Lie algebras with nilpotent length greater than that of each of their subalgebras

Towers, David Anthony (2017) Lie algebras with nilpotent length greater than that of each of their subalgebras. Algebras and Representation Theory, 20 (3). pp. 735-750. ISSN 1386-923X

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Abstract

The main purpose of this paper is to study the finite-dimensional solvable Lie algebras described in its title, which we call minimal non-N . To facilitate this we investigate solvable Lie algebras of nilpotent length k, and of nilpotent length ≤ k, and extreme Lie algebras, which have the property that their nilpotent length is equal to the number of conjugacy classes of maximal subalgebras. We characterise the minimal non-N Lie algebras in which every nilpotent subalgebra is abelian, and those of solvability index ≤ 3.