SYMMETRY ANALYSIS OF THE GEODESIC EQUATIONS ON SIX-DIMENSIONAL LIE GROUPS: THE NON-ABELIAN NILRADICAL AND NON-ABELIAN COMPLEMENT CASE

In this article, we continue our investigation and classification of the symmetry Lie algebra of the geodesic equations of the canonical connection on a Lie group.In particular, we consider the list of indecomposable solvable six-dimensional Lie algebras whose nilradical is four-dimensional non-abelian and its complement is two-dimensional non-abelian as well.According to the classification of the six-dimensional Lie algebras given by Turkowski [1], there are thirteen Lie algebras to consider, namely A 6,28 -A 6,40 .For each of these algebras, we list the system of the geodesic equations, a basis for the symmetry algebra in terms of vector fields and the non-zero brackets of the symmetry Lie algebra.A comprehensive analysis and classification of the symmetry Lie algebra are given.