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arXiv · 2305.09232

A Cuntz--Krieger Uniqueness theorem for C*-algebras of relative generalized Boolean dynamical systems

Toke Meier Carlsen·Eun Ji Kang
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Abstract

We prove a version of the Cuntz--Krieger Uniqueness Theorem for $C^*$-algebras of arbitrary relative generalized Boolean dynamical systems. We then describe properties of a $C^*$-algebra of a relative generalized Boolean dynamical system when the underlying Boolean dynamical system satisfies Condition (K). We also define a notion of minimality of a Boolean dynamical system and give sufficient and necessary conditions for the minimality. Using these results, we characterize the generalized Boolean dynamical systems who's $C^*$-algebra is simple.

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Toke Meier Carlsen, Eun Ji Kang. 2023-05-16. A Cuntz--Krieger Uniqueness theorem for C*-algebras of relative generalized Boolean dynamical systems. https://arxiv.org/abs/2305.09232

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