论文标题
几乎基本性和典型类固醇的纤维舒适性
Almost elementariness and fiberwise amenability for étale groupoids
论文作者
论文摘要
在本文中，我们介绍了两个新的近似属性属性属于类别的类别，几乎是基本性和（普遍）的纤维修正性，灵感来自Matui和Kerr几乎有限的概念。实际上，我们表明，在其适用性的各自范围内，几乎有限的两个概念都等同于我们这两个属性的结合。这些新的特性源于将étaleglopoid视为几何群体理论精神的粗几何对象。纤维舒适性是étalegroupoids的粗几何特性，与单位空间上的不变度度量密切相关，并且对应于contration Group的作用组的合理性。几乎基本性可能被视为C* - 代数的规律性特性更好的动态类似物，而不是几乎有限的，因为与后者不同，前者也可以应用于纯粹的无限情况。为了支持这种类比，我们显示几乎基本的最小类固醇会导致Z稳定的减少群体c* - 代数。特别是，在Matui的意义上，第二可计数的几乎有限的群体的C* - 代数减少是Z稳定的。
In this paper, we introduce two new approximation properties for étale groupoids, almost elementariness and (ubiquitous) fiberwise amenability, inspired by Matui's and Kerr's notions of almost finiteness. In fact, we show that, in their respective scopes of applicability, both notions of almost finiteness are equivalent to the conjunction of our two properties. These new properties stem from viewing étale groupoids as coarse geometric objects in the spirit of geometric group theory. Fiberwise amenability is a coarse geometric property of étale groupoids that is closely related to the existence of invariant measures on unit spaces and corresponds to the amenability of the acting group in a transformation groupoid. Almost elementariness may be viewed as a better dynamical analogue of the regularity properties of C*-algebras than almost finiteness, since, unlike the latter, the former may also be applied to the purely infinite case. To support this analogy, we show almost elementary minimal groupoids give rise to tracially Z-stable reduced groupoid C*-algebras. In particular, the reduced C*-algebras of second countable amenable almost finite groupoids in Matui's sense are Z-stable.
