A new matrix method for the Casimir operators of the Lie algebras and

Abstract

A method is given to determine the Casimir operators of the perfect Lie algebras and the inhomogeneous Lie algebras in terms of polynomials associated with a parametrized (2N + 1) × (2N + 1)-matrix. For the inhomogeneous symplectic algebras this matrix is shown to be associated to a faithful representation. We further analyse the invariants for the extended Schrodinger algebra in (N + 1) dimensions, which arises naturally as a subalgebra of . The method is extended to other classes of Lie algebras, and some applications to the missing label problem are given.