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

J.M. Casas
M.A. Insua
M. Ladra
S. Ladra
Journal / Anthology

Linear Algebra and its Applications
Year: 2012
Volume: 436
Issue: 9
Page range: 3747-3756

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.