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Artículo
An obstruction to represent abelian lie algebras by unipotent matrices
(2004)
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 ...
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Simply connected lie subgroups of the unipotent Lie group of order 4
(Soochow University, Department of Mathematics, 2006-04)
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 ...
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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 ...
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Artículo
Application of statistical techniques for comparing Lie algebra algorithms
(International Center for Scientific Research and Studies Publication, 2012-03)
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 ...
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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 ...
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A historical review of the classifications of Lie algebras
(Unión Matemática Argentina, 2013)
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 ...
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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 ...