Contractions and generalized Casimir invariants

Abstract

We prove that if ${\mathfrak{g}}^{\prime }$ is a contraction of a Lie algebra $\mathfrak{g}$ then the number of functionally independent invariants of ${\mathfrak{g}}^{\prime }$ is at least that of $\mathfrak{g}$. This allows to determine explicitly the number of invariants of Lie algebras carrying a supplementary structure, such as linear contact or linear forms whose differential is symplectic.