Computational method for obtaining filiform Lie algebras of arbitrary dimension

This paper shows a new computational method to obtain filiform Lie algebras, which is based on the relation between some known invariants of these algebras and the maximal dimension of their abelian ideals. Using this relation, the law of each of these algebras can be completely determined and characterized by means of the triple consisting of its dimension and the invariants z1 and z2. As examples of application, we have included a table showing all valid triples determining filiform Lie algebras for dimension 13

A particular type of non-associative algebras and graph theory

Evolution algebras have many connections with other mathematical fields, like group theory, stochastics processes, dynamical systems and other related ones. The main goal of this paper is to introduce a novel non-usual research on Discrete Mathematics regarding the use of graphs to solve some open problems related to the theory of graphicable algebras, which constitute a subset of those algebras. We show as many our advances in this field as other non solved problems to be tackled in future

Low-dimensional filiform Lie algebras over finite fields

In this paper we use some objects of Graph Theory to classify low-dimensional filiform Lie algebras 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 results, which can be applied in several branches of Physics or Engineering, for instance, we find out that there exist, up to isomorphism, six 6-dimensional filiform Lie algebras over Z/pZ, for p = 2, 3, 5.Plan Andaluz de Investigación (Junta de Andalucía