Unitary representation theory for solvable Lie groups

1968 ◽  
Vol 0 (79) ◽  
pp. 0-0 ◽  
Author(s):  
Jonathan Brezin
Keyword(s):  
Representation Theory ◽  
Lie Groups ◽  
Unitary Representation ◽  
Solvable Lie Groups

Representation Theory of Solvable Lie Groups and Related Topics

2021 ◽  
Author(s):  
Ali Baklouti ◽  
Hidenori Fujiwara ◽  
Jean Ludwig
Keyword(s):  
Representation Theory ◽  
Lie Groups ◽  
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

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.

Invariant orderings in solvable Lie groups

1989 ◽  
Vol 30 (1) ◽  
pp. 44-53 ◽  
Author(s):  
V. M. Gichev
Keyword(s):  
Lie Groups ◽  
Solvable Lie Groups

scholarly journals Corrigendum: Analytic representation theory of Lie groups: general theory and analytic globalizations of Harish-Chandra modules

2017 ◽  
Vol 153 (1) ◽  
pp. 214-217
Author(s):  
Heiko Gimperlein ◽  
Bernhard Krötz ◽  
Henrik Schlichtkrull
Keyword(s):  
General Theory ◽  
Representation Theory ◽  
Lie Groups ◽  
Analytic Representation ◽  
Corrected Proof ◽  
Intermediate Results

We correct the proof of the main result of the paper, Theorem 5.7. Our corrected proof relies on weaker versions of a number of intermediate results from the paper. The original, more general, versions of these statements are not known to be true.

Sign in / Sign up

Export Citation Format

Share Document