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Omirov, B. A.

On the derivations of filiform Leibniz algebras. (English) Zbl 1130.17001

Math. Notes 77, No. 5, 677-685 (2005); translation from Mat. Zametki 77, No. 5, 733-742 (2005).
Summary: 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.

Cited in 1 Review
Cited in 14 Documents

MSC:

17A32 Leibniz algebras
17A36 Automorphisms, derivations, other operators (nonassociative rings and algebras)

Keywords:

graded Leibniz algebra; filiform algebra; characteristically nilpotent algebra; derivation; Lie algebra
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References:

[1] N. Jacobson, ”A note on automorphisms and derivations of Lie algebras,” Proc. Amer. Math. Soc., 6 (1955), 281–283. · Zbl 0064.27002 · doi:10.1090/S0002-9939-1955-0068532-9
[2] J. Dixmier and W. G. Lister, ”Derivations of nilpotent Lie algebras,” Proc. Amer. Math. Soc., 8 (1957), 155–158. · Zbl 0079.04802 · doi:10.1090/S0002-9939-1957-0083101-4
[3] You. B. Hakimjanov (Khakimdzhanov), ”Variete des lois d’algebres de Lie nilpotentes,” Geometrie Dedicata, 40 (1991), no. 3, 269–295.
[4] M. Goze and Yu. Khakimdjanov (Khakimdzhanov), Nilpotent Lie Algebras, Mathematics and its Applications, vol. 361, Kluwer, Dordrecht, 1996. · Zbl 0932.17011
[5] Sh. A. Ayupov and B. A. Omirov, ”On some classes of nilpotent Leibniz algebras,” Sibirsk. Mat. Zh. [Siberian Math. J.], 42 (2001), no. 1, 18–29. · Zbl 1017.17002
[6] J.-L. Loday and T. Pirashvili, ”Universal enveloping algebras of Leibniz algebras and (co)homology,” Math. Ann., 296 (1993), no. 1, 139–158. · Zbl 0821.17022 · doi:10.1007/BF01445099
[7] Yu. B. Khakimdzhanov, ”Characteristically nilpotent Lie algebras,” Mat. Sb. [Math. USSR-Sb.], 181 (1990), no. 5, 642–655. · Zbl 0716.17008
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