Symmetries of the Canonical Geodesic Equations of Five-Dimensional Nilpotent Lie Algebras

Hassan Almusawa, Ryad Ghanam

Abstract

Symmetries of the canonical geodesic equations of indecomposable nilpotent Lie groups of dimension five are constructed. For each case, the associated system of geodesics is provided. In addition, a basis for the associated Lie algebra of symmetries as well as the corresponding non-zero Lie brackets are listed and classified.