Nonexistence of reflexive ideals in Iwasawa algebras of Chevalley type

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