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...
Збережено в:
| Дата: | 2018 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| 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| Резюме: | 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 \(p=char F\). |
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