Orthosymplectic Jordan superalgebras and the Wedderburn principal theorem
An analogue of the Wedderburn Principal Theorem (WPT) is considered for finite-dimensional Jordan superalgebras \(\mathcal{A}\) with solvable radical \(\mathcal{N}\), \(\mathcal{N}^2=0\), and such that \(\mathcal{A}/\mathcal{N}\cong\mathfrak{J}\mathrm{osp}_{n|2m}(\mathbb{F})\), where \(\mathbb{F}\)...
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| Дата: | 2018 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2018
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/336 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua:article-3362018-10-20T08:02:25Z Orthosymplectic Jordan superalgebras and the Wedderburn principal theorem Gómez González, Faber Velasquez, Raul Jordan superalgebras, Wedderburn theorem 17C70, 17C27, 17C55 An analogue of the Wedderburn Principal Theorem (WPT) is considered for finite-dimensional Jordan superalgebras \(\mathcal{A}\) with solvable radical \(\mathcal{N}\), \(\mathcal{N}^2=0\), and such that \(\mathcal{A}/\mathcal{N}\cong\mathfrak{J}\mathrm{osp}_{n|2m}(\mathbb{F})\), where \(\mathbb{F}\) is a field of characteristic zero.We prove that the WPT is valid under some restrictions over the irreducible \(\mathfrak{J}\mathrm{osp}_{n|2m}(\mathbb{F})\)-bimodules contained in \(\mathcal{N}\), and show with counter-examples that these restrictions cannot be weakened. Lugansk National Taras Shevchenko University Universidad de Antioquia, Codi 2014-1032 2018-10-20 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/336 Algebra and Discrete Mathematics; Vol 26, No 1 (2018) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/336/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/336/144 Copyright (c) 2018 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| collection |
OJS |
| language |
English |
| topic |
Jordan superalgebras Wedderburn theorem 17C70 17C27 17C55 |
| spellingShingle |
Jordan superalgebras Wedderburn theorem 17C70 17C27 17C55 Gómez González, Faber Velasquez, Raul Orthosymplectic Jordan superalgebras and the Wedderburn principal theorem |
| topic_facet |
Jordan superalgebras Wedderburn theorem 17C70 17C27 17C55 |
| format |
Article |
| author |
Gómez González, Faber Velasquez, Raul |
| author_facet |
Gómez González, Faber Velasquez, Raul |
| author_sort |
Gómez González, Faber |
| title |
Orthosymplectic Jordan superalgebras and the Wedderburn principal theorem |
| title_short |
Orthosymplectic Jordan superalgebras and the Wedderburn principal theorem |
| title_full |
Orthosymplectic Jordan superalgebras and the Wedderburn principal theorem |
| title_fullStr |
Orthosymplectic Jordan superalgebras and the Wedderburn principal theorem |
| title_full_unstemmed |
Orthosymplectic Jordan superalgebras and the Wedderburn principal theorem |
| title_sort |
orthosymplectic jordan superalgebras and the wedderburn principal theorem |
| description |
An analogue of the Wedderburn Principal Theorem (WPT) is considered for finite-dimensional Jordan superalgebras \(\mathcal{A}\) with solvable radical \(\mathcal{N}\), \(\mathcal{N}^2=0\), and such that \(\mathcal{A}/\mathcal{N}\cong\mathfrak{J}\mathrm{osp}_{n|2m}(\mathbb{F})\), where \(\mathbb{F}\) is a field of characteristic zero.We prove that the WPT is valid under some restrictions over the irreducible \(\mathfrak{J}\mathrm{osp}_{n|2m}(\mathbb{F})\)-bimodules contained in \(\mathcal{N}\), and show with counter-examples that these restrictions cannot be weakened. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/336 |
| work_keys_str_mv |
AT gomezgonzalezfaber orthosymplecticjordansuperalgebrasandthewedderburnprincipaltheorem AT velasquezraul orthosymplecticjordansuperalgebrasandthewedderburnprincipaltheorem |
| first_indexed |
2024-04-12T06:26:49Z |
| last_indexed |
2024-04-12T06:26:49Z |
| _version_ |
1796109195633754112 |