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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.04663 |
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Table of Contents:
- Let $\mathcal G\simeq H\rtimesΓ$ be the semidirect product of a finite group $H$ and $Γ\simeq\mathbb Z_p$. 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 $F[H]$.