Classification of 5-Dimensional MD-Algebras Having Non-Commutative Derived Ideals

TL;DR

This paper classifies all 5-dimensional solvable Lie algebras with non-commutative derived ideals, focusing on a specific subclass of MD5-algebras and MD5-groups, completing the classification of such algebras.

Contribution

It provides a complete classification up to isomorphism of all MD5-algebras with non-commutative derived ideals, advancing the understanding of 5-dimensional solvable Lie algebras.

Findings

Classification of MD5-algebras with non-commutative derived ideals

Complete classification of 5-dimensional solvable Lie algebras

Identification of a subclass of MD5-algebras and MD5-groups

Abstract

The paper presents a subclass of the class of MD5-algebras and MD5-groups, i.e. five dimensional solvable Lie algebras and Lie groups such that their orbits in the co-adjoint representation (K-orbits) are orbits of zero or maximal dimension. The main result of the paper is the classification up to an isomorphism of all MD5-algebras with the non-commutative derived ideal. With this result, we have the complete classification of 5-dimensional solvable Lie algebras.