HIGHER-ORDER SIMPLE LIE-ALGEBRAS

It is shown that the non-trivial cocycles on simple Lie algebras may b e used to introduce antisymmetric multibrackets which lead to higher-o rder Lie algebras, the definition of which is given. Their generalised Jacobi identities turn out to be satisfied by the antisymmetric tenso rs (or higher-order ''structure constants'') which characterise the Li e algebra cocycles. This analysis allows us to present a classificatio n of the higher-order simple Lie algebras as well as a constructive pr ocedure for them. Our results are synthesised by the introduction of a single, complete BRST operator associated with each simple algebra.