论文标题
下均匀c* - 代数的发电机等级
The generator rank of subhomogeneous C*-algebras
论文作者
论文摘要
我们根据其原始理想空间的覆盖尺寸来计算下均衡c* - 代数的发电机等级，这与固定尺寸的不可减至表示相对应。我们推断出每个Z稳定的Ash-Elgebra都有生成器等级，这意味着该代数中的通用元素是生成器。 这导致了对于可分类，简单的，核C* - 代数的强大解决方案：每个代数中的一个通用元素是生成器。维拉德森（Villadsen）的例子表明，对于所有可分离，简单，核C* - 代数都不是这种情况。
We compute the generator rank of a subhomgeneous C*-algebra in terms of the covering dimension of the pieces of its primitive ideal space corresponding to irreducible representations of a fixed dimension. We deduce that every Z-stable ASH-algebra has generator rank one, which means that a generic element in such an algebra is a generator. This leads to a strong solution of the generator problem for classifiable, simple, nuclear C*-algebras: a generic element in each such algebra is a generator. Examples of Villadsen show that this is not the case for all separable, simple, nuclear C*-algebras.
