Discrete Subgroups of Solvable Lie Groups I

1956 ◽  
Vol 64 (1) ◽  
pp. 1 ◽  
Author(s):  
Hsien-Chung Wang
Keyword(s):  
Lie Groups ◽  
Solvable Lie Groups ◽  
Discrete Subgroups

scholarly journals Some groups with T1 primitive ideal spaces

1985 ◽  
Vol 38 (1) ◽  
pp. 55-64 ◽  
Author(s):  
A. L. Carey ◽  
W. Moran
Keyword(s):  
Normal Subgroup ◽  
Lie Groups ◽  
Lie Group ◽  
Locally Compact Group ◽  
Primitive Ideal ◽  
Ideal Space ◽  
Solvable Lie Groups ◽  
Locally Compact ◽  
Simply Connected ◽  
Connected Lie Group

AbstractLet 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.

Discrete Subgroups Isomorphic to Lattices in Lie Groups

1976 ◽  
Vol 98 (4) ◽  
pp. 853 ◽  
Author(s):  
Gopal Prasad
Keyword(s):  
Lie Groups ◽  
Discrete Subgroups

scholarly journals Lattices of some solvable Lie groups and actions of products of affine groups

2009 ◽  
Vol 61 (3) ◽  
pp. 349-364 ◽  
Author(s):  
Nobuo Tsuchiya ◽  
Aiko Yamakawa
Keyword(s):  
Lie Groups ◽  
Solvable Lie Groups ◽  
Affine Groups

Analysis of a Distinguished Laplacian on Solvable Lie Groups

1993 ◽  
Vol 163 (1) ◽  
pp. 151-162 ◽  
Author(s):  
Saverio Giulini ◽  
Giancarlo Mauceri
Keyword(s):  
Lie Groups ◽  
Solvable Lie Groups
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