论文标题
稳定等级的C* - 代数的统一Cuntz Semigroup
A unitary Cuntz semigroup for C*-algebras of stable rank one
论文作者
论文摘要
我们引入了稳定等级的C*-Algebras的新不变性，将Cuntz Semigroup信息与K $ _1 $ -Group信息合并。这个被称为cu $ _1 $ - 元素的半群构建为对等元素的对等元素，由给定的c*algebra稳定中的积极元素，以及给定正元素生成的遗传subalgebra的单一元素。我们表明，Cu $ _1 $ -Semigroup是一个定义明确的连续函数，来自稳定等级的c*-代数级别，即我们编写Cu $^\ sim $的合适的Codomain类别。此外，我们计算了某些特定类别的C*-Algebras类的Cu $ _1 $ -Semigroup。最后，在调查过程中，我们表明我们可以从cu $ _1 $中恢复功能上的CU，K $ _1 $和K $ _*：= $ K $ _0 $ _0 $ _0 $ _0 $ _1 $ k $ _1 $。
We introduce a new invariant for C*-algebras of stable rank one that merges the Cuntz semigroup information together with the K$_1$-group information. This semigroup, termed the Cu$_1$-semigroup, is constructed as equivalence classes of pairs consisting of a positive element in the stabilization of the given C*-algebra together with a unitary element of the unitization of the hereditary subalgebra generated by the given positive element. We show that the Cu$_1$-semigroup is a well-defined continuous functor from the category of C*-algebras of stable rank one to a suitable codomain category that we write Cu$^\sim$. Furthermore, we compute the Cu$_1$-semigroup of some specific classes of C*-algebras. Finally, in the course of our investigation, we show that we can recover functorially Cu, K$_1$ and K$_*:=$K$_0$$\oplus$ K$_1$ from Cu$_1$.
