RT doctoral thesis
T1 Métodos de clasificación de álgebras con anulador no nulo
A1 Fernández Ouaridi, Amir
A2 Matemáticas
K1 álgebra
K1 anulador
K1 clasificación algebraica
K1 álgebra de Lie
K1 álgebra de Malcev
AB The classification of algebras is an important and an interesting problem inModern Algebra. There are algebraic classifications, geometric classifications,degeneration level classifications and some other. In this essay, wefocus on the algebraic classification, that is, on the problem of finding all the algebrasmodule isomorphisms of a certain dimension. Specifically, in the classification ofalgebras with non null annihilator. To this end, we make use of one type of algebraextensions: the so-called annihilator extensions.This concept has been studied in depth in Theory of Lie Algebras, due to its numerousapplications, especially outstanding in Physics. Due to this remarkable interest,the study of annihilator extensions of Lie algebras has a long history. However, theuse of this notion to classify algebraically different classes of algebras is relativelyrecent, and that’s the center of our study.As a result of our research, we obtain a procedure to algebraically classify allalgebras, of a certain class defined by polynomial identities, of dimension n with a mdimensionalannihilator, using the classification of algebras of dimensión n-m. In addition,we apply this procedure in different specific cases, obtaining the classificationof the n-dimensional algebras with (n - 2)-dimensional annihilator, the classificationof the n-dimensional anticommutative algebras with (n - 3)-dimensional annihilatorand the classification of the n-dimensional non-malcev binary-Lie algebras with(n - 4)-dimensional annihilator.
YR 2020
FD 2020-11-06
LK http://hdl.handle.net/10498/24274
UL http://hdl.handle.net/10498/24274
LA spa
DS Repositorio Institucional de la Universidad de Cádiz
RD 10-may-2026