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Classification of the symmetry Lie algebras for six-dimensional co-dimension two Abelian nilradical Lie algebras.
- Source :
- AIMS Mathematics (2473-6988); 2024, Vol. 9 Issue 1, p1969-1996, 28p
- Publication Year :
- 2024
-
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<subscript>6,1</subscript>-A<subscript>6,19</subscript> 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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 24736988
- Volume :
- 9
- Issue :
- 1
- Database :
- Complementary Index
- Journal :
- AIMS Mathematics (2473-6988)
- Publication Type :
- Academic Journal
- Accession number :
- 174776433
- Full Text :
- https://doi.org/10.3934/math.2024098