发表机构
Universidad ECCI; Universidad Distrital Francisco José de Caldas（ECCI大学; 弗朗西斯科·何塞·德卡拉斯市立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文引入源锚定代数amenability概念，在Steinberg代数中刻画群胚的amenability，建立多种构造下的永久性，并利用迷向群特征化遗传代数amenability。
AI 中文摘要
我们为Hausdorff ample群胚引入了源锚定代数amenability，这是在Steinberg代数中表述的Følner条件，并定位于单位空间的紧致开子集。无锚定的二分条件恰好是Steinberg代数的代数amenability，而锚定版本则恢复了一单位群胚的普通amenability，并检测到无锚定理论不可见的行为。我们建立了在同构、开不变约化、不相交并、有限积、有向并和AF逼近下的永久性，而任意子群胚不必继承该性质。对于可数传递离散群胚，无限单位空间通过范围逃逸是amenable的，而有限单位空间恰好当其迷向群是amenable时才是amenable的。这给出了以迷向性表示的遗传代数amenability的特征化。
英文摘要
We introduce source-anchored algebraic amenability for Hausdorff ample groupoids, a Følner condition formulated in the Steinberg algebra and localized at compact open subsets of the unit space. The unanchored bisectional condition is exactly algebraic amenability of the Steinberg algebra, whereas the anchored version recovers ordinary amenability for one-unit groupoids and detects behavior invisible to the unanchored theory. We establish permanence under isomorphisms, open invariant reductions, disjoint unions, finite products, directed unions and AF approximations, while arbitrary subgroupoids need not inherit the property. For countable transitive discrete groupoids, infinite unit spaces are amenable through range escape, whereas finite unit spaces are amenable precisely when their isotropy groups are. This yields a characterization of hereditary algebraic amenability in terms of isotropy.
Comments50 pages
