论文标题
关于groupoids和$ c^*$ - 自相似动作的代数
On groupoids and $C^*$-algebras from self-similar actions
论文作者
论文摘要
给定有限图的路径空间上的自相似的groupoid动作$（g，e）$，我们研究了相关的exel-pardoétalegroupoid $ {\ mathcal g}（g，e）$及其$ c^*$ - algebra $ c^*（g，e）$。我们回顾了一些有关类动作，偏斜产品和半导体产品的事实，并概括了雷诺关于类似于takai二元性的群体相似性的结果。我们还描述了计算$ c^*（g，e）$的$ k $ - 理论的一般策略，以及在某些情况下的$ {\ Mathcal g}（g，e）$的同源性，并用示例说明。
Given a self-similar groupoid action $(G,E)$ on the path space of a finite graph, we study the associated Exel-Pardo étale groupoid ${\mathcal G}(G,E)$ and its $C^*$-algebra $C^*(G,E)$. We review some facts about groupoid actions, skew products and semi-direct products and generalize a result of Renault about similarity of groupoids which resembles Takai duality. We also describe a general strategy to compute the $K$-theory of $C^*(G,E)$ and the homology of ${\mathcal G}(G,E)$ in certain cases and illustrate with an example.
