On action of outer derivations on nilpotent ideals of Lie algebras
Action of outer derivations on nilpotent ideals of Lie algebras are considered. It is shown that for a nilpotent ideal \(I\) of a Lie algebra \(L\) over a field \(F\) the ideal \(I+D(I)\) is nilpotent, provided that \(charF=0\) or \(I\) nilpotent of nilpotency class less than \(p-1\), where \(p=ch...
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| Дата: | 2018 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2018
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| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/770 |
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| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| _version_ | 1856543317559345152 |
|---|---|
| author | Maksimenko, Dmitriy V. |
| author_facet | Maksimenko, Dmitriy V. |
| author_sort | Maksimenko, Dmitriy V. |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2018-04-04T08:31:48Z |
| description | Action of outer derivations on nilpotent ideals of Lie algebras are considered. It is shown that for a nilpotent ideal \(I\) of a Lie algebra \(L\) over a field \(F\) the ideal \(I+D(I)\) is nilpotent, provided that \(charF=0\) or \(I\) nilpotent of nilpotency class less than \(p-1\), where \(p=char F\). In particular, the sum \(N(L)\) of all nilpotent ideals of a Lie algebra \(L\) is a characteristic ideal, if \(charF=0\) or \(N(L)\) is nilpotent of class less than \(p-1\), where \(p=char F\). |
| first_indexed | 2025-12-02T15:27:50Z |
| format | Article |
| id | admjournalluguniveduua-article-770 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:27:50Z |
| publishDate | 2018 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-7702018-04-04T08:31:48Z On action of outer derivations on nilpotent ideals of Lie algebras Maksimenko, Dmitriy V. Lie algebra, derivation, solvable radical, nilpotent ideal 17B40 Action of outer derivations on nilpotent ideals of Lie algebras are considered. It is shown that for a nilpotent ideal \(I\) of a Lie algebra \(L\) over a field \(F\) the ideal \(I+D(I)\) is nilpotent, provided that \(charF=0\) or \(I\) nilpotent of nilpotency class less than \(p-1\), where \(p=char F\). In particular, the sum \(N(L)\) of all nilpotent ideals of a Lie algebra \(L\) is a characteristic ideal, if \(charF=0\) or \(N(L)\) is nilpotent of class less than \(p-1\), where \(p=char F\). Lugansk National Taras Shevchenko University 2018-04-04 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/770 Algebra and Discrete Mathematics; Vol 8, No 1 (2009) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/770/300 Copyright (c) 2018 Algebra and Discrete Mathematics |
| spellingShingle | Lie algebra derivation solvable radical nilpotent ideal 17B40 Maksimenko, Dmitriy V. On action of outer derivations on nilpotent ideals of Lie algebras |
| title | On action of outer derivations on nilpotent ideals of Lie algebras |
| title_full | On action of outer derivations on nilpotent ideals of Lie algebras |
| title_fullStr | On action of outer derivations on nilpotent ideals of Lie algebras |
| title_full_unstemmed | On action of outer derivations on nilpotent ideals of Lie algebras |
| title_short | On action of outer derivations on nilpotent ideals of Lie algebras |
| title_sort | on action of outer derivations on nilpotent ideals of lie algebras |
| topic | Lie algebra derivation solvable radical nilpotent ideal 17B40 |
| topic_facet | Lie algebra derivation solvable radical nilpotent ideal 17B40 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/770 |
| work_keys_str_mv | AT maksimenkodmitriyv onactionofouterderivationsonnilpotentidealsofliealgebras |