Nonexistence of reflexive ideals in Iwasawa algebras of Chevalley type

Abstract

Let $\Phi$ be a root system and let $Φ(\Zp)$ be the standard Chevalley $\Zp$-Lie algebra associated to $\Phi$. For any integer $t\ge 1$, let $G$ be the uniform pro-$p$ group corresponding to the powerful Lie algebra $p^t Φ(\Zp)$ and suppose that $p\ge 5$. Then the Iwasawa algebra ${\Omega }_G$ has no nontrivial reflexive two-sided ideals. This was previously proved by the authors for the root system $A_1$.

Minor changes made, mostly due to helpful comments from the referee