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.
Categories: math.RT