Geodesic
$n$-Ary Mal'tsev Algebras
Algebra i logika, Tome 40 (2001) no. 3, pp. 309-329

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By analogy with $n$-Lie algebras, which are a natural generalization of Lie algebras to the case of $n$-ary multiplication, we define the concept of an $n$-ary Mal'tsev algerba. It is shown that exceptional algebras of a vector cross product are ternary central simple Mal'tsev algebras, which are not 3-Lie algebras if the characteristic of a ground field is distinct from 2 and 3. The basic result is that every $n$-ary algebra of the vector cross product is an $n$-ary central simple Mal'tsev algebra.
Keywords: $n$-ary Mal'tsev algebra. 
@article{AL_2001_40_3_a4,
     author = {A. P. Pozhidaev},
     title = {$n${-Ary} {Mal'tsev} {Algebras}},
     journal = {Algebra i logika},
     pages = {309--329},
     publisher = {mathdoc},
     volume = {40},
     number = {3},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2001_40_3_a4/}
}
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A. P. Pozhidaev. $n$-Ary Mal'tsev Algebras. Algebra i logika, Tome 40 (2001) no. 3, pp. 309-329. http://geodesic.mathdoc.fr/item/AL_2001_40_3_a4/