论文标题
$ t_1 $原始理想空间的谎言群体的af-限制性
AF-embeddability for Lie groups with $T_1$ primitive ideal spaces
论文作者
论文摘要
我们研究了原始理想空间的赫尔 - 内基拓扑$ \ text {prim}（g）$ $ c^*$ - algebra $ c^*（g）$是$ t_1 $，即$ \ text {prim}（g）$已关闭。因此，我们证明$ c^*（g）$是af-abeddable。为此，我们表明，如果$ g $是可以解决的，并且其在$ [g，g] $的中心的操作至少具有一个假想的重量，则$ \ text {prim}（g）$没有非空的准紧凑式开放子集。我们还证明，将本地紧凑的组与$ t_1 $的理想空间相连，这是很强的准二角形。
We study simply connected Lie groups $G$ for which the hull-kernel topology of the primitive ideal space $\text{Prim}(G)$ of the group $C^*$-algebra $C^*(G)$ is $T_1$, that is, the finite subsets of $\text{Prim}(G)$ are closed. Thus, we prove that $C^*(G)$ is AF-embeddable. To this end, we show that if $G$ is solvable and its action on the centre of $[G, G]$ has at least one imaginary weight, then $\text{Prim}(G)$ has no nonempty quasi-compact open subsets. We prove in addition that connected locally compact groups with $T_1$ ideal spaces are strongly quasi-diagonal.
