Real C*-algebras, United KK-theory, and the Universal Coefficient Theorem

Universal coefficient theorems for C*-algebras over finite topological spaces

We determine the class of finite T_0-spaces allowing for a universal coefficient theorem computing equivariant KK-theory by filtrated K-theory.

有限平方自由阶循环群在C*-代数上的通用系数定理

A universal coefficient theorem for actions of finite cyclic groups of square-free order on C*-algebras

本文在等效Kasparov范畴中，为有限平方自由阶循环群证明了对象在bootstrap类中的通用系数定理。

A short note on the continuous Rokhlin property and the universal coefficient theorem

Let $G$ be a metrizable compact group, $A$ a separable C*-algebra and $α$ a strongly continuous action of $G$ on $A$. Provided that $α$ satisfies the continuous Rokhlin property, we show that the property of satisfying the UCT in E-theory passes from $A$ to the crossed product C*-algebra $A\rtimes_αG$ and the fixed point algebra $A^α$. This extends a result by Gardella in the case that $G$ is the circle and $A$ is nuclear. For circle actions on separable, unital C*-algebras with the continuous Rokhlin property, we establish a connection between the $E$-theory equivalence class of the coefficie…

Gorenstein homological algebra and universal coefficient theorems

We study criteria for a ring - or more generally, for a small category - to be Gorenstein and for a module over it to be of finite projective dimension. The goal is to unify the universal coefficient theorems found in the literature and to develop a machinery for proving new ones. Among the universal coefficient theorems covered by our methods we find, besides all the classic examples, several exotic examples arising from the KK-theory of C*-algebras and also Neeman's Brown-Adams representability theorem for compactly generated categories.

有限群在C*-代数上的通用系数定理

A universal coefficient theorem for actions of finite groups on C*-algebras

本文提出了一种有限群在C*-代数上的通用系数定理，通过生成bootstrap类来分类稳定Kirchberg代数上的G作用。