Abstract
The word problem is said to be solvable in a variety of Lie algebras if it is solvable in every algebra, finitely presented in this variety. Let [Formula: see text] denote the variety of (2-step nilpotent)-by-abelian Lie algebra and [Formula: see text] the variety of abelian-by-(2-step nilpotent) Lie algebras. It is proved that the word problem is unsolvable in the “interval” of varieties containing the variety [Formula: see text] (of centre-by-[Formula: see text] Lie algebras over a field of characteristic zero), and contained in the variety [Formula: see text].
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