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

Abstract

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