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Ponencia
Combinatorial structures of three vertices and Lie algebras
(Computational and Mathematical Methods in Science and Engineering, 2011)
In this paper, we characterize digraphs of 3 vertices associated with Lie algebras according to isomorphism classes of these associated Lie algebras. At this respect, we introduce and implement two algorithmic methods: the ...
Tesis Doctoral
Abelian subalgebras and ideals of maximal dimension in Lie algebras
(2012-03-27)
En esta tesis se han estudiado subálgebras e ideales abelianos de álgebras de Lie, considerando dos invariantes, llamados alfa y beta, que representan el máximo entre la dimensión de todas las subálgebras abelianas (ideales ...
Artículo
Minimal faithful upper-triangular matrix representations for solvable Lie algebras
(Elsevier, 2017-07)
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 ...
Artículo
Relations between combinatorial structures and Lie algebras: centers and derived Lie algebras
(Springer, 2015-04)
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 ...
Artículo
Computing abelian subalgebras for linear algebras of upper-triangular matrices from an algorithmic perspective
(Ovidius University, 2016)
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 ...
Ponencia
Ponencia
Obtaining combinatorial structures associated with low-dimensional Leibniz algebras
(2013)
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 ...
Artículo
The computation of Abelian subalgebras in low-dimensional solvable Lie algebras
(World Scientific and Engineering Academy and Society (WSEAS), 2010-01)
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 ...
Ponencia
Computational method for obtaining filiform Lie algebras of arbitrary dimension
(WSEAS Press, 2011-09)
This paper shows a new computational method to obtain filiform Lie algebras, which is based on the relation between some known invariants of these algebras and the maximal dimension of their abelian ideals. Using this ...