**DIPS 6/98**[tex source, PostScript, PDF file, dvi]-
**Title:**ON MULTIPLE GENERALIZATIONS OF LIE ALGEBRAS AND POISSON MANIFOLDS**Authors:**Alexandre VINOGRADOV, Michael VINOGRADOVThe 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.

15 pages, LaTeX-2e (AmSLaTeX 1.2) and Xy-pic 3.3.

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