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arXiv · 2510.09527

Minimality and effectiveness of the groupoid associated to a self-similar ultragraph

Hossein Larki·Najmeh Rajabzadeh-Hasiri
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Abstract

The notion of a self-similar ultragraph $(G,\mathcal{U},\varphi)$ and its $C^*$-algebra $\mathcal{O}_{G,\mathcal{U}}$ were introduced in our recent work, where we proposed inverse semigroup and groupoid models for such $C^*$-algebras as well. In this paper, we investigate minimality and effectiveness of the groupoid of a self-similar ultragraph $(G,\mathcal{U},\varphi)$. In particular, we obtain a result for simplicity of the $C^*$-algebras $\mathcal{O}_{G,\mathcal{U}}$ in a certain case.

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Hossein Larki, Najmeh Rajabzadeh-Hasiri. 2025-10-10. Minimality and effectiveness of the groupoid associated to a self-similar ultragraph. https://arxiv.org/abs/2510.09527

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