DOI: 10.12732/ijam.v38i2.9
SYMMETRY ANALYSIS OF THE GEODESIC
EQUATIONS ON SIX-DIMENSIONAL LIE GROUPS:
THE NON-ABELIAN NILRADICAL AND
NON-ABELIAN COMPLEMENT CASE
Nouf Almutiben 1, Ryad A. Ghanam 2,§,
G. Thompson 3 and Edward L. Boone 4
1 Department of Mathematics, College of Sciences
Jouf University, King Khalid Road
Sakaka, Kingdom of SAUDI ARABIA
2 Department of Liberal Arts and Sciences
Virginia Commonwealth University in Qatar
Doha, QATAR
3 Department of Mathematics and Statistics
University of Toledo, Toledo, OH, U.S.A
4 Dept. of Statistical Sci. and Operations Res.
Virginia Commonwealth University, Richmond, VA, U.S.A
Abstract. 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 field and the non-zero brackets of the symmetry Lie algebra. A comprehensive analysis and classification of the symmetry Lie algebra are given.
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to cite this paper?
DOI: 10.12732/ijam.v38i2.9
Source: International Journal of
Applied Mathematics
ISSN printed version: 1311-1728
ISSN on-line version: 1314-8060
Year: 2025
Volume: 38
Issue: 2
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