Juan Núñez Valdés

Isomorphism and Isotopism Classes of Filiform Lie Algebras of Dimension up to Seven Over Finite Fields

This paper deals with a new series of isotopism invariants that enable us to determine explicitly the distribution of n-dimensional filiform Lie algebras into isomorphism and isotopism classes. For

Computing abelian subalgebras for linear algebras of upper-triangular matrices from an algorithmic perspective

n\le 6

An Obstruction to Represent Abelian Lie Algebras by Unipotent Matrices

n≤6, this distribution is explicitly obtained over any field. For

A particular case of extended isotopisms: Santilli's isotopisms

n=7

Las Álgebras de Lie Filiformes Complejas según sean o no derivadas de otras

n=7, this is determined over algebraically closed fields and over finite fields.

Computing the sets of totally symmetric and totally conjugate orthogonal partial Latin squares by means of a SAT solver

Abstract This paper tries to develop a recent research which consists in using Discrete Mathematics as a tool in the study of the problem of the classification of Lie algebras in general, dealing in this case with filiform Lie algebras up to dimension 7 over finite fields. The idea lies in the representation of each Lie algebra by a certain type of graphs. Then, some properties on Graph Theory make easier to classify the algebras. As main results, we find out that there exist, up to isomorphism, six, five and five 6-dimensional filiform Lie algebras and fifteen, eleven and fifteen 7-dimensional ones, respectively, over ℤ/pℤ, for p = 2, 3, 5. In any case, the main interest of the paper is not the computations itself but both to provide new strategies to find out properties of Lie algebras and to exemplify a suitable technique to be used in classifications for larger dimensions.