Complemented *-primitive ideals inL 1-algebras of exponential lie groups and of motion groups

1990 ◽  
Vol 204 (1) ◽  
pp. 515-526 ◽  
Author(s):  
M. E. B. Bekka ◽  
J. Ludwig
Keyword(s):  
Lie Groups ◽  
Primitive Ideals ◽  
Motion Groups ◽  
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 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

scholarly journals Weakly Exponential Lie Groups

1996 ◽  
Vol 179 (2) ◽  
pp. 331-361 ◽  
Author(s):  
Karl-Hermann Neeb
Keyword(s):  
Lie Groups ◽  
Exponential Lie Groups

Representations of exponential lie groups

1973 ◽  
Vol 7 (2) ◽  
pp. 151-152 ◽  
Author(s):  
I. K. Busyatskaya
Keyword(s):  
Lie Groups ◽  
Exponential Lie Groups

scholarly journals Affinoid Dixmier Modules and the Deformed Dixmier-Moeglin Equivalence

2021 ◽  
Author(s):  
Adam Jones
Keyword(s):  
Representation Theory ◽  
Lie Groups ◽  
Lie Algebra ◽  
Algebraic Structure ◽  
Verma Module ◽  
Finitely Generated ◽  
Enveloping Algebra ◽  
Primitive Ideals

AbstractThe affinoid enveloping algebra $\widehat {U({\mathscr{L}})}_{K}$ U ( L ) ̂ K of a free, finitely generated $\mathbb {Z}_{p}$ ℤ p -Lie algebra ${\mathscr{L}}$ L has proven to be useful within the representation theory of compact p-adic Lie groups, and we aim to further understand its algebraic structure. To this end, we define the notion of a Dixmier module over $\widehat {U({\mathscr{L}})}_{K}$ U ( L ) ̂ K , a generalisation of the Verma module, and we prove that when ${\mathscr{L}}$ L is nilpotent, all primitive ideals of $\widehat {U({\mathscr{L}})}_{K}$ U ( L ) ̂ K can be described in terms of annihilator ideals of Dixmier modules. Using this, we take steps towards proving that this algebra satisfies a version of the classical Dixmier-Moeglin equivalence.

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