Primitive ideals in the enveloping algebra of a semisimple Lie algebra

1987 ◽  
pp. 29-36
Author(s):  
J. Jantzen
Keyword(s):  
Lie Algebra ◽  
Semisimple Lie Algebra ◽  
Enveloping Algebra ◽  
Primitive Ideals

scholarly journals Chern characters, reduced ranks and -modules on the flag variety

1994 ◽  
Vol 37 (3) ◽  
pp. 477-482 ◽  
Author(s):  
T. J. Hodges ◽  
M. P. Holland
Keyword(s):  
Lie Algebra ◽  
Euler Characteristic ◽  
Maximal Ideal ◽  
Chern Character ◽  
Flag Variety ◽  
Central Character ◽  
Geometric Description ◽  
Semisimple Lie Algebra ◽  
Enveloping Algebra ◽  
Chern Characters

Let D be the factor of the enveloping algebra of a semisimple Lie algebra by its minimal primitive ideal with trival central character. We give a geometric description of the Chern character ch: K0(D)→HC0(D) and the state (of the maximal ideal m) s: K0(D)→K0(D/m) = ℤ in terms of the Euler characteristic χ:K0()→ℤ, where is the associated flag variety.

scholarly journals Primitive ideals of the quantised enveloping algebra of a complex lie algebra

1994 ◽  
Vol 49 (1) ◽  
pp. 81-84 ◽  
Author(s):  
Sei-Qwon Oh
Keyword(s):  
Lie Algebra ◽  
Enveloping Algebra ◽  
Primitive Ideals

In this paper, we characterise all primitive ideals of the quantised enveloping algebra Uq[sl(2, ℂ)] of the complex Lie algebra sl(2, ℂ) and show how they are similar to those of U[sl(2, ℂ)], the enveloping algebra of sl(2, ℂ).

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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