%0 Journal Article 
%A Fernández Ouaridi, Amir
%T Métodos de clasificación de álgebras con anulador no nulo
%D 2020
%U http://hdl.handle.net/10498/24274
%X The classification of algebras is an important and an interesting problem in
Modern Algebra. There are algebraic classifications, geometric classifications,
degeneration level classifications and some other. In this essay, we
focus on the algebraic classification, that is, on the problem of finding all the algebras
module isomorphisms of a certain dimension. Specifically, in the classification of
algebras with non null annihilator. To this end, we make use of one type of algebra
extensions: the so-called annihilator extensions.
This concept has been studied in depth in Theory of Lie Algebras, due to its numerous
applications, especially outstanding in Physics. Due to this remarkable interest,
the study of annihilator extensions of Lie algebras has a long history. However, the
use of this notion to classify algebraically different classes of algebras is relatively
recent, and that’s the center of our study.
As a result of our research, we obtain a procedure to algebraically classify all
algebras, of a certain class defined by polynomial identities, of dimension n with a mdimensional
annihilator, using the classification of algebras of dimensión n-m. In addition,
we apply this procedure in different specific cases, obtaining the classification
of the n-dimensional algebras with (n - 2)-dimensional annihilator, the classification
of the n-dimensional anticommutative algebras with (n - 3)-dimensional annihilator
and the classification of the n-dimensional non-malcev binary-Lie algebras with
(n - 4)-dimensional annihilator.
%K álgebra
%K anulador
%K clasificación algebraica
%K álgebra de Lie
%K álgebra de Malcev
%~ Universidad de Cádiz