A Control Theorem for Primitive ideals in Iwasawa algebras

TL;DR

This paper proves a control theorem for primitive ideals in Iwasawa algebras of certain p-adic groups, linking these ideals to the centraliser of a specific subgroup, advancing understanding of their structure.

Contribution

It establishes a new control theorem for primitive ideals in Iwasawa algebras of nilpotent uniform pro-p groups, relating them to centralisers.

Findings

Primitive ideals are controlled by the centraliser of the second term in the upper central series.

The theorem applies to faithful, primitive ideals in Iwasawa algebras of nilpotent, uniform pro-p groups.

Provides a structural insight into the primitive ideals in Iwasawa algebras.

Abstract

Let p be a prime, K a p-adic field, G a nilpotent, uniform pro-p group. We prove that all faithful, primitive ideals in the Iwasawa algebra KG are controlled by the centraliser of the second term in the upper central series for G.