  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.

Rings and Algebras;Number Theory;Representation Theory