An alternative interpretation of the Beltrametti–Blasi formula by means of differential forms

Abstract

The Beltrametti–Blasi formula that gives the number N(g) of functional independent invariants for the coadjoint representation of a finite dimensional Lie algebra g admits a natural reformulation by means of the Maurer–Cartan equations associated to the algebra. This functional approach toN(g) turns out to be more convenient than the traditional matrix methods,and allows to obtain bounds of N(g) using only exterior products of the Maurer–Cartan equations of g, as well as to estimate the number of missing label operators. Applications to the problem of missing label operators, to the number of invariants of various inhomogeneous Lie algebras and contractions of Lie algebras are given.