only if is strongly cofinal and satisfies condition , and for any and , there is such that , and if and only if is minimal and satisfies condition , and if and only if is minimal and satisfies condition .
"The simplicity of the -algebras associated to arbitrary labeled spaces." Rocky Mountain J. Math. 52 (1) 133 - 152, February 2022. https://doi.org/10.1216/rmj.2022.52.133