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AF-embeddability for Lie groups with T1 primitive ideal spaces
Journal of the London Mathematical Society ( IF 1.0 ) Pub Date : 2021-01-14 , DOI: 10.1112/jlms.12432
Ingrid Beltiţă 1 , Daniel Beltiţă 1
Affiliation  

We study simply connected Lie groups G for which the hull-kernel topology of the primitive ideal space Prim ( G ) of the group C -algebra C ( G ) is T 1 , that is, the finite subsets of 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 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.

中文翻译:

具有 T1 原始理想空间的李群的 AF 可嵌入性

我们研究单连通李群 G 原始理想空间的壳核拓扑 普里姆 ( G ) 组的 C -代数 C ( G ) 1 ,即有限子集 普里姆 ( G ) 关闭。因此,我们证明 C ( G ) 可嵌入 AF。为此,我们证明如果 G 是可解的,其作用在 [ G , G ] 至少有一个虚权重,那么 普里姆 ( G ) 没有非空的拟紧开子集。我们另外证明连接局部紧群与 1 理想空间是强拟对角空间。
更新日期:2021-01-14
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