On a Subclass of 5-Dimensional Solvable Lie Algebras Which Have 3-Dimensional Commutative Derived Ideal

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-orbit) are orbit of zero or maximal dimension. The main results of the paper is the classification up to an isomorphism of all MD5-algebras $\mathcal{G}$ with the derived ideal ${\mathcal{G}}^{1} := [\mathcal{G}, \mathcal{G}]$ is a 3-dimensional commutative Lie algebra.