论文标题
关于非正约的简单简单C* - 代数，III的分类，范围和降低
On classification of non-unital amenable simple C*-algebras, III, the range and the reduction
论文作者
论文摘要
在埃利奥特（Elliott）的早期工作之后，我们表明，任何有限的可分离简单$ c^*$ - 具有有限核维度的代数的Elliott不变性，可以描述为一个缩放的简单有序的订购组与一个可数的Abelian群体配对，该群体与一个统一的Unive and Unitial and Unital and Norital and Unital and Unital，并且稳定地预测案例。我们还表明，对于任何给定的这种不变的集合，都有一个有限的可分开的简单$ c^*$ - 代数，其埃利奥特不变是给定的集合，在稳定的情况下，Elliott的范围定理的改进。 在稳定的无投影案例中，修改模型$ c^*$ - 代数的构建方式使它们具有广义的奇特等级，并且具有其他技术功能。 我们还表明，每个稳定的无分离的简单简单的简单可分开的$ c^*$ - 代数在UCT类中都有一个合理概括的Tracial等级。
Following Elliott's earlier work, we show that the Elliott invariant of any finite separable simple $C^*$-algebra with finite nuclear dimension can always be described as a scaled simple ordered group pairing together with a countable abelian group which unifies the unital and nonunital, as well as stably projectionless cases. We also show that, for any given such invariant set, there is a finite separable simple $C^*$-algebra, whose Elliott invariant is the given set, a refinement of the range theorem of Elliott in the stable case. In the stably projectionless case, modified model $C^*$-algebras are constructed in such a way that they are of generalized tracial rank one and have other technical features. We also show that every stably projectionless separable simple amenable $C^*$-algebra in the UCT class has rationally generalized tracial rank one.
