Realizations of Galilei algebras

TL;DR

This paper systematically constructs all inequivalent realizations of low-dimensional Galilei algebras, explores their deformations, and links them to invariant equations, advancing understanding of their algebraic structures and physical applications.

Contribution

It provides a comprehensive classification of realizations and deformations of Galilei algebras up to dimension five, including explicit forms and physical relevance.

Findings

All inequivalent realizations of Galilei algebras up to dimension five are constructed.

Families of one-parametric deformations of Galilei algebras are explicitly presented.

Several well-known physical equations are shown to be invariant under these algebras or their deformations.

Abstract

All inequivalent realizations of the Galilei algebras of dimensions not greater than five are constructed using the algebraic approach proposed by I. Shirokov. The varieties of the deformed Galilei algebras are discussed and families of one-parametric deformations are presented in explicit form. It is also shown that a number of well-known and physically interesting equations and systems are invariant with respect to the considered Galilei algebras or their deformations.