论文标题
$ \ mathrm {c}（x）\rtimesγ$的稳定等级
Stable rank of $\mathrm{C}(X)\rtimesΓ$
论文作者
论文摘要
结果表明，对于紧凑的hausdorff space $ x $的任意免费和最小的$ \ mathbb z^n $ - 交叉产品C*-Algebra $ \ Mathrm {c}（x）\ rtimes \ rtimes \ rtimes \ mathbb z^n $始终具有稳定的排名，即一个稳定的等级。这概括了Alboiu和Lutley在$ \ Mathbb z $ -Actions上的结果。 实际上，对于任何免费和最小的拓扑动力系统$（x，γ）$，$γ$是一个可数的离散amenable组，如果它具有统一的rokhlin属性和开放式套装的cuntz比较，则交叉产品c*-algebra $ \ ablerm $ \ mathrm {c}（x）\ rtimesγ$ s an s stor-star s and。此外，在这种情况下，c*-algebra $ \ mathrm {c}（x）\rtimesγ$在加触时会加强江-su代数，并且只有严格比较正面元素。
It is shown that, for an arbitrary free and minimal $\mathbb Z^n$-action on a compact Hausdorff space $X$, the crossed product C*-algebra $\mathrm{C}(X)\rtimes\mathbb Z^n$ always has stable rank one, i.e., invertible elements are dense. This generalizes a result of Alboiu and Lutley on $\mathbb Z$-actions. In fact, for any free and minimal topological dynamical system $(X, Γ)$, where $Γ$ is a countable discrete amenable group, if it has the uniform Rokhlin property and Cuntz comparison of open sets, then the crossed product C*-algebra $\mathrm{C}(X)\rtimesΓ$ has stable rank one. Moreover, in this case, the C*-algebra $\mathrm{C}(X)\rtimesΓ$ absorbs the Jiang-Su algebra tensorially if, and only if, it has strict comparison of positive elements.
