On Casimir Operators of Conformal Galilei Algebras

TL;DR

This paper extends an existing algorithm to compute polynomial Casimir operators for finite-dimensional conformal Galilei algebras with central extension, emphasizing the role of algebra anti-automorphisms through key examples.

Contribution

It applies a differential operator-based algorithm to new classes of conformal Galilei algebras, demonstrating its effectiveness and highlighting the importance of algebra anti-automorphisms.

Findings

Successfully computed Casimir operators for several conformal Galilei algebras

Demonstrated the utility of algebra anti-automorphisms in the process

Provided detailed examples illustrating the algorithm's application

Abstract

In previous work, we introduced an algorithm that utilises differential operator realisations to find polynomial Casimir operators of Lie algebras. In this article we build on this work by applying the algorithm to several classes of finite dimensional conformal Galilei algebras with central extension. In these cases we highlight the utility of an algebra anti-automorphism, and give relevant details through key examples.