On the Wedderburn decomposition of the total ring of quotients of certain Iwasawa algebras
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arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866912769545076736 |
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| author | Forrás, Ben |
| author_facet | Forrás, Ben |
| 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 $F[H]$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_04663 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Wedderburn decomposition of the total ring of quotients of certain Iwasawa algebras Forrás, Ben Rings and Algebras Number Theory 16H10 (Primary), 11R23 (Secondary) 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 $F[H]$. |
| title | On the Wedderburn decomposition of the total ring of quotients of certain Iwasawa algebras |
| topic | Rings and Algebras Number Theory 16H10 (Primary), 11R23 (Secondary) |
| url | https://arxiv.org/abs/2403.04663 |