Bi-invariant differential operators on the Galilean group

TL;DR

This paper investigates the algebraic structure of the Galilean group's symmetries, identifying generators for the center of its universal enveloping algebra through coadjoint orbits, advancing understanding of Newtonian mechanics symmetries.

Contribution

It introduces a method to find algebraically independent generators for the center of the universal enveloping algebra of the Galilean Lie algebra using coadjoint orbit techniques.

Findings

Identified algebraically independent generators for the center.

Applied coadjoint orbit method to the Galilean group.

Enhanced understanding of symmetries in Newtonian mechanics.

Abstract

The Galilean group is the group of symmetries of Newtonian mechanics, with Lie a lgebra $\gal(n)$. We find algebraically independent generators for the center of the universal enveloping algebra of $\gal(n)$ using coadjoint orbits.