论文标题
$ \ mathcal z $ - $ \ mathrm {c}（x）\rtimesγ$的稳定性
$\mathcal Z$-stability of $\mathrm{C}(X)\rtimesΓ$
论文作者
论文摘要
令$（x，γ）$是一个免费的最小拓扑动力系统，其中$ x $是一个可分开的紧凑型Hausdorff空间，而$γ$是一个可计数的无限无限离散群体。结果表明，如果$（x，γ）$具有统一的rokhlin属性和cuntz的比较，则$ \ sathrm {mdim}（mdim}（x，γ）= 0 $表示$（\ mathrm {c}（c}（c}（x）\rtimesγ）\ imimes \ imimes \ mathcal z \ mathcal z \ mathimes $ \ $ \ $ \ math} $ \ mathrm {mdim} $是平均维度，$ \ Mathcal z $是江-su代数。特别是在这种情况下，$ \ mathrm {mdim}（x，γ）= 0 $表示C*-Algebra $ \ Mathrm {C}（x）\rtimesγ$由Elliott Infortiant分类。
Let $(X, Γ)$ be a free and minimal topological dynamical system, where $X$ is a separable compact Hausdorff space and $Γ$ is a countable infinite discrete amenable group. It is shown that if $(X, Γ)$ has the Uniform Rokhlin Property and Cuntz comparison of open sets, then $\mathrm{mdim}(X, Γ)=0$ implies that $(\mathrm{C}(X) \rtimesΓ)\otimes\mathcal Z \cong \mathrm{C}(X) \rtimesΓ$, where $\mathrm{mdim}$ is the mean dimension and $\mathcal Z$ is the Jiang-Su algebra. In particular, in this case, $\mathrm{mdim}(X, Γ)=0$ implies that the C*-algebra $\mathrm{C}(X) \rtimesΓ$ is classified by the Elliott invariant.
