C^＊-代数的迹迹秩

Tracially Tracial Rank of C^＊-Algebras

引入C^＊-代数迹迹秩的概念,讨论它的基本性质.另外,迹迹秩为零和迹拓扑秩为零的C^＊-代数等价,同时讨论这类代数的拟对角扩张性质.设O→I→A→A/I→O是拟对角扩张的短正合列,证明如果TTR（I）≤k且TTR（A/I）=0,则TTR（A）≤k.

This paper introduces tracially tracial rank of C^＊-algebra, and discusses some basic properties of this kind of C^＊-algebra. TTR（A）=0 is equivalent to TR（A）=0. Other- wise, the authors discuss the quasidiagonal extension property of this kind of C^＊-algebra. Suppose O→I→A→A/I→O be a short exact sequence of quasidiagonal extension, the authors prove that TTR（A）≤k if TTR（I）≤k and TTR（A/I）=O. Keywords