Abstract
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.
Funder
Engineering and Physical Sciences Research Council
Publisher
Springer Science and Business Media LLC
Reference17 articles.
1. Ardakov, K., Wadsley, S.: $\widehat {\mathcal {D}}$-modules on Rigid Analytic Spaces I. J. Reine Angew. Math. 747, 221–275 (2019)
2. Ardakov, K., Wadsley, S.: On irreducible representations of compact p-adic analytic groups. Ann. Math. 178, 453–557 (2013)
3. Bell, J.: On the importance of being primitive Revista Colombiana de Matemá,ticas. 53,87–112 (2019)
4. Borel, A.: Linear Algebraic Groups, 2nd edn. Springer, New York (1991)
5. Bosch, S.: Lectures on Formal and Rigid Analytic Geometry, Volume 2105 of Lecture Notes in Mathematics. Springer, Cham (2014)
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献