Defense Date
2024
Document Type
Dissertation
Degree Name
Doctor of Philosophy
Department
Mathematical Sciences
First Advisor
Ryad Ghanam
Abstract
We consider the symmetry algebra of the geodesic equations of the canonical
connection on a Lie groups. We mainly consider the solvable indecomposable four,
five and six-dimensional Lie algebras with co-dimension two abelian nilradical, that
have an abelian and not abelian complement. In this particular case, we have only
one algebra in dimension four namely; A4,12 , and three algebras in dimension five
namely; A5,33, A5,34, and A5,35 In dimension six, based on the list of Lie algebras in
Turkowski’s list, there are nineteen such algebras namely; A6,1- A6,19 that have an
abelian complement, and there are eight algebras that have a non-abelian complement
namely; A6,20- A6,27. For each algebra, we give the geodesic equations, a basis for the
symmetry Lie algebra in terms of vector fields. Finally we examine each case and
identify the symmetry Lie algebra.
Rights
© The Author
Is Part Of
VCU University Archives
Is Part Of
VCU Theses and Dissertations
Date of Submission
4-16-2024