Abstract
In this paper, we study the classification of finite-dimensional real solvable Lie algebras whose derived algebras are of codimension 1 or 2. We present an effective method to classify (Formula presented.) -dimensional real solvable Lie algebras having 1-codimensional derived algebras provided that a full classification of n-dimensional nilpotent Lie algebras is given. In addition, the problem of classifying (Formula presented.) -dimensional real solvable Lie algebras having 2-codimensional derived algebras is proved to be wild. In this case, we 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.
| Original language | English |
|---|---|
| Pages (from-to) | 3775-3793 |
| Number of pages | 19 |
| Journal | Communications in Algebra |
| Volume | 50 |
| Issue number | 9 |
| Early online date | 12 Mar 2022 |
| DOIs | |
| Publication status | Published - 31 Mar 2022 |
Bibliographical note
Publisher Copyright:© 2022 Taylor & Francis Group, LLC.
Acknowledgements
The authors would like to thank the referees for pointing-out references [Citation23, Citation24, Citation31, Citation32] as well as helpful suggestions that help us to improve the exposition of the paper.Keywords
- derived algebra
- Lie algebra
- wild problem
ASJC Scopus subject areas
- Algebra and Number Theory