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The nilpotency of Leibniz algebras with Engel condition

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Abstract

It is proved that a Leibniz algebra over a field of zero characteristic with the Engel condition is nilpotent.

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References

  1. A. M. Blokh, “A Generalization of the Concept of a Lie Algebra,” Dokl. Akad. Nauk SSSR 18(3), 471 (1965) [Sov. Math. Dokl. 6, 1450 (1966)].

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  2. Yu. A. Bakhturin, Identical Relations in Lie Algebras (Nauka, Moscow, 1985; VNU Science Press, b.v., Utrecht, 1987).

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  3. E. I. Zelmanov, “Engel Lie Algebras,” Dokl. Akad. Nauk SSSR 292(2), 265 (1987) [Sov. Math. Dokl. 35, 44 (1987)].

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  4. S. P. Mishchenko and O. I. Cherevatenko, “Necessary and Sufficient Conditions for a Variety of Leibniz Algebras to Have Polynomial Growth,” Fund. i Priklad. Natem. 12(8), 207 (2006) [J. Math. Sci. (N.Y.) 152 (2), 282 (2008)].

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Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Ulyanovsk State University, ul. L. Tolstogo, 43, Ulyanovsk, 432970, Russia

    Yu. Yu. Frolova

Authors
  1. Yu. Yu. Frolova
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Additional information

Original Russian Text © Yu.Yu. Frolova, 2011, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2011, Vol. 66, No. 3, pp. 63–65.

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Frolova, Y.Y. The nilpotency of Leibniz algebras with Engel condition. Moscow Univ. Math. Bull. 66, 136–138 (2011). https://doi.org/10.3103/S0027132211030120

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  • DOI: https://doi.org/10.3103/S0027132211030120

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