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.
Citation: Nouf Almutiben, Edward L. Boone, Ryad Ghanam, G. Thompson. Classification of the symmetry Lie algebras for six-dimensional co-dimension two Abelian nilradical Lie algebras[J]. AIMS Mathematics, 2024, 9(1): 1969-1996. doi: 10.3934/math.2024098
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.
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Nouf Almutiben, Edward L. Boone, Ryad Ghanam, G. Thompson. Classification of the symmetry Lie algebras for six-dimensional co-dimension two Abelian nilradical Lie algebras[J]. AIMS Mathematics, 2024, 9(1): 1969-1996. doi: 10.3934/math.2024098
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