@article{Almutiben2024, 
author = {Nouf Almutiben and Edward L. Boone and Ryad Ghanam and G. Thompson},
title = {Classification of the symmetry Lie algebras for six-dimensional co-dimension two Abelian nilradical Lie algebras},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {1},
pages = {1969-1996},
keywords = {Lie symmetry, Lie group, canonical connection, geodesic system},
url = {https://www.sciopen.com/article/10.3934/math.2024098},
doi = {10.3934/math.2024098},
abstract = {In this paper, we consider the symmetry algebra of the geodesic equations of the canonical connection on a Lie group. We mainly consider the solvable indecomposable six-dimensional Lie algebras with co-dimension two abelian nilradical that have an abelian complement. In dimension six, there are nineteen such algebras, namely,        A          6      ,      1      –       A          6      ,      19       in Turkowski's list. For each algebra, we give the geodesic equations, a basis for the symmetry Lie algebra in terms of vector fields, and finally we identify the symmetry Lie algebra from standard lists.}
}