On action of outer derivations on nilpotent ideals of Lie algebras

• Date: 2018
• Main Author: Maksimenko, Dmitriy V.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: Lie algebra; derivation; solvable radical; nilpotent ideal; 17B40
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/770
• Journal Title: Algebra and Discrete Mathematics

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...