  We introduce higher-order (or multibracket) simple Lie algebras that
generalize the ordinary Lie algebras. Their `structure constants' are given by
Lie algebra cohomology cocycles which, by virtue of being such, satisfy a
suitable generalization of the Jacobi identity. Finally, we introduce a
nilpotent, complete BRST operator associated with the l multibracket algebras
which are based on a given simple Lie algebra of rank l.
