Higher-order simple Lie algebras

It is shown that the non-trivial cocycles on simple Lie algebras may be used to introduce antisymmetric multibrackets which lead to higher-order Lie algebras, the definition of which is given. Their generalized Jacobi identities turn out to be satisfied by the antisymmetric tensors (or higher-order `structure constants') which characterize the Lie algebra cocycles. This analysis allows us to present a classification of the higher-order simple Lie algebras and to synthesize our results by introducing a single, complete BRST operator associated with each simple algebra