Classification of Solvable Lie algebras whose non-trivial Coadjoint Orbits of simply connected Lie groups are all of Codimension 2

TL;DR

This paper classifies real solvable Lie algebras with the property that all non-trivial coadjoint orbits of their simply connected Lie groups have codimension 2, focusing on a specific class known as MD-algebras.

Contribution

It provides a complete classification of such Lie algebras, expanding understanding of their structure within the MD-algebras class.

Findings

Identifies all solvable Lie algebras with coadjoint orbits of codimension 2.

Shows these algebras belong to the MD-algebras class.

Provides structural criteria for these Lie algebras.

Abstract

We give a classification of real solvable Lie algebras whose non-trivial coadjoint orbits of corresponding simply connected Lie groups are all of codimension 2. These Lie algebras belong to a well-known class, called the class of MD-algebras.