Primitive ideals in rational, nilpotent Iwasawa algebras

2021/02/08 by Jones, Adam
#16D25 #16S34 #17B10 #20F18 #22E35 #FOS: Mathematics #Group Theory (math.GR) #Number Theory (math.NT) #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2102.04165

Abstract

Given a p-adic field K and a nilpotent uniform pro-p group G, we prove that all primitive ideals in the K-rational Iwasawa algebra KG are maximal, and can be reduced to a particular standard form. Setting L as the associated ℤ_p-Lie algebra of G, our approach is to study the action of KG on a Dixmier module \widehatD(λ) over the affinoid envelope \widehatU(L)_K, and to prove that all primitive ideals can be reduced to annihilators of modules of this form.

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