On the Wedderburn decomposition of the total ring of quotients of certain Iwasawa algebras

2024/03/07 by Forrás, Ben
#11R23 (Secondary) #16H10 (Primary) #FOS: Mathematics #Number Theory (math.NT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2403.04663

Abstract

Let \mathcal G≃ H\rtimesΓ be the semidirect product of a finite group H and Γ≃\mathbb Z_p. Let F/\mathbb Q_p be a finite extension with ring of integers \mathcal O_F. Then the total ring of quotients \mathcal Q^F(\mathcal G) of the completed group ring \mathcal O_F[[\mathcal G]] is a semisimple ring. We determine its Wedderburn decomposition under a ramification hypothesis by relating it to the Wedderburn decomposition of the group ring F[H].

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