Skip to main content
Log in

On Some Zero-Filiform Algebras

  • Published:
Ukrainian Mathematical Journal Aims and scope

We present the description of algebras with the maximum nilpotency index given by certain special identities.

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.

Institutional subscriptions

Similar content being viewed by others

References

  1. Sh. A. Ayupov and B. A. Omirov, “Some classes of nilpotent Leibniz algebras,” Sib. Mat. Zh., 42, 18–29 (2001).

    Article  MATH  MathSciNet  Google Scholar 

  2. B. A. Omirov, “Classification of two-dimensional complex Zinbiel algebras,” Uzb. Mat. Zh., No. 2, 55–59 (2002).

  3. J. Q. Adashev, B. A. Omirov, and A. Kh. Khudoyberdiyev, “Classifications of some classes of Zinbiel algebras,” J. Gen. Lie Theory Appl., 3(4), 1–10 (2010).

    Article  MathSciNet  Google Scholar 

  4. Sh. A. Ayupov and B. A. Omirov, “On Leibniz algebras,” in: Proc. of the Colloquium “Algebra and Operators Theory” (Tashkent, 1997), Kluwer, Dordrecht (1998), pp. 1–13.

  5. L. M. Camacho, J. R. Gómez, A. J. González, and B. A. Omirov, “Naturally graded quasifiliform Leibniz algebras,” J. Symbol. Comput., 44, No. 5, 527–539 (2009).

    Article  MATH  Google Scholar 

  6. A. S. Dzhumadil’daev and K. M. Tulenbaev, “Nilpotency of Zinbiel algebras,” J. Dynam. Control Syst., 11, No. 2, 195–213 (2005).

    Article  MATH  MathSciNet  Google Scholar 

  7. J.-L. Loday, “Une version non commutative des algebres de Lie: les algebres de Leibniz,” Enseign. Math., 39, 269–293 (1993).

    MATH  MathSciNet  Google Scholar 

  8. J.-L. Loday, A. Frabetti, and F. Goichot, Dialgebras and Related Operads, Springer, Berlin (2001).

    MATH  Google Scholar 

  9. B. A. Omirov, “Conjugacy of Cartan subalgebras of complex finite-dimensional Leibniz algebras,” J. Algebra, 302, 887–896 (2006).

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 66, No. 4, pp. 482–492, April, 2014.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Masutova, K.K., Omirov, B.A. On Some Zero-Filiform Algebras. Ukr Math J 66, 541–552 (2014). https://doi.org/10.1007/s11253-014-0951-6

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11253-014-0951-6

Keywords

Navigation