scholarly journals Nilpotent Lie Groups: Fourier Inversion and Prime Ideals

2017 ◽  
Vol 25 (2) ◽  
pp. 345-376
Author(s):  
Ying-Fen Lin ◽  
Jean Ludwig ◽  
Carine Molitor-Braun
Keyword(s):  
Lie Groups ◽  
Prime Ideals ◽  
Nilpotent Lie Groups ◽  
Fourier Inversion

scholarly journals An invariant for unitary representations of nilpotent Lie groups.

1987 ◽  
Vol 34 (1) ◽  
pp. 23-30 ◽  
Author(s):  
C. Benson ◽  
G. Ratcliff
Keyword(s):  
Lie Groups ◽  
Unitary Representations ◽  
Nilpotent Lie Groups

CRITERION OF PROPER ACTIONS FOR 3-STEP NILPOTENT LIE GROUPS

2007 ◽  
Vol 18 (07) ◽  
pp. 783-795 ◽  
Author(s):  
TARO YOSHINO
Keyword(s):  
Homogeneous Space ◽  
Lie Groups ◽  
Lie Group ◽  
Closed Subgroup ◽  
Nilpotent Lie Groups ◽  
Nilpotent Lie Group ◽  
Proper Actions ◽  
Affirmative Solution

For a nilpotent Lie group G and its closed subgroup L, Lipsman [13] conjectured that the L-action on some homogeneous space of G is proper in the sense of Palais if and only if the action is free. Nasrin [14] proved this conjecture assuming that G is a 2-step nilpotent Lie group. However, Lipsman's conjecture fails for the 4-step nilpotent case. This paper gives an affirmative solution to Lipsman's conjecture for the 3-step nilpotent case.

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