论文标题
全球Glimm属性
The Global Glimm Property
论文作者
论文摘要
众所周知，具有全局Glimm属性的C*-Algebra无处可分散（它没有基本的理想品质），而全局的Glimm问题询问是否存在匡威。我们通过证明c* - 代数具有全球性格的属性，只有在且仅当它无处散布并且其cuntz semogroup是理想的过滤时（产生给定理想的Cuntz类是向下定向）并且具有属性（v）（一种弱的命令）。 我们表明，对于具有稳定等级或实际等级零的C*代数的理想过滤和属性（V）是自动的，从而在这些情况下恢复了全局GLIMM问题的解决方案。我们还使用我们的方法来解决新的c* - 代数类别的全球GLIMM问题。
It is known that a C*-algebra with the Global Glimm Property is nowhere scattered (it has no elementary ideal-quotients), and the Global Glimm Problem asks if the converse holds. We provide a new approach to this long-standing problem by showing that a C*-algebra has the Global Glimm Property if and only if it is nowhere scattered and its Cuntz semigroup is ideal-filtered (the Cuntz classes generating a given ideal are downward directed) and has property (V) (a weak form of being sup-semilattice ordered). We show that ideal-filteredness and property (V) are automatic for C*-algebras that have stable rank one or real rank zero, thereby recovering the solutions to the Global Glimm Problem in these cases. We also use our approach to solve the Global Glimm Problem for new classes of C*-algebras.
