This article is concerned with classifying seven dimensional Lie algebras that have a four-
dimensional nilradical. It is shown that any such indecomposable algebra necessarily has …

Abstract We discuss Lagrangian and Hamiltonian field theories that are invariant under a
symmetry group. We apply the polysymplectic reduction theorem for both types of field …

This paper studies the canonical symmetric connection∇ associated to any Lie group G.
The salient properties of∇ are stated and proved. The Lie symmetries of the geodesic …

We discuss two generalizations of the inverse problem of the calculus of variations, one in
which a given mechanical system can be brought into the form of Lagrangian equations with …

We discuss the problem of the existence of a regular invariant Lagrangian for a given system
of invariant second-order differential equations on a Lie group $ G $, using approaches …

We study the tangent TG and cotangent bundles T* G of a Lie group G which are also Lie
groups. Our main results are to show that on TG the canonical Jacobi endomorphism field S …

The inverse problem in the calculus of variations for a given set of second-order ordinary
differential equations consists of deciding whether their solutions are those of Euler …

In this investigation, we present symmetry algebras of the canonical geodesic equations of
the indecomposable solvable Lie groups of dimension five, confined to algebras A 5, 7 abc …

We recall the notion of Jacobi fields, as it was extended to systems of second-order ordinary
differential equations. Two points along a base integral curve are conjugate if there exists a …

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 …