ON A SUBCLASS OF 5-DIMENSIONAL SOLVABLE LIE ALGEBRAS WHICH HAVE 3-DIMENSIONAL COMMUTATIVE DERIVED IDEALS

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-orbit) are orbit of

zero or maximal dimension. The main results of the paper is the clas-

sification up to an isomorphism of all MD5-algebras G with the derived

1

ideal G

:= [G, G] is a 3-dimensional commutative Lie algebra.