论文标题
$ c^*$ - 稳定等级的代数一
A total Cuntz semigroup for $C^*$-algebras of stable rank one
论文作者
论文摘要
在本文中，我们表明，对于Unital，$ C^*$ - 稳定等级的代数和真实等级零的代数，统一的Cuntz Semigroup fundor和Founder $ {\ rm k} _*$是自然的。然后，我们介绍了统一的Cuntz Semogroup的改进，例如，Cuntz Semigroup的总数是可分离的$ C^*$ - 稳定排名第一代数的新不变性，是$ C^*$ - 稳定等级的稳定函数的稳定连续函数，对类别的稳定等级为代数。我们证明，这个新的函子和函子$ {\ rm \ usewissline {k}} $对于Unital，可分离，k-pure $ c^*$ - 代数是自然的。因此，总Cuntz Semigroup是大型$ C^*$ - 真实等级零代数的完全不变。
In this paper, we show that for unital, separable $C^*$-algebras of stable rank one and real rank zero, the unitary Cuntz semigroup functor and the functor ${\rm K}_*$ are naturallly equivalent. Then we introduce a refinement of the unitary Cuntz semigroup, say the total Cuntz semigroup, which is a new invariant for separable $C^*$-algebras of stable rank one, is a well-defined continuous functor from the category of $C^*$-algebras of stable rank one to the category ${\rm\underline{ Cu}}$. We prove that this new functor and the functor ${\rm \underline{K}}$ are naturallly equivalent for unital, separable, K-pure $C^*$-algebras. Therefore, the total Cuntz semigroup is a complete invariant for a large class of $C^*$-algebras of real rank zero.
