Skip to main content
Log in

On the Derivations of Filiform Leibniz Algebras

  • Published:
Mathematical Notes Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

REFERENCES

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

    Google Scholar 

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

    Google Scholar 

  3. You. B. Hakimjanov (Khakimdzhanov), “Variete des lois d’algebres de Lie nilpotentes,” Geometrie Dedicata, 40 (1991), no. 3, 269–295.

    Google Scholar 

  4. M. Goze and Yu. Khakimdjanov (Khakimdzhanov), Nilpotent Lie Algebras, Mathematics and its Applications, vol. 361, Kluwer, Dordrecht, 1996.

    Google Scholar 

  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.

    Google Scholar 

  6. J.-L. Loday and T. Pirashvili, “Universal enveloping algebras of Leibniz algebras and (co)homology,” Math. Ann., 296 (1993), no. 1, 139–158.

    Article  Google Scholar 

  7. Yu. B. Khakimdzhanov, “Characteristically nilpotent Lie algebras,” Mat. Sb. [Math. USSR-Sb.], 181 (1990), no. 5, 642–655.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

__________

Translated from Matematicheskie Zametki, vol. 77, no. 5, 2005, pp. 733–742.

Original Russian Text Copyright ©2005 by B. A. Omirov.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Omirov, B.A. On the Derivations of Filiform Leibniz Algebras. Math Notes 77, 677–685 (2005). https://doi.org/10.1007/s11006-005-0068-1

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11006-005-0068-1

Key words

Navigation