Affinoid Dixmier Modules and the Deformed Dixmier-Moeglin Equivalence

Adam Jones

    Research output: Contribution to journalArticlepeer-review

    Abstract

    The affinoid enveloping algebra U(L)ˆK of a free, finitely generated Zp-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 U(L)ˆK, a generalisation of the Verma module, and we prove that when L is nilpotent, all primitive ideals of U(L)ˆK 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.
    Original languageEnglish
    Pages (from-to)23-70
    JournalAlgebras and Representation Theory
    Volume26
    Issue number1
    DOIs
    Publication statusPublished - 12 Aug 2021

    Keywords

    • Non-commutative algebra
    • Dixmier-Moeglin equivalence
    • Lie lattices
    • Affinoid envelopes

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