Geodesic
On the Derivations of Filiform Leibniz Algebras
Matematičeskie zametki, Tome 77 (2005) no. 5, pp. 733-742 
B. A. Omirov. On the Derivations of Filiform Leibniz Algebras. Matematičeskie zametki, Tome 77 (2005) no. 5, pp. 733-742. http://geodesic.mathdoc.fr/item/MZM_2005_77_5_a7/
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     title = {On the {Derivations} of {Filiform} {Leibniz} {Algebras}},
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Voir la notice de l'article provenant de la source Math-Net.Ru

The algebras of derivations of naturally graded Leibniz algebras are described. The existence of characteristically nilpotent Leibniz algebras in any dimension greater than 4 is proved.

[1] Jacobson N., “A note on automorphisms and derivations of Lie algebras”, Proc. Amer. Math. Soc., 6 (1955), 281–283 | DOI | MR | Zbl

[2] Dixmier J., Lister W. G., “Derivations of nilpotent Lie algebras”, Proc. Amer. Math. Soc., 8 (1957), 155–158 | DOI | Zbl

[3] Khakimjanov Yu., “Variété des lois d'algébres de Lie nilpotentes”, Geometrie Dedicata, 40 (1991), 269–295

[4] Goze M., Khakimdjanov Yu., Nilpotent Lie Algebras, Mathematics and its Applications, 361, Kluwer, Dordrecht, 1996 | Zbl

[5] Ayupov Sh. A., Omirov B. A., “O nekotorykh klassakh nilpotentnykh algebr Leibnitsa”, Sib. matem. zh., 42:1 (2001), 18–29

[6] Loday J.-L., Pirashvili T., “Universal enveloping algebras of Leibniz algebras and (co)homology”, Math. Ann., 296 (1993), 139–158 | DOI

[7] Khakimdzhanov Yu. B., “Kharakteristicheskie nilpotentnye algebry Li”, Matem. sb., 181:5 (1990), 642–655