Affinoid Dixmier modules and the deformed DixmierMoeglin equivalence
Abstract
The affinoid envelope, $\widehat{U(\mathcal{L})}$ of a free, finitely generated $\mathbb{Z}_p$Lie algebra $\mathcal{L}$ has proven to be useful within the representation theory of compact $p$adic Lie groups. Our aim is to further understand the algebraic structure of $\widehat{U(\mathcal{L})}$, and to this end, we will define a Dixmier module over $\widehat{U(\mathcal{L})}$, and prove that this object is generally irreducible in case where $\mathcal{L}$ is nilpotent. Ultimately, we will prove that all primitive ideals in the affinoid envelope can be described in terms of the annihilators of Dixmier modules, and using this, we aim towards proving that these algebras satisfy a version of the classical DixmierMoeglin equivalence.
 Publication:

arXiv eprints
 Pub Date:
 February 2021
 DOI:
 10.48550/arXiv.2102.03330
 arXiv:
 arXiv:2102.03330
 Bibcode:
 2021arXiv210203330J
 Keywords:

 Mathematics  Representation Theory;
 Mathematics  Number Theory;
 Mathematics  Rings and Algebras;
 16G30;
 17B30;
 17B35;
 16D70;
 22E35
 EPrint:
 52 pages, Algebr Represent Theor (2021)