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

By José Manuel Casas, Manuel A. Insua, Manuel Ladra, Susana Ladra. 2012

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Abstract We propose an algorithm using Grobner 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.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/bd97448f5fdeb20342b818a3ee2592a1b8a8d51d