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A unitary Cuntz semigroup for C⁎-algebras of stable rank one
Journal of Functional Analysis ( IF 1.7 ) Pub Date : 2021-07-01 , DOI: 10.1016/j.jfa.2021.109175
Laurent Cantier

We introduce a new invariant for C-algebras of stable rank one that merges the Cuntz semigroup information together with the K1-group information. This semigroup, termed the Cu1-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 Cu1-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. Furthermore, we compute the Cu1-semigroup of some specific classes of C-algebras. Finally, in the course of our investigation, we show that we can recover functorially Cu, K1 and K:=K0K1 from Cu1.



中文翻译:

酉Cuntz半群为Ç 稳定的排名之一-代数

我们引入了一个新的不变量 C-将 Cuntz 半群信息与 1- 组信息。这个半群称为1-semigroup,被构造为由稳定给定的正元素组成的对的等价类 C-algebra 连同由给定正元素生成的遗传子代数的单元化的酉元素。我们表明1-semigroup 是一个定义良好的连续函子,来自 C-稳定排名第一的代数到我们写的合适的codomain类别 . 此外,我们计算1- 某些特定类别的半群 C-代数。最后,在我们的调查过程中,我们表明我们可以在函数上恢复 Cu,1=011.

更新日期:2021-07-09
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