论文标题
$ C^*$ - 可解决的组的代数的痕迹
Traces of $C^*$-algebras of connected solvable groups
论文作者
论文摘要
我们对$ c^*$ - 代数$ c^*（g）的奇特状态简称的明确说明，任意连接的，第二可计数，本地紧凑，可解决的组$ g $。我们表明，从$ c^*$ - $ c^*$ - ABELIANIANT GROUP的代数的奇特状态下的每个奇特状态，除非$ c^*（g）$的所有奇异状态的核心的交集是适当的理想，除非$ g $是Abelian。结果，连接的可解决的非亚伯谎言组的$ c^*$ - 代数不能嵌入简单的Unital Af-Elgebra中。
We give an explicit description of the tracial state simplex of the $C^*$-algebra $C^*(G)$ of an arbitrary connected, second countable, locally compact, solvable group $G$. We show that every tracial state of $C^*(G)$ lifts from a tracial state of the $C^*$-algebra of the abelianized group, and the intersection of the kernels of all the tracial states of $C^*(G)$ is a proper ideal unless $G$ is abelian. As a consequence, the $C^*$-algebra of a connected solvable nonabelian Lie group cannot embed into a simple unital AF-algebra.
