scholarly journals Unitary representations of solvable Lie groups

1971 ◽  
Vol 4 (4) ◽  
pp. 457-608 ◽  
Author(s):  
L. Pukanszky
Keyword(s):  
Lie Groups ◽  
Unitary Representations ◽  
Solvable Lie Groups

Polarization and unitary representations of solvable Lie groups

1971 ◽  
Vol 14 (4) ◽  
pp. 255-354 ◽  
Author(s):  
L. Auslander ◽  
B. Kostant
Keyword(s):  
Lie Groups ◽  
Unitary Representations ◽  
Solvable Lie Groups

Unitary representations of solvable Lie groups

1966 ◽  
Vol 0 (62) ◽  
pp. 0-0 ◽  
Author(s):  
Louis Auslander ◽  
Calvin C. Moore
Keyword(s):  
Lie Groups ◽  
Unitary Representations ◽  
Solvable Lie Groups

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.

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

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

Harmonicity of vector fields on a class of Lorentzian solvable Lie groups

2018 ◽  
Vol 18 (3) ◽  
pp. 337-344 ◽  
Author(s):  
Ju Tan ◽  
Shaoqiang Deng
Keyword(s):  
Vector Field ◽  
Lie Groups ◽  
Lie Algebras ◽  
Critical Points ◽  
Vector Fields ◽  
Energy Functional ◽  
Smooth Vector ◽  
Solvable Lie Groups ◽  
Invariant Vector ◽  
Invariant Vector Fields

AbstractIn this paper, we consider a special class of solvable Lie groups such that for any x, y in their Lie algebras, [x, y] is a linear combination of x and y. We investigate the harmonicity properties of invariant vector fields of this kind of Lorentzian Lie groups. It is shown that any invariant unit time-like vector field is spatially harmonic. Moreover, we determine all vector fields which are critical points of the energy functional restricted to the space of smooth vector fields.

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