Nonexistence of reflexive ideals in Iwasawa algebras of Chevalley type

Details Nonexistence of reflexive ideals in Iwasawa algebras of Chevalley type Nonexistence of reflexive ideals in Iwasawa algebras of Chevalley type

2007-10-02

arxiv.org/abs/0710.0635v2

Mathematics

Rings and Algebras

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

Scientific paper

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

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