Abstract
In the case of characteristic zero, the Engel identity implies nilpotence in the variety generated by simple infinite-dimensional Lie algebras of Cartan type. An analogous result is also true for 2-metabelian Lie algebras (an algebra is called 2-metabelian if every 2-generator subalgebra is metabelian) over a field whose characteristic does not divide 5!, which in this case permits one to prove solvability of the variety of 2-metabelian Lie algebras.Bibliography: 10 titles.
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