论文标题
C* - 代理的Cuntz半群的现代理论
The modern theory of Cuntz semigroups of C*-algebras
论文作者
论文摘要
我们详细介绍了C* - 代数的Cuntz Semigroups理论。从最基本的定义和技术引理开始，我们提出了历史重要性的几个结果，例如Cuntz关于准则存在的定理，Rørdam证明了$ \ Mathcal {z} $ - 稳定性意味着严格的比较，以及Toms的非$ \ Mathcal {z} $ \ syge {z} $ stable simple sime clue cluit c*-al c*-al-allbra。我们还为读者提供了对理论的现状和现代方法的广泛概述，包括稳定等级的C* - 代数的最新结果（例如，Blackadar Handelman的猜想和等级的实现），以及Cuntz类别$ \ MathBf {Cu {Cu {Cu} $的抽象研究。
We give a detailed introduction to the theory of Cuntz semigroups for C*-algebras. Beginning with the most basic definitions and technical lemmas, we present several results of historical importance, such as Cuntz's theorem on the existence of quasitraces, Rørdam's proof that $\mathcal{Z}$-stability implies strict comparison, and Toms' example of a non $\mathcal{Z}$-stable simple, nuclear C*-algebra. We also give the reader an extensive overview of the state of the art and the modern approach to the theory, including the recent results for C*-algebras of stable rank one (for example, the Blackadar-Handelman conjecture and the realization of ranks), as well as the abstract study of the Cuntz category $\mathbf{Cu}$.
