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Zbl 1210.17005
Goze, M.; Goze, N.; Remm, E.
$n$-Lie algebras. (English)
[J] Afr. J. Math. Phys. 8, No. 1, 17-28, Article No. 1002, electronic only (2010).

Summary: The notion of $n$-ary algebras, that is vector spaces with a multiplication concerning $n$-arguments, $n\geq 3$, became fundamental since the works of Nambu. Here we first present general notions concerning $n$-ary algebras and associative $n$-ary algebras. Then we are interested in the notion of $n$-Lie algebras, initiated by Filippov, and which is attached to the Nambu algebras. We study the particular case of nilpotent or filiform $n$-Lie algebras to obtain a beginning of classification. This notion of $n$-Lie algebra admits a natural generalization in strong homotopy $n$-Lie algebras in which the Maurer-Cartan calculus is well adapted.

MSC 2000:: *17A42 Other n-ary compositions
17B60 Lie rings associated with other structures

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	Scientific prize winners of the ICM 2010
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	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

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Zentralblatt MATH Berlin [Germany]