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February 2022 The simplicity of the C*-algebras associated to arbitrary labeled spaces
Eun Ji Kang
Rocky Mountain J. Math. 52(1): 133-152 (February 2022). DOI: 10.1216/rmj.2022.52.133

Abstract

We consider the simplicity of the C-algebra associated to an arbitrary weakly left-resolving labeled space (E,,), where is the smallest nondegenerate accommodating set. We classify all gauge-invariant ideals of C(E,,) and characterize minimality of (E,,) in terms of ideal structure of C(E,,). Using these results, we prove that C(E,,) is simple if and only if (E,,) is strongly cofinal and satisfies condition (L), and for any A{} and B, there is Creg such that BC(A), and if and only if (E,,) is minimal and satisfies condition (L), and if and only if (E,,) is minimal and satisfies condition (K).

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Eun Ji Kang. "The simplicity of the C*-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

Information

Received: 9 February 2021; Accepted: 13 May 2021; Published: February 2022
First available in Project Euclid: 19 April 2022

Digital Object Identifier: 10.1216/rmj.2022.52.133

Subjects:
Primary: 46L05 , 46L55

Keywords: Boolean dynamical systems , gauge invariant ideals , generalized Boolean dynamical systems , labeled graph C∗-algebras , simple C∗-algebras

Rights: Copyright © 2022 Rocky Mountain Mathematics Consortium

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Vol.52 • No. 1 • February 2022
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