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# A computational algebraic geometry approach to enumerate Malcev magma algebras over finite fields

A computational algebraic geometry approach to enumerate Malcev magma algebras over finite fields
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 Author: Falcón Ganfornina, Óscar Jesús Falcón Ganfornina, Raúl Manuel Núñez Valdés, Juan Department: Universidad de Sevilla. Departamento de Geometría y TopologíaUniversidad de Sevilla. Departamento de Matemática Aplicada I (ETSII) Date: 2016 Published in: Mathematical Methods in the Applied Sciences, 39 (16), 4901-4913. Document type: Article Abstract: The set of n-dimensional Malcev magma algebras over a finite field can be identified with algebraic sets defined by zero-dimensional radical ideals for which the computation of their reduced Gröbner bases makes feasible their enumeration and distribution into isomorphism and isotopism classes. Based on this computation and the classification of Lie algebras over finite fields given by De Graaf and Strade, we determine the mentioned distribution for Malcev magma algebras of dimension $n\leq 4$. We also prove that every 3-dimensional Malcev algebra is isotopic to a Lie magma algebra. For n=4, this assertion only holds when the characteristic of the base field is distinct of two. Cite: Falcón Ganfornina, Ó.J., Falcón Ganfornina, R.M. y Núñez Valdés, J. (2016). A computational algebraic geometry approach to enumerate Malcev magma algebras over finite fields. Mathematical Methods in the Applied Sciences, 39 (16), 4901-4913.
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DOI: 10.1002/mma.4054

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