On nilpotency in Leibniz algebras
- arXiv preprint arXiv:1605.08115
Résumé
The main result of this paper is to prove that if a (right) Leibniz algebra L is right nilpotent of degree
n, then L is strongly nilpotent of degree less or equal to 4n2 − 2n + 1. Résumé Nous prouvons
que toute algèbre de Leibniz (droite) L nilpotente à droite d'indice n est fortement nilpotente
d'un indice inférieur ou égal à 4n2 − 2n + 1 … Keywords. Leibniz algebra, right nilpotency, left
nilpotency, nilpotency, strong nilpotency, index. 2010 Mathematics Subject Classification:
17A32, 17B30 … In [1] it is proved that a Malcev algebra is strongly nilpotent if and only if it
is right nilpotent. So for Malcev algebras right nilpotency, left nilpotency and strong nilpotency
are equivalent to nilpotency. Since Malcev algebra is anti-commutative, right nilpotency and
left nilpotency are equivalent. This result fails for Leibniz algebras, see for example [4, Exemple
3.3], which is left nilpotent and not right nilpotent … ∗: bere_jean0@yahoo.fr † …
Mots-clés
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