Geodesic
Pre-derivations and description of non-strongly nilpotent filiform Leibniz algebras
Communications in Mathematics, Tome 29 (2021) no. 2, pp. 187-213

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In this paper we give the description of some non-strongly nilpotent Leibniz algebras. We pay our attention to the subclass of nilpotent Leibniz algebras, which is called filiform. Note that the set of filiform Leibniz algebras of fixed dimension can be decomposed into three disjoint families. We describe the pre-derivations of filiform Leibniz algebras for the first and second families and determine those algebras in the first two classes of filiform Leibniz algebras that are non-strongly nilpotent.
Classification : 17A32, 17A36, 17B30
Keywords: Lie algebra; Leibniz algebra; derivation; pre-derivation; nilpotency; characteristically nilpotent algebra; strongly nilpotent algebra 
@article{COMIM_2021__29_2_a3,
     author = {Abdurasulov, K.K. and Khudoyberdiyev, A.Kh. and Ladra, M. and Sattarov, A.M.},
     title = {Pre-derivations and description of non-strongly nilpotent filiform {Leibniz} algebras},
     journal = {Communications in Mathematics},
     pages = {187--213},
     publisher = {mathdoc},
     volume = {29},
     number = {2},
     year = {2021},
     mrnumber = {4285751},
     zbl = {07426418},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/COMIM_2021__29_2_a3/}
}
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Abdurasulov, K.K.; Khudoyberdiyev, A.Kh.; Ladra, M.; Sattarov, A.M. Pre-derivations and description of non-strongly nilpotent filiform Leibniz algebras. Communications in Mathematics, Tome 29 (2021) no. 2, pp. 187-213. http://geodesic.mathdoc.fr/item/COMIM_2021__29_2_a3/