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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