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.
Categories: math.OA
