Authors: Alexandre VINOGRADOV, Michael VINOGRADOV

The notion of $(n,k,r)$-Lie algebra ($n>k\ge r\ge 0$), an $n$-ary generalization of that of Lie algebra, is introduced and studied. The standard Lie algebras turn out to be $(2,1,0)$-Lie algebras. Two types of $n$-ary Lie structures studied in recent few years in the context of the Nambu and ``non-Nambu'' generalizations of dynamics correspond to $(n,n-1,0)$- and $(n,1,0)$- Lie algebras, respectively.

To appear in Proceedings of Conference on "Secondary Calculus and Cohomological Physics", Contemporary Mathematics, vol. 219, 1998.

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