ECHARTE REULA , Francisco Javier

In this paper we describe some families of filiform Lie algebras by giving a method which allows to obtain them in any arbitrary dimension n starting from the triple (p, q, m), where m = n and p and q are, respectively, invariants z1 and z2 of those algebras. After obtaining the general law of complex filiform Lie algebras corresponding to...

In this paper, we characterize those Complex Filiform Lie Algeoras of dimension 0 which are derived from other Solvable Lie ALgebras of higher dimensions. This result and the previous one given in ({0]) allow us to lind a complete list of Characteristically Nilpotent Filiform Lie Algebras of dimension 0.

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In this paper we use cohomology of Lie algebras to study the variety of laws associated with filiform Lie algebras of a given dimension. As the main result, we describe a constructive way to find a small set of polynomials which define this variety. It allows to improve previous results related with the cardinal of this set. We have also...

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.