Reduction (by stages) in the whole Lagrange Poincare category

TL;DR

This paper completes the reduction scheme in the entire Lagrange Poincare category, affirming that reduction can be performed in this broad setting and exploring related geometric and theoretical aspects.

Contribution

It extends the Lagrangian reduction by stages to the full LP category and analyzes its connections with Hamiltonian reduction and Noether's theorem.

Findings

Reduction can be performed in the entire LP category.

Established relationships between LP reduction and Hamiltonian reduction.

Analyzed geometric aspects of the LP category and Noether theorem.

Abstract

We complete the reduction scheme in the whole LP category, introduced in [7] to perform Lagrangian reduction by stages. We answer affirmatively the open question of whether reduction can be done in the whole category and analyze the Noether theorem on LP-bundles, the relationship with Hamiltonian reduction by stages and the geometric aspects of the definition of this category.