An algorithm for the classification of 3-dimensional complex Leibniz algebras

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Abstract

We propose an algorithm using Gröbner bases that decides in terms of the existence of a non singular matrix P if two Leibniz algebra structures over a finite dimensional C-vector space are representative of the same isomorphism class. We apply this algorithm in order to obtain a reviewed classification of the 3-dimensional Leibniz algebras given by Ayupov and Omirov. The algorithm has been implemented in a Mathematica notebook. © 2011 Elsevier Inc. All rights reserved.

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Casas, J. M., Insua, M. A., Ladra, M., & Ladra, S. (2012). An algorithm for the classification of 3-dimensional complex Leibniz algebras. Linear Algebra and Its Applications, 436(9), 3747–3756. https://doi.org/10.1016/j.laa.2011.11.039

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