$C^*$ -代数的Spanier-Whitehead K-对偶
Spanier-Whitehead K-duality for $C^*$-algebras
摘要：
对有限CW复形的稳定同伦范畴引入了经典Spanier-Whitehead对偶。在这里，我们提供了一个全面的治疗的非交换的版本，称为Spanier-Whitehead $K$ -对偶，这是定义在范畴的$C^*$ -代数的$K$ -理论是非线性生成的，并满足UCT与态射的$KK$ -群。我们将探讨当这些假设以各种方式放松时会发生什么。特别地，我们考虑Paschke对偶和Spanier-Whitehead $K$ -对偶之间的关系。
英文摘要：
Classical Spanier-Whitehead duality was introduced for the stable homotopy category of finite CW complexes. Here we provide a comprehensive treatment of a noncommutative version, termed Spanier-Whitehead $K$-duality, which is defined on the category of $C^*$-algebras whose $K$-theory is finitely generated and that satisfy the UCT with morphisms the $KK$-groups. We explore what happens when these assumptions are relaxed in various ways. In particular, we consider the relationship between Paschke duality and Spanier-Whitehead $K$-duality.
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