自相似群胚作用的Higman-Thompson群
Higman-Thompson groups from self-similar groupoid actions
摘要：
给定有限有向图上的自相似广群作用$(G,E)$，证明了芽$\mathcal G(G,E)$的相应的充分广群的一些性质。我们研究了与$(G,E)$相关的Higman-Thompson群的类似物，并使用$G$ -表将其与$\mathcal G(G,E)$的拓扑完全群联系起来，该拓扑全群同构于代数$C^*(G,E)$中的酉子群。在回顾了广群同调中的一些概念后，我们讨论了在某些特殊情况下关于$\mathcal G(G,E)$的Matui的AH-猜想.
英文摘要：
Given a self-similar groupoid action $(G,E)$ on a finite directed graph, we prove some properties of the corresponding ample groupoid of germs $\mathcal G(G,E)$. We study the analogue of the Higman-Thompson group associated to $(G,E)$ using $G$-tables and relate it to the topological full group of $\mathcal G(G,E)$, which is isomorphic to a subgroup of unitaries in the algebra $C^*(G,E)$. After recalling some concepts in groupoid homology, we discuss the Matui's AH-conjecture for $\mathcal G(G,E)$ in some particular cases.
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