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(...
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| Published in: | Algebra and Discrete Mathematics |
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| Date: | 2009 |
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| Format: | Article |
| Language: | English |
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Інститут прикладної математики і механіки НАН України
2009
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/153383 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862626743165124608 |
|---|---|
| author | Maksimenko, D.V. |
| author_facet | Maksimenko, D.V. |
| citation_txt | 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. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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=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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| first_indexed | 2025-12-07T13:37:03Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-153383 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T13:37:03Z |
| publishDate | 2009 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Maksimenko, D.V. 2019-06-14T03:42:59Z 2019-06-14T03:42:59Z 2009 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. 1726-3255 2000 Mathematics Subject Classification: 17B40. https://nasplib.isofts.kiev.ua/handle/123456789/153383 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. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics On action of outer derivations on nilpotent ideals of Lie algebras Article published earlier |
| spellingShingle | On action of outer derivations on nilpotent ideals of Lie algebras Maksimenko, D.V. |
| 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 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/153383 |
| work_keys_str_mv | AT maksimenkodv onactionofouterderivationsonnilpotentidealsofliealgebras |