The Poisson Characteristic Variety of Unitary Irreducible Representations of Exponential Lie Groups

2019 ◽  
pp. 207-217
Author(s):  
Ali Baklouti ◽  
Sami Dhieb ◽  
Dominique Manchon
Keyword(s):  
Lie Groups ◽  
Irreducible Representations ◽  
Characteristic Variety ◽  
Exponential Lie Groups

Primitive ideals with bounded approximate units in L1-algebras of exponential lie groups

1986 ◽  
Vol 41 (3) ◽  
pp. 411-420 ◽  
Author(s):  
Mohammed El Bachir Bekka
Keyword(s):  
Lie Groups ◽  
Solvable Group ◽  
Lie Group ◽  
Irreducible Representations ◽  
Primitive Ideals ◽  
Exponential Lie Group ◽  
Exponential Lie Groups

AbstractLet G be an exponential Lie group. We study primitive ideals (i.e. kernels of irreducible *-representations of L1(G)), with bounded approximate units (b.a.u.). We prove a result relating the existence of b.a.u. in certain primitive ideals with the geometry of the corresponding Kirillov orbits. This yields for a solvable group of class 2, a characterization of the primitive ideals with b.a.u.

scholarly journals OPERATOR KERNELS FOR IRREDUCIBLE REPRESENTATIONS OF EXPONENTIAL LIE GROUPS

2008 ◽  
Vol 78 (2) ◽  
pp. 301-316
Author(s):  
DETLEV POGUNTKE
Keyword(s):  
Lie Groups ◽  
Lie Algebra ◽  
Unitary Representation ◽  
Kernel Function ◽  
Lie Group ◽  
Linear Form ◽  
Irreducible Representations ◽  
Compactly Supported ◽  
Exponential Lie Group ◽  
Exponential Lie Groups

AbstractA nine-dimensional exponential Lie group G and a linear form ℓ on the Lie algebra of G are presented such that for all Pukanszky polarizations 𝔭 at ℓ the canonically associated unitary representation ρ=ρ(ℓ,𝔭) of G has the property that ρ(ℒ1(G)) does not contain any nonzero operator given by a compactly supported kernel function. This example shows that one of Leptin’s results is wrong, and it cannot be repaired.

scholarly journals Construction of canonical coordinates for exponential Lie groups

2009 ◽  
Vol 361 (12) ◽  
pp. 6283-6348 ◽  
Author(s):  
Didier Arnal ◽  
Bradley Currey ◽  
Bechir Dali
Keyword(s):  
Lie Groups ◽  
Canonical Coordinates ◽  
Exponential Lie Groups
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