Verma modules for Iwasawa algebras are faithful - Ardakov, K; Wadsley, S (Münster Journal of Mathematics, 2014)
We establish the faithfulness of Verma modules for rational Iwasawa algebras of split semisimple compact $L$-analytic groups. We also prove the algebraic independence of Arens-Michael envelopes over Iwasawa algebras and compute the centre of affinoid enveloping algebras of semisimple $p$-adic Lie algebras.