Non-existence of reflexive ideals in Iwasawa algebras of Chevalley type

Let Φ be a root system and let Φ(Zp) be the standard Chevalley Zp-Lie algebra associated to Φ. For any integer t⩾1, let G be the uniform pro-p group corresponding to the powerful Lie algebra ptΦ(Zp) and suppose that p⩾5. Then the Iwasawa algebra ΩG has no non-trivial two-sided reflexive ideals. This was previously proved by the authors for the root system A1.