论文标题
简单自相似图的二分法$ c^\ ast $ - 代理
A dichotomy for simple self-similar graph $C^\ast$-algebras
论文作者
论文摘要
我们研究了exel-pardo $ c^*$ - 代数$ \ Mathcal {o} _ {g，e} $的纯净无限和稳定性，用于可数自相似图$（g，e，φ）$。特别是，我们将特定的普通图$ \ widetilde {e} $与$（g，e，φ）$关联，使得某些属性，例如简单性，稳定的有限性或纯粹的无限性，$ c^*$ - algebra $ c^*（\ widetilde {e}）$ subly of $ \ n Mathcal} $}除其他外，这是在简单的$ \ MATHCAL {O} _ {g，e} $的二分法之后：如果$（g，e，φ）$包含no $ g $ -circuits，则$ \ Mathcal {o} _ {g，e} $是稳定的限制性的；否则，$ \ MATHCAL {O} _ {G，E} $纯粹是无限的。 此外，Li和Yang最近引入了自相似于$ k $ -graph $ c^*$ - 代数$ \ Mathcal {o} _ {g，λ} $。我们还表明，当$ |λ^0 | <\ infty $和$ \ mathcal {o} _ {g，λ} $很简单时，它纯粹是无限的。
We investigate the pure infiniteness and stable finiteness of the Exel-Pardo $C^*$-algebras $\mathcal{O}_{G,E}$ for countable self-similar graphs $(G,E,φ)$. In particular, we associate a specific ordinary graph $\widetilde{E}$ to $(G,E,φ)$ such that some properties such as simpleness, stable finiteness or pure infiniteness of the graph $C^*$-algebra $C^*(\widetilde{E})$ imply that of $\mathcal{O}_{G,E}$. Among others, this follows a dichotomy for simple $\mathcal{O}_{G,E}$: if $(G,E,φ)$ contains no $G$-circuits, then $\mathcal{O}_{G,E}$ is stably finite; otherwise, $\mathcal{O}_{G,E}$ is purely infinite. Furthermore, Li and Yang recently introduced self-similar $k$-graph $C^*$-algebras $\mathcal{O}_{G,Λ}$. We also show that when $|Λ^0|<\infty$ and $\mathcal{O}_{G,Λ}$ is simple, then it is purely infinite.
