Minimality and effectiveness of the groupoid associated to a self-similar ultragraph
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911252881604608 |
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| author | Larki, Hossein Rajabzadeh-Hasiri, Najmeh |
| author_facet | Larki, Hossein Rajabzadeh-Hasiri, Najmeh |
| contents | The notion of a self-similar ultragraph $(G,\mathcal{U},φ)$ 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 $(G,\mathcal{U},φ)$. In particular, we obtain a result for simplicity of the $C^*$-algebras $\mathcal{O}_{G,\mathcal{U}}$ in a certain case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_09527 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Minimality and effectiveness of the groupoid associated to a self-similar ultragraph Larki, Hossein Rajabzadeh-Hasiri, Najmeh Operator Algebras 46L55 The notion of a self-similar ultragraph $(G,\mathcal{U},φ)$ 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 $(G,\mathcal{U},φ)$. In particular, we obtain a result for simplicity of the $C^*$-algebras $\mathcal{O}_{G,\mathcal{U}}$ in a certain case. |
| title | Minimality and effectiveness of the groupoid associated to a self-similar ultragraph |
| topic | Operator Algebras 46L55 |
| url | https://arxiv.org/abs/2510.09527 |