Portal de Periódicos da CAPES

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

2016; Wiley; Volume: 39; Issue: 16 Linguagem: Inglês

10.1002/mma.4054

1099-1476

Óscar J. Falcón, Raúl Manuel Falcón Ganfornina, Juan Núñez Valdés,

Polynomial and algebraic computation

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 ≤4. We also prove that every three‐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. Copyright © 2016 John Wiley & Sons, Ltd.