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On the existence of ad-nilpotent elements

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Abstract

In this paper, we give a sufficient condition to guarantee the nilpotency of a derivation or an anti-derivation of a Leibniz algebra. This result is used to obtain an elementary proof of the statement that a finite dimensional Leibniz algebra over an algebraically closed field of arbitrary characteristic not 2, necessarily contains a nontrivial ad-nilpotent element and a nontrivial ad-nilpotent element.

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Authors and Affiliations

  1. Laboratory T.N. AGATA, Department of Mathematics and Computer Science, University of Ouagadougou Burkina Faso, 03 B.P. 7021, Ouagadougou 03, Burkina Faso

    Côme J. A. Béré, M. Françoise Ouedraogo & Nakelgbamba B. Pilabré

Authors
  1. Côme J. A. Béré
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  2. M. Françoise Ouedraogo
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  3. Nakelgbamba B. Pilabré
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Corresponding author

Correspondence to Côme J. A. Béré.

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Thank you to Emmanuel Sana.

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Béré, C.J.A., Ouedraogo, M.F. & Pilabré, N.B. On the existence of ad-nilpotent elements. Afr. Mat. 26, 813–823 (2015). https://doi.org/10.1007/s13370-014-0246-y

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  • DOI: https://doi.org/10.1007/s13370-014-0246-y

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