Galilean Isometries

TL;DR

This paper introduces three nested Lie algebras of infinitesimal isometries in Galilei space-time, analogous to Killing vector fields in relativity, and explores their extensions via Newton-Cartan-Bargmann automorphisms.

Contribution

It defines new Lie algebras of Galilean isometries and connects them to Newton-Cartan-Bargmann automorphisms, expanding the understanding of symmetries in non-relativistic space-times.

Findings

Defined three nested Lie algebras of Galilean isometries

Identified natural extensions from Newton-Cartan-Bargmann automorphisms

Established analogy with relativistic Killing vector fields

Abstract

We introduce three nested Lie algebras of infinitesimal `isometries' of a Galilei space-time structure which play the r\^ole of the algebra of Killing vector fields of a relativistic Lorentz space-time. Non trivial extensions of these Lie algebras arise naturally from the consideration of Newton-Cartan-Bargmann automorphisms.