Coherence of augmented Iwasawa algebras
<p>The augmented Iwasawa algebra of a <em>p</em>-adic Lie group is a generalisation of the Iwasawa algebra of a compact <em>p</em>-adic Lie group. We prove that a split-semisimple group over a <em>p</em>-adic field has a coherent a...
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| Format: | Journal article |
| Language: | English |
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Elsevier
2023
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| _version_ | 1797111292301934592 |
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| author | Timmins, J |
| author_facet | Timmins, J |
| author_sort | Timmins, J |
| collection | OXFORD |
| description | <p>The augmented Iwasawa algebra of a <em>p</em>-adic Lie group is a generalisation of the Iwasawa algebra of a compact <em>p</em>-adic Lie group. We prove that a split-semisimple group over a <em>p</em>-adic field has a coherent augmented Iwasawa algebra if and only if its root system is of rank one. We deduce that the general linear group of degree <em>n</em> has a coherent augmented Iwasawa algebra precisely when <em>n</em> is at most two. We also characterise when certain solvable <em>p</em>-adic Lie groups have a coherent augmented Iwasawa algebra.</p> |
| first_indexed | 2024-03-07T08:06:44Z |
| format | Journal article |
| id | oxford-uuid:83275358-7fa0-4768-b730-fe89a9bcadd2 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T08:06:44Z |
| publishDate | 2023 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | oxford-uuid:83275358-7fa0-4768-b730-fe89a9bcadd22023-11-02T16:02:20ZCoherence of augmented Iwasawa algebrasJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:83275358-7fa0-4768-b730-fe89a9bcadd2EnglishSymplectic ElementsElsevier2023Timmins, J<p>The augmented Iwasawa algebra of a <em>p</em>-adic Lie group is a generalisation of the Iwasawa algebra of a compact <em>p</em>-adic Lie group. We prove that a split-semisimple group over a <em>p</em>-adic field has a coherent augmented Iwasawa algebra if and only if its root system is of rank one. We deduce that the general linear group of degree <em>n</em> has a coherent augmented Iwasawa algebra precisely when <em>n</em> is at most two. We also characterise when certain solvable <em>p</em>-adic Lie groups have a coherent augmented Iwasawa algebra.</p> |
| spellingShingle | Timmins, J Coherence of augmented Iwasawa algebras |
| title | Coherence of augmented Iwasawa algebras |
| title_full | Coherence of augmented Iwasawa algebras |
| title_fullStr | Coherence of augmented Iwasawa algebras |
| title_full_unstemmed | Coherence of augmented Iwasawa algebras |
| title_short | Coherence of augmented Iwasawa algebras |
| title_sort | coherence of augmented iwasawa algebras |
| work_keys_str_mv | AT timminsj coherenceofaugmentediwasawaalgebras |