论文标题
$ c^*$ - 几乎有限群体产生的代数的严格比较
Strict comparison for $C^*$-algebras arising from Almost finite groupoids
论文作者
论文摘要
在本文中，我们表明，对于几乎有限的最小ampure groupoid $ g $，其减少的$ \ mathrm {c}^*$ - algebra $ c_r^*（g）$即使$ C_R^*（g）$也可能不是核核。此外，如果我们进一步假设$ g $也是第二个可计数和非元素，那么它的cuntz semigroup $ {\ rm cu}（c_r^*（g））$几乎是可分开的，$ {\ rm cu}（c_r^*（g））是规范上的命令，其中$ \ MATHCAL {z} $表示Jiang-Su代数。
In this paper we show that for an almost finite minimal ample groupoid $G$, its reduced $\mathrm{C}^*$-algebra $C_r^*(G)$ has real rank zero and strict comparison even though $C_r^*(G)$ may not be nuclear in general. Moreover, if we further assume $G$ being also second countable and non-elementary, then its Cuntz semigroup ${\rm Cu}(C_r^*(G))$ is almost divisible and ${\rm Cu}(C_r^*(G))$ and ${\rm Cu}(C_r^*(G)\otimes \mathcal{Z})$ are canonically order-isomorphic, where $\mathcal{Z}$ denotes the Jiang-Su algebra.
