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arXiv · 2003.04652

On the problem of classifying solvable Lie algebras having small codimensional derived algebras

Hoa Q. Duong·Vu A. Le·Tuan A. Nguyen·Hai T. T. Cao·Thieu N. Vo
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Abstract

This paper concerns the problem of classifying finite-dimensional real solvable Lie algebras whose derived algebras are of codimension 1 or 2. On the one hand, we present an effective method to classify all $(n+1)$-dimensional real solvable Lie algebras having 1-codimensional derived algebras provided that a full classification of $n$-dimensional nilpotent Lie algebras is given. On the other hand, the problem of classifying all $(n+2)$-dimensional real solvable Lie algebras having 2-codimensional derived algebras is proved to be wild. In this case, we provide a method to classify a subclass of the considered Lie algebras which are extended from their derived algebras by a pair of derivations containing at least one inner derivation.

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Hoa Q. Duong, Vu A. Le, Tuan A. Nguyen, Hai T. T. Cao, Thieu N. Vo. 2020-03-10. On the problem of classifying solvable Lie algebras having small codimensional derived algebras. https://arxiv.org/abs/2003.04652

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