On Strongly Inert Subalgebras of an Infinite-Dimensional Lie Algebra
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 <. We show that the condition of local finiteness of L is essential in this statement.
English version (Springer): Ukrainian Mathematical Journal 54 (2002), no. 7, pp 1234-1238.
Citation Example: Petravchuk A. P. On Strongly Inert Subalgebras of an Infinite-Dimensional Lie Algebra // Ukr. Mat. Zh. - 2002. - 54, № 7. - pp. 1025-1028.