Nonexistence of reflexive ideals in Iwasawa algebras of Chevalley type

Journal article

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 $A_1$.

Authors: Ardakov, K; Wei, F; Zhang, J

• Journal: Journal of Algebra
• Volume: 320
• Issue: 1
• Pages: 259-275
• Publication date: 2007-10-02
• DOI: 10.1016/j.jalgebra.2007.12.020
• EISSN: 1090-266X
• ISSN: 0021-8693
• Language: English
• Keywords: math.NT; 16L30, 16P40; math.RA