The affinoid enveloping algebra (K) of a free, finitely generated Z(p)-Lie algebra 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 (K), a generalisation of the Verma module, and we prove that when L is nilpotent, all primitive ideals of (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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