On Casimir Operators of Conformal Galilei Algebras

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.

18 pages

References in corpus (12)

• The BMS/GCA correspondence
• Non-relativistic conformal symmetries and Newton-Cartan structures
• Acceleration-Extended Galilean Symmetries with Central Charges and their Dynamical Realizations
• (2+1)D Exotic Newton-Hooke Symmetry, Duality and Projective Phase
• Remarks on l-conformal extension of the Newton-Hooke algebra
• Kinematical Lie algebras via deformation theory
• Galilean Conformal Algebra in Two Dimensions and Cosmological Topologically Massive Gravity
• On dynamical realizations of l-conformal Galilei and Newton-Hooke algebras
• Kinematical Lie algebras in 2+1 dimensions
• Virtual copies of semisimple Lie algebras in enveloping algebras of semidirect products and Casimir operators
• Coset spaces and Einstein manifolds with l-conformal Galilei symmetry
• Possible Central Extensions of Non-Relativistic Conformal Algebras in 1+1

Cited by in corpus (5)

• Lie algebra modules which are locally finite over the semi-simple part
• Casimir operators of centrally extended l-conformal Galilei algebra
• Generalized conformal pseudo-Galilean algebras and their Casimir operators
• The Lie algebra of the lowest transitively differential group of degree three
• ${\mathfrak{sl}}_2$-Harish-Chandra modules for ${\mathfrak{sl}}_2⋉L(4)$