On Casimir operators of conformal Galilei algebras

Abstract

In a previous work (F. Alshammari, P. S. Isaac, and I. Marquette, J. Phys. A: Math. Theor. 51, 065206 (2018)), 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.