迹分解秩(英文)

Tracial Decomposition Rank

首先引入迹分解秩的概念,具有这个结构的稳定有限的顺从C^＊-代数非常多.这个概念和Elliott的用K-理论来分类顺从C~＊-代数的分类计划有重要的联系.然后研究C^＊-代数扩张.设0→I→A-→A/I→0是C^＊-代数的一个短正合序列,其中A有单位元.假设I有分解秩k,A/I有迹分解秩k,那么如果扩张是拟对角的,本文将证明A的迹分解秩不超过k.

We introduce the notion of tracial decomposition rank, a structural property shared by many stably finite nuclear C^＊-algebras. The concept is particularly relevant for Elliott＇s program to classify nuclear C^＊-algebras by K-theory data. We study the extension of C^＊-algebras. Let 0→I→A-→A/I→0 be a short exact sequence of C^＊-algebras with A unital. Suppose that I has decomposition rank k and A/I has tracial decomposition rank k. It will be proved that A has tracial decomposition rank no more than k if the extension is quasidiagonal.