Reflexive Ideals in Iwasawa Algebras
نویسنده
چکیده
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 nonzero 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.
منابع مشابه
Nonexistence of Reflexive Ideals in Iwasawa Algebras of Chevalley Type
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 pΦ(Zp) and suppose that p > 5. Then the Iwasawa algebra ΩG has no nontrivial reflexive ideals. This was previously proved by authors for the root system A1.
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