Elsevier

Advances in Mathematics

Volume 218, Issue 3, 20 June 2008, Pages 865-901
Advances in Mathematics

Reflexive ideals in Iwasawa algebras

https://doi.org/10.1016/j.aim.2008.02.004Get rights and content
Under an Elsevier user license
open archive

Abstract

Let G be a torsionfree compact p-adic analytic group. We give sufficient conditions on p and G which ensure that the Iwasawa algebra ΩG of G has no non-trivial two-sided reflexive ideals. Consequently, these conditions imply that every non-zero normal element in ΩG is a unit. We show that these conditions hold in the case when G is an open subgroup of SL2(Zp) and p is arbitrary. Using a previous result of the first author, we show that there are only two prime ideals in ΩG when G is a congruence subgroup of SL2(Zp): the zero ideal and the unique maximal ideal. These statements partially answer some questions asked by the first author and Brown.

MSC

16L30
16P40

Keywords

Iwasawa algebra
Uniform pro-p group
Reflexive ideal
Normal element
Microlocalisation

Cited by (0)