Some groups with T1 primitive ideal spaces

Journal of the Australian Mathematical Society

A. L. Carey¹ 

[1] W. Moran

关键词: primary 22 D 10;    22 D 25;    secondary 46 L 55;   

DOI  :  10.1017/S144678870002259X

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

Let G be a second countable locally compact group possessing a normal subgroup N with G/N abelian. We prove that if G/N is discrete then G has T1 primitive ideal space if and only if the G-quasiorbits in Prim N are closed. This condition on G-quasiorbits arose in Pukanzky's work on connected and simply connected solvable Lie groups where it is equivalent to the condition of Auslander and Moore that G be type R on N (-nilradical). Using an abstract version of Pukanzky's arguments due to Green and Pedersen we establish that if G is a connected and simply connected Lie group then Prim G is T1 whenever G-quasiorbits in [G, G] are closed.

【 授权许可】

Unknown