论文标题
比较半径和平均共同体独立性维度
Radius of comparison and mean cohomological independence dimension
论文作者
论文摘要
我们介绍了平均共同体独立性维度的概念，该概念是在紧凑的可衡量空间上作为平均维度的变体的分离式符合群体的作用，并使用它来获得下限，以比较相关的交叉产物C*-ergebras的比较半径。我们的一般理论给出了Dou在2017年构建的最低次数的以下基础。让G为可数的群体，让Z为多面体，让T为Dou的dou子的Z^g（也取决于密度参数）。然后，交叉产物比较的半径大于r（1/2）mdim（t）-2，其中r取决于密度参数，当密度参数接近1时，r的密度参数接近1。密度参数为。
We introduce a notion of mean cohomological independence dimension for actions of discrete amenable groups on compact metrizable spaces, as a variant of mean dimension, and use it to obtain lower bounds for the radius of comparison of the associated crossed product C*-algebras. Our general theory gives the following for the minimal subshifts constructed by Dou in 2017. Let G be a countable amenable group, let Z be a polyhedron, and let T be Dou's subshift of Z^G (which also depends on a density parameter). Then the radius of comparison of the crossed product is greater than r (1/2) mdim (T) - 2, in which r depends on the density parameter and is close to 1 when the density parameter is close to 1. If Z is even dimensional and has nonvanishing rational cohomology in degree dim (Z), then the radius of comparison of the crossed product is greater than (1/2) mdim (T) - 1, regardless of what the density parameter is.
