On Strongly Inert Subalgebras of an Infinite-Dimensional Lie Algebra |
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Authors: | Petravchuk A. P. |
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Affiliation: | (1) Kiev University, Kiev |
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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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