Journal of the Australian Mathematical Society | |
Some groups with T1 primitive ideal spaces | |
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
【 预 览 】
Files | Size | Format | View |
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RO201912040543643ZK.pdf | 461KB | download |