On action of outer derivations on nilpotent ideals of Lie algebras

• Veröffentlicht in: Algebra and Discrete Mathematics
• Datum: 2009
• 1. Verfasser: Maksimenko, D.V.
• Format: Artikel
• Sprache: Englisch
• Veröffentlicht: Інститут прикладної математики і механіки НАН України 2009
• Online Zugang: https://nasplib.isofts.kiev.ua/handle/123456789/153383
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Zitieren: 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.

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(...