On Strongly Inert Subalgebras of an Infinite-Dimensional Lie Algebra

• Date: 2002
• Main Authors: Petravchuk, A. P., Петравчук, А. П.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2002
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/4143
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We study infinite-dimensional Lie algebras L over an arbitrary field that contain a subalgebra A such that dim(A + [A, L])/A < ∞. We prove that if an algebra L is locally finite, then the subalgebra A is contained in a certain ideal I of the Lie algebra L such that dimI/A