On the problem of classifying solvable Lie algebras having small codimensional derived algebras
Rings and Algebras
2020-03-11 v1
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 -dimensional real solvable Lie algebras having 1-codimensional derived algebras provided that a full classification of -dimensional nilpotent Lie algebras is given. On the other hand, the problem of classifying all -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.
Cite
@article{arxiv.2003.04652,
title = {On the problem of classifying solvable Lie algebras having small codimensional derived algebras},
author = {Hoa Q. Duong and Vu A. Le and Tuan A. Nguyen and Hai T. T. Cao and Thieu N. Vo},
journal= {arXiv preprint arXiv:2003.04652},
year = {2020}
}