## n-Lie algebras

Goze, Michel
Goze, Nicolas
Remm, Elisabeth
##### Description
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 will be 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.
Comment: To appear in Journal Africain de Physique Mathematique
##### Keywords
Mathematics - Rings and Algebras, Mathematical Physics, 17A42, 58F05, 70H05