Weak containment of measure-preserving group actions
Weak containment of measure-preserving group actions
复制标题
对保措施团体行动的遏制薄弱
DOI：
--
复制
发表时间：
2016
影响因子：
0.9
通讯作者：
A. Kechris
中科院分区：
文献类型：
--
作者：
P. Burton;A. Kechris
本文研究了标准概率空间上可数群的保测作用的整体结构。弱包容是一个层次概念的复杂性，这种行动，动机是一个类似的概念，在理论的酉表示。这个概念产生了一个相关的等价作用的概念，称为弱等价，它比同构（共轭）的概念粗糙得多。现在已经很好地理解了，一般来说，同构是一个非常复杂的概念，例如，在模同构的作用空间中缺乏任何合理的结构。另一方面，弱等价类空间表现得相当好。另一个有趣的事实是，与弱包含研究相关的许多重要参数，如类型，成本和组合参数，都是弱等价的不变量，并且实际上表现出相对于弱包含的前序的理想单调性，这在某些应用中可能是有用的。在过去的几年里，在这方面已经有了很多的活动，我们在本文中的目标是提供一个调查这项工作。
This paper concerns the study of the global structure of measure-preserving actions of countable groups on standard probability spaces. Weak containment is a hierarchical notion of complexity of such actions, motivated by an analogous concept in the theory of unitary representations. This concept gives rise to an associated notion of equivalence of actions, called weak equivalence, which is much coarser than the notion of isomorphism (conjugacy). It is well understood now that, in general, isomorphism is a very complex notion, a fact which manifests itself, for example, in the lack of any reasonable structure in the space of actions modulo isomorphism. On the other hand, the space of weak equivalence classes is quite well behaved. Another interesting fact that relates to the study of weak containment is that many important parameters associated with actions, such as the type, cost, and combinatorial parameters, turn out to be invariants of weak equivalence and in fact exhibit desirable monotonicity properties with respect to the pre-order of weak containment, a fact that can be useful in certain applications. There has been quite a lot of activity in this area in the last few years, and our goal in this paper is to provide a survey of this work.
DOI：
10.4171/jems/344
发表时间：
2007-01
期刊：
arXiv: Group Theory
影响因子：
--
作者：
Miklós Abért;N. Nikolov
通讯作者：
Miklós Abért;N. Nikolov