Abstract

Re: Algebra seminar You replied on Tue 24/05/2022 15:38 You replied on Tue 24/05/2022 15:38 Stephen Mann Title: Faithfulness of highest-weight modules for Iwasawa algebras Abstract: Iwasawa algebras are completed group algebras for profinite groups and have applications in Number Theory. It is an ongoing project to study the prime ideals of noncommutative Iwasawa algebras.

In the case of an Iwasawa algebra KG corresponding to a split simple Lie algebra, we can embed KG as a subalgebra of a completed enveloping algebra. This allows us to study KG-modules that arise as completions of highest-weight modules.

If we can show that all infinite-dimensional highest-weight modules are faithful over KG, it will be possible to show that all non-zero prime ideals of KG arise as annihilators of finite-dimensional simple modules. In this talk I will outline the progress that has been made towards showing the faithfulness of infinite-dimensional highest-weight modules for KG, and how this applies to prime ideals of KG.