Almost elementariness and fiberwise amenability for \'etale groupoids.
Almost elementariness and fiberwise amenability for \'etale groupoids.
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对于etale groupoids 来说几乎是基本的和纤维化的顺应性。
DOI：
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发表时间：
2020
期刊：
影响因子：
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通讯作者：
Jianchao Wu
中科院分区：
文献类型：
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作者：
Xin Ma;Jianchao Wu
在本文中，我们从Matui和Kerr的几乎有限的概念中得到启发，引入了两个新的奇异群拟的近似性质，即几乎初等性和（泛在）纤维可调性。事实上，我们证明，在它们各自的适用范围内，两个几乎有限的概念等价于我们的两个性质的合取。这些新性质源于将奇异群类群视为几何群论精神中的粗糙几何对象。纤维柔顺性是线性群拟的一个粗糙几何性质，它与单位空间上不变测度的存在性密切相关，对应于变换群拟中作用群的柔顺性。几乎初等性可以被看作是C*-代数正则性的一个比几乎有限性更好的动力学模拟，因为与后者不同，前者也可以应用于纯粹无限的情况。为了支持这个类比，我们证明了几乎初等最小群可以产生迹z稳定的约化群C*-代数。特别地，在Matui意义下二阶可数可调几乎有限群的约简C*-代数是z稳定的。
In this paper, we introduce two new approximation properties for \'etale 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 \'etale groupoids as coarse geometric objects in the spirit of geometric group theory. Fiberwise amenability is a coarse geometric property of \'etale 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.
核 C* 代数的拟对角性
DOI：
10.4007/annals.2017.185.1.4
发表时间：
2017
期刊：
arXiv: Operator Algebras
影响因子：
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作者：
A. Tikuisis;S. White;W. Winter
通讯作者：
W. Winter