BENJUMEA ACEVEDO , Juan Carlos

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...

The aim of this paper is to study the interconnectivity among Lie algebras that are characteristically nilpotent, derived and c-graded filiform, establishing some characterization theorems involving them. At the same time we offer an algorithm that will allow us to know, given a complex filiform Lie algebra, which of those properties hold.

The main goal of this poster, which is written in the form of a survey and tries to show some aspects of the research of authors on Lie algebras, is to pay homage to the memory of Pilar Pisón Casares, who was firstly teacher of some of them and later colleague of all of them during different stages of her stay as a member of the Departamento de...