论文标题
平移谎言组的翻译作用的动态渐近维度
Dynamic Asymptotic Dimension of Translation Actions on Compact Lie Groups
论文作者
论文摘要
我们开发了一种方法来绑定等距组动作的动态渐近维度$γ\ curvearrowrowright x $在图形空间的渐近维度上，类似于$γ$的盒子空间（这也决定了有限差异性），以及$ x $的几何属性与$ x $相关。我们应用这种方法来描述有限生成的紧凑型谎言组的子群体的翻译行动的父亲，表征了此类行动的有限维度，并绑定了$ C^*$ - 代数的核维度，由ableable群体产生的代数。
We develop a method to bound the dynamic asymptotic dimension of isometric group actions $Γ\curvearrowright X$ in terms of the asymptotic dimension of a space of graphs similar to a box space of $Γ$ (which also determines finite-dimensionality), and a geometric property of $X$ related to the doubling dimension. We apply this method to describe the DAD of translation actions by finitely generated subgroups of compact Lie groups, characterize finite dimensionality of such actions, and consequently bound the nuclear dimension of $C^*$-algebras arising from such actions by amenable groups.
