Nonexistence of reflexive ideals in Iwasawa algebras of Chevalley type

2007/10/02 by Konstantin Ardakov, Feng Wei, Ardakov, Konstantin +3
Mathematics · #16L30 #16P40 #FOS: Mathematics #Number Theory (math.NT) #Rings and Algebras (math.RA) #math.NT #math.RA #msc:16L30 #msc:16P40

paper · pdf · doi:10.48550/arxiv.0710.0635

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

arxiv created 2007/12/05 · arxiv updated 2009/12/01

Abstract

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 p^t Φ(\Zp) and suppose that p≥ 5. Then the Iwasawa algebra Ω_G has no nontrivial reflexive two-sided ideals. This was previously proved by the authors for the root system A₁.

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