论文标题
对角灰代数的稳定等级和通过最小同构的交叉产品
The Stable Rank of Diagonal ASH Algebras and Crossed Products by Minimal Homeomorphisms
论文作者
论文摘要
我们介绍了递归的亚均质代数的亚类，其中每个回调图在适当的意义上都是对角线的。我们定义了两个这样的代数之间的对角图的概念，并表明这些代数的每个简单的电感限制具有对角粘合图的概念都具有稳定的等级。作为一个应用程序，我们证明，对于任何无限紧凑的度量空间$ t $和最小同构$ h \ colon t \ to t $，相关的动态交叉产品$ \ mathrm {c^*}（\ mathbb {z}，t，t，h）$具有稳定的排名。这肯定了Archey，Niu和Phillips的猜想。我们还表明，Toms-Winter猜想对此类交叉产品具有。
We introduce a subclass of recursive subhomogeneous algebras, in which each of the pullback maps is diagonal in a suitable sense. We define the notion of a diagonal map between two such algebras and show that every simple inductive limit of these algebras with diagonal bonding maps has stable rank one. As an application, we prove that for any infinite compact metric space $T$ and minimal homeomorphism $h\colon T\to T$, the associated dynamical crossed product $\mathrm{C^*}(\mathbb{Z},T,h)$ has stable rank one. This affirms a conjecture of Archey, Niu, and Phillips. We also show that the Toms-Winter Conjecture holds for such crossed products.
