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- \({\mathcal N}\). 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-\({\mathcal N}\) Lie algebras in which every nilpotent subalgebra is abelian, and those of solvability index ≤3.
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Presented by Yuri Drozd
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Towers, D.A. Lie Algebras with Nilpotent Length Greater than that of each of their Subalgebras. Algebr Represent Theor 20, 735–750 (2017). https://doi.org/10.1007/s10468-016-9662-z
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DOI: https://doi.org/10.1007/s10468-016-9662-z
Keywords
- Lie algebras
- Solvable
- Nilpotent series
- Nilpotent length
- Chief factor
- Extreme
- Nilregular
- Characteristic ideal
- A-algebra