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arXiv · 1608.06793

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

David A. Towers
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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 {\em minimal non-${\mathcal N}$}. To facilitate this we investigate solvable Lie algebras of nilpotent length $k$, and of nilpotent length $\leq k$, and {\em 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-${\mathcal N}$ Lie algebras in which every nilpotent subalgebra is abelian, and those of solvability index $\leq 3$.

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David A. Towers. 2016-08-24. Lie algebras with nilpotent length greater than that of each of their subalgebras. https://arxiv.org/abs/1608.06793

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