Mathematica Eterna
Open Access

Abstract

Symmetry algebras of the canonical Lie group geodesic equations in dimension three

Ryad Ghanam and Gerard Thompson

For each of the two and three-dimensional indecomposable Lie algebras the geodesic equations of the associated canonical Lie group connection are given. In each case a basis for the associated Lie algebra of symmetries is constructed and the corresponding Lie brackets are written down.