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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
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
Artículo
An algorithm to compute abelian subalgebras in linear algebras of upper-triangular matrices
(American Institute of Physics, 2009)
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 ...
Artículo
Computational algorithm for obtaining Abelian subalgebras in Lie algebras
(World Academy of Science, Engineering and Technology, 2009)
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 ...
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 ...