标题： 收缩自相似群的$C^*$-代数的简单性 显示英文标题

标题： Simplicity of $C^*$-algebras of contracting self-similar groups

摘要： 我们证明了由Nekrashevych对一个收缩自相似群所关联的$C^*$-代数是简化的，当且仅当相应的复数$\ast$-代数是简化的。 我们还改进了Steinberg和Szakać的算法，以确定$\ast$-代数是否是简化的。 这提供了一个有趣的非Hausdorff可换、有效且最小的丰富群胚类，其中$C^*$-代数和复数$\ast$-代数的简化性是等价的。 显示英文摘要

摘要： We show that the $C^*$-algebra associated by Nekrashevych to a contracting self-similar group is simple if and only if the corresponding complex $\ast$-algebra is simple. We also improve on Steinberg and Szaka\'c's algorithm to determine if the $\ast$-algebra is simple. This provides an interesting class of non-Hausdorff amenable, effective and minimal ample groupoids for which simplicity of the $C^*$-algebra and the complex $\ast$-algebra are equivalent.