New directions in the study of prime ideals in rational, nilpotent Iwasawa algebras

Abstract

Let G be a nilpotent p-valuable (compact p-adic Lie) group. There is an ongoing investigation into the prime ideals of its completed group algebra (Iwasawa algebra), and there remains an open conjecture that they can all be proved to have a canonical standard form. We very this conjecture for several new classes of nilpotent groups, including those corresponding to the positive subalgebra of almost all classical and exceptional types, curiously excluding those of type C.