Abstract
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.
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Petravchuk, A.P. On Strongly Inert Subalgebras of an Infinite-Dimensional Lie Algebra. Ukrainian Mathematical Journal 54, 1234–1238 (2002). https://doi.org/10.1023/A:1022043215520
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DOI: https://doi.org/10.1023/A:1022043215520