Primitive ideals in rational, nilpotent Iwasawa algebras

Abstract

Given a p-adic field K and a nilpotent uniform pro-p group G, we prove that all primitive ideals in the K-rational Iwasawa algebra KG are maximal, and can be reduced to a particular standard form. Setting L as the associated Zp-Lie algebra of G, our approach is to study the action of KG on a Dixmier module D(λ)ˆ over the affinoid envelope U(L)ˆK, and to prove that all primitive ideals can be reduced to annihilators of modules of this form.