On n-ary Lie algebras of type (r, l)

Abstract

These notes are devoted to the multiple generalization of a Lie algebra introduced by A.M. Vinogradov and M.M. Vinogradov. We compare definitions of such algebras in the usual and invariant case. Furthermore, we show that there are no simple n-ary Lie algebras of type (n - 1, l) for l > 0.