论文标题
奇特的可符合的动作和纯粹的无限交叉产品
Tracially amenable actions and purely infinite crossed products
论文作者
论文摘要
我们介绍了奇异的奇异性对离散群体对曲面C $^*$ - 代数的作用的概念，作为弱化性的弱化性，所有相关近似都在统一的痕量标准中完成。我们表征具有各种等效条件的奇异性，包括诱导作用在痕量空间上的拓扑性舒适性。我们的主要结果涉及交叉产品的结构：对于包含免费组$ f_2 $的组，我们表明，外部的，可纹身的动作对简单，Unital，$ \ Mathcal {z} $ - 稳定的C $^*$ - 代数始终具有纯粹的无限交叉产品。最后，我们给出了自由群体对简单的，统一的AF-Elgebras的特殊符合作用的具体例子。
We introduce the notion of tracial amenability for actions of discrete groups on unital, tracial C$^*$-algebras, as a weakening of amenability where all the relevant approximations are done in the uniform trace norm. We characterize tracial amenability with various equivalent conditions, including topological amenability of the induced action on the trace space. Our main result concerns the structure of crossed products: for groups containing the free group $F_2$, we show that outer, tracially amenable actions on simple, unital, $\mathcal{Z}$-stable C$^*$-algebras always have purely infinite crossed products. Finally, we give concrete examples of tracially amenable actions of free groups on simple, unital AF-algebras.
