TENORIO VILLALÓN , Ángel Francisco

En esta tesis se plantea el problema de determinar a partir de un álgebra de Lie, cuáles son los grupos Lie cuya álgebra de Lie es L. El objetivo fundamental entonces consiste en introducir mecanismos adecuados para hallar un grupo de Lie simplemente conexo asociado a un álgebra de Lie y calcular explícitamente dichos grupos de Lie en álgebras...

We give some considerations about the use of geometric algebras in the context of visibility, showing some advantages and disadvantages for their use as the underlying framework. We emphasize the use of conformal geometric algebra since, among other reasons, it allows us to study easily the visibility for flat varieties and, due to the same...

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The main goal of this paper is to compute the maximal abelian dimension of each solvable nondecomposable Lie algebra of dimension less than 7. To do it, we apply an algorithmic method which goes ruling out non-valid maximal abelian dimensions until obtaining its exact value. Based on Mubarakzyanov and Turkowsky's classical classifications of...

This paper is devoted to study and compare two algebraic algorithms related to the computation of Lie algebras by using statistical techniques. These techniques allow us to decide which of them is more suitable and less costly depending on several variables, like the dimension of the considered algebra.

This paper deals with the maximal abelian dimension of the Lie algebra hn, of nxn upper-triangular matrices. Regarding this, we obtain an algorithm which computes abelian subalgebras of hn as well as its implementation (and a computational study) by using the symbolic computation package MAPLE, where the order n of the matrices in hn is the...

A diferencia de una mera exposici´on de datos puramente biogr´aficos, este art´ıculo pretende dar a conocer a cualquier persona en general, y a los matem´aticos y cient´ıficos en particular, aquellas an´ecdotas menos conocidas, leyendas m´as o menos ajustadas a la realidad, correspondencia enviada y recibida, y sobre todo, opiniones de otras...

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In this paper, we study how two important ideals of a given Lie algebra g (namely, the center Z(g) and the derived Lie algebra D(g)) can be translated into the language of Graph Theory. In this way, we obtain some criteria and characterizations of these ideals using Graph Theory.

In this paper, the maximal abelian dimension is algorithmically and computationally studied for the Lie algebra hn, of n×n upper-triangular matrices. More concretely, we define an algorithm to compute abelian subalgebras of hn besides programming its implementation with the symbolic computation package MAPLE. The algorithm returns a...

A well-known result on Lie Theory states that every finite-dimensional complex solvable Lie algebra can be represented as a matrix Lie algebra, with upper-triangular square matrices as elements. However, this result does not specify which is the minimal order of the matrices involved in such representations. Hence, the main goal of this paper...

In this paper, we analyze the relation between Leibniz algebras and combinatorial structures. More concretely, we study the properties to be satisfied by (pseudo)digraphs so that they are associated with low-dimensional Leibniz algebras. We present some results related to this association and show an algorithmic method to obtain them, which has...

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The set of all abelian subalgebras is computationally obtained for any given finite-dimensional Lie algebra, starting from the nonzero brackets in its law. More concretely, an algorithm is described and implemented to compute a basis for each nontrivial abelian subalgebra with the help of the symbolic computation package MAPLE. Finally, it is...

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The main goal of this paper is to compute a minimal matrix representation for each non-isomorphic nilpotent Lie algebra of dimension less than 6. Indeed, for each of these algebras, we search the natural number n ∈ N \ {1} such that the linear algebra n, formed by all the n × n complex strictly upper-triangular matrices, contains a...

In this paper we obtain simply connected Lie subgroups (up to isomorphism) of the Lie group G4 of upper triangular matrices of order 4 having "1" in its main diagonal. To do it, we determine Lie subalgebras of the Lie algebra g4 associated with G4. We find that there exist 4 simply connected subgroups of G4 for dimension less than 4, 3 for...

The aim of this paper is the study of abelian Lie algebras as subalgebras of the nilpotent Lie algebra gn associated with Lie groups of upper-triangular square matrices whose main diagonal is formed by 1. We also give an obstruction to obtain the abelian Lie algebra of dimension one unit less than the corresponding to gn as a Lie subalgebra of...

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This paper is devoted to show and explain some applications of Lie theory to solve some problems in Economics and Mathematical Finance. So we put forward and discuss mathematical aspects and approaches for several economic problems which have been previously considered in the literature. Besides we also show our advances on this...

The problem of Lie algebras' classification, in their different varieties, has been dealt with by theory researchers since the early 20th century. This problem has an intrinsically infinite nature since it can be inferred from the results obtained that there are features specific to each field and dimension. Despite the hundreds of attempts...

En este artículo se presenta una visión global de lo que se entiende por WebQuest (WQ en lo sucesivo) y se muestra su posible utilización por el profesor de Matemáticas de Secundaria y de Bachillerato para motivar al alumnado en sus clases y despertar en él el interés y el gusto por la asignatura. Se comentan algunas de las escasas WQ...

La ponencia que aquí se presenta persigue un triple objetivo. Por una parte, mostrarle al lector en general, y al profesorado de Secundaria y Bachillerato en particular, el concepto de WebQuest (WQ) y sus principales aplicaciones a la enseñanza como herramienta sencilla y cómoda de utilizar por el alumnado de estos niveles en el estudio de...

Este artículo trata el concepto y la utilización de las WebQuest por parte del profesorado de Matemáticas en los diferentes niveles educativos, haciendo énfasis tanto en Educación Secundaria Obligatoria como en Bachillerato. Más concretamente, se comentan algunas de las escasas WebQuest existentes en Internet y versando sobre la Historia de las...