arXiv subjects

O. J. Falcón

Publications and source records attributed to O. J. Falcón.

3 recordsLinked to original sources

arXiv2016

Classification of asexual diploid organisms by means of strongly isotopic evolution algebras defined over any field

Evolution algebras were introduced into Genetics to deal with the mechanism of inheritance of asexual organisms. Their distribution into isotopism classes is uniquely related with the mutation of alleles in non-Mendelian Genetics. This paper deals with such a distribution by means of Computational Algebraic Geometry. We focus in particular on the two-dimensional case, which is related to the asexual reproduction processes of diploid organisms. Specifically, we determine the existence of four isotopism classes, whatever the base field is, and we characterize the corresponding isomorphism classes.

math.RA↗

arXiv2016

Computation of isotopisms of algebras over finite fields by means of graph invariants

In this paper we define a pair of faithful functors that map isomorphic and isotopic finite-dimensional algebras over finite fields to isomorphic graphs. These functors reduce the cost of computation that is usually required to determine whether two algebras are isomorphic. In order to illustrate their efficiency, we determine explicitly the classification of two- and three-dimensional partial quasigroup rings.

math.RA↗

arXiv2015

Isomorphism and isotopism classes of filiform Lie algebras of dimension up to seven

Since the introduction of the concept of isotopism of algebras by Albert in 1942, a prolific literature on the subject has been developed for distinct types of algebras. Nevertheless, there barely exists any result on the problem of distributing Lie algebras into isotopism classes. The current paper is a first step to deal with such a problem. Specifically, we define a new series of isotopism invariants and we determine explicitly the distribution into isotopism classes of $n$-dimensional filiform Lie algebras, for $n\leq 7$. We also deal with the distribution of such algebras into isomorphism classes, for which we confirm some known results and we prove that there exist $p+8$ isomorphism classes of seven-dimensional filiform Lie algebras over the finite field $\mathbb{F}_p$ if $p\neq 2$.

math.RA↗