Classification of 5-dimensional MD-algebras having commutive derived ideals

TL;DR

This paper classifies all 5-dimensional MD-algebras with commutative derived ideals, focusing on solvable Lie algebras where the K-orbits are either zero-dimensional or of maximal dimension.

Contribution

It provides a complete classification, up to isomorphism, of a specific subclass of 5-dimensional MD-algebras with commutative derived ideals.

Findings

Complete classification of 5-dimensional MD-algebras with commutative derived ideals.

Identification of the structure of K-orbits in these algebras.

Clarification of the conditions under which these algebras are solvable.

Abstract

In this paper, we study a subclass of the class of MD-algebras, i.e., the class of solvable real Lie algebras such that the K-orbits of its corresponding connected and simply connected Lie groups are either orbits of dimension zero or orbits with maximal dimensions. Our main result is to classify, up to isomorphism, all the 5-dimensional MD-algebras having commutative derived ideals.