Algorithmic method to obtain combinatorial structures associated with Leibniz algebras

Manuel Ceballos, Juan Núñez and Ángel F. Tenorio

Mathematics and Computers in Simulation (MATCOM), 2016, vol. 125, issue C, 126-138

Abstract: In this paper, we introduce an algorithmic process to associate Leibniz algebras with combinatorial structures. More concretely, we have designed an algorithm to automatize this method and to obtain the restrictions over the structure coefficients for the law of the Leibniz algebra and so determine its associated combinatorial structure. This algorithm has been implemented with the symbolic computation package Maple. Moreover, we also present another algorithm (and its implementation) to draw the combinatorial structure associated with a given Leibniz algebra, when such a structure is a (pseudo)digraph. As application of these algorithms, we have studied what (pseudo)digraphs are associated with low-dimensional Leibniz algebras by determination of the restrictions over edge weights (i.e. structure coefficients) in the corresponding combinatorial structures.

Keywords: Pseudodigraph; Combinatorial structure; Leibniz algebra; Structure theory; Algorithm (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:125:y:2016:i:c:p:126-138

DOI: 10.1016/j.matcom.2014.11.001

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