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As it is well-known there exist matrix representations of any given finite-dimensional complex Lie algebra. More concretely, such representations can be obtained by means of an isomorphic matrix Li...

In this paper, we show an algorithmic procedure to compute abelian subalgebras and ideals of a given finite-dimensional Leibniz algebra, starting from the non-zero brackets in its law. In order to implement this method, the symbolic computation package MAPLE 12 is used. Moreover, we also show a brief computational study considering both the computing time and the memory used in the two main routines of the implementation. Finally, we determine the maximal dimension of abelian subalgebras and ideals for 3-dimensional Leibniz algebras and 4-dimensional solvable ones over .

This paper deals with several operations on graphs and combinatorial structures linking them with their associated Lie algebras. More concretely, our main goal is to obtain some criteria to determine when there exists a Lie algebra associated with a combinatorial structure arising from those operations. Additionally, we show an algorithmic method for one of those operations.

This paper shows a characterization of digraphs of three vertices associated with Lie algebras, as well as determining the list of isomorphism classes for Lie algebras associated with these digraphs. Additionally, we introduce and implement two algorithmic procedures related to this study: the first is devoted to draw, if exists, the digraph associated with a given Lie algebra; whereas the other corresponds to the converse problem and allows us to test if a given digraph is associated or not with a Lie algebra. Finally, we give the complete list of all non-isomorphic combinatorial structures of three vertices associated with Lie algebras and we study the type of Lie algebra associated with each configuration.

In this paper, we show an algorithmic procedure to compute abelian subalgebras and ideals of finite-dimensional Lie algebras, starting from the non-zero brackets in its law. In order to implement this method, we use the symbolic computation package MAPLE 12. Moreover, we also give a brief computational study considering both the computing time and the memory used in the two main routines of the implementation. Finally, we determine the maximal dimension of abelian subalgebras and ideals for non-decomposable solvable non-nilpotent Lie algebras of dimension 6 over both the fields ℝ and ℂ, showing the differences between these fields.

In this paper, we study the families of n-dimensional Lie algebras associated with a combinatorial structure made up of n vertices and with its edges forming a complete simple, undirected graph. Moreover, some properties are characterized for these structures using Lie theory, giving some examples and representations. Furthermore, we also study the type of Lie algebras associated with them in order to get their classification. Finally, we also show an implementation of the algorithmic method used to associate Lie algebras with complete triangular structures.