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Classification of p-adic 6-dimensional filiform Leibniz algebras by solutions of x q = a

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Central European Journal of Mathematics

Abstract

We study the p-adic equation x q = a over the field of p-adic numbers. We construct an algorithm which gives a solvability criteria in the case of q = p m and present a computer program to compute the criteria for any fixed value of m ≤ p − 1. Moreover, using this solvability criteria for q = 2; 3; 4; 5; 6, we classify p-adic 6-dimensional filiform Leibniz algebras.

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Authors and Affiliations

  1. Department of Algebra, University of Santiago de Compostela, 15782, Santiago de Compostela, Spain

    Manuel Ladra

  2. Institute of Mathematics, National University of Uzbekistan, Do’rmon yo’li str. 29, Tashkent, 100125, Uzbekistan

    Bakhrom A. Omirov & Utkir A. Rozikov

Authors
  1. Manuel Ladra
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  2. Bakhrom A. Omirov
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  3. Utkir A. Rozikov
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Correspondence to Manuel Ladra.

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Ladra, M., Omirov, B.A. & Rozikov, U.A. Classification of p-adic 6-dimensional filiform Leibniz algebras by solutions of x q = a . centr.eur.j.math. 11, 1083–1093 (2013). https://doi.org/10.2478/s11533-013-0225-9

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  • DOI: https://doi.org/10.2478/s11533-013-0225-9

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