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=charF. In particular, the sum N(...
Збережено в:
| Дата: | 2009 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2009
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/153383 |
| Теги: |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | On action of outer derivations on nilpotent ideals of Lie algebras / D.V. Maksimenko // Algebra and Discrete Mathematics. — 2009. — Vol. 8, № 1. — С. 74–82. — Бібліогр.: 6 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| 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=charF. 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=charF. |
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