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arXiv · 2403.04663

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

Ben Forrás
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Abstract

Let $\mathcal G\simeq H\rtimes\Gamma$ be the semidirect product of a finite group $H$ and $\Gamma\simeq\mathbb Z_p$. 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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Ben Forrás. 2024-03-07. On the Wedderburn decomposition of the total ring of quotients of certain Iwasawa algebras. https://arxiv.org/abs/2403.04663

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