On the Wedderburn decomposition of the total ring of quotients of certain Iwasawa algebras II
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914328245960704 |
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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 semisimple artinian. We determine its Wedderburn decomposition in full generality in terms of the Wedderburn decomposition of the group ring $ F[H]$. Such a description was previously available only for those simple components for which a certain associated field extension is totally ramified. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_19860 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the Wedderburn decomposition of the total ring of quotients of certain Iwasawa algebras II Forrás, Ben Rings and Algebras Number Theory 16S35, 16W60, 11R23, 16H10 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 semisimple artinian. We determine its Wedderburn decomposition in full generality in terms of the Wedderburn decomposition of the group ring $ F[H]$. Such a description was previously available only for those simple components for which a certain associated field extension is totally ramified. |
| title | On the Wedderburn decomposition of the total ring of quotients of certain Iwasawa algebras II |
| topic | Rings and Algebras Number Theory 16S35, 16W60, 11R23, 16H10 |
| url | https://arxiv.org/abs/2601.19860 |