Algorithmic method to obtain combinatorial structures associated with Leibniz algebras

Ceballos, Manuel; Núñez, Juan; Villalón, Ángel Francisco Tenorio

doi:10.1016/j.matcom.2014.11.001

Cited by 3 publications

(4 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Let us consider the combinatorial structure of Figure , which corresponds to configuration ( v ) of Figure . According to the notation that we are using in this algorithm and the association explained in Ceballos et al, we have to consider Now, we run all the procedures obtaining Therefore, the combinatorial structure is associated with a 3‐dimensional Leibniz algebra.…”

Section: Algorithm To Decide If a Given Combinatorial Structure Is Asmentioning

confidence: 99%

“…Let  be a n-dimensional Leibniz algebra with basis  = {e i } n i=1 . The pair (, ) is associated with a combinatorial structure by using the procedure explained in Ceballos et al 13 From here on, we will use this association.…”

Section: Definitionmentioning

confidence: 99%

“…According to the notation that we are using in this algorithm and the association explained in Ceballos et al, 13 Therefore, the combinatorial structure is associated with a 3-dimensional Leibniz algebra.…”

Section: Algorithm To Decide If a Given Combinatorial Structure Is Asmentioning

confidence: 99%

See 2 more Smart Citations

(Pseudo)digraphs and Leibniz algebra isomorphisms

Ceballos

Núñez

Villalón

2018

Math Methods in App Sciences

Self Cite

View full text Add to dashboard Cite

This paper studies the link between isomorphic digraphs and isomorphic Leibniz algebras, determining in detail this fact when using (psuedo)digraphs of 2 and 3 vertices associated with Leibniz algebras according to their isomorphism classes. Moreover, we give the complete list with all the combinatorial structures of 3 vertices associated with Leibniz algebras, studying their isomorphism classes. We also compare our results with the current classifications of 2‐ and 3‐dimensional Leibniz algebras. Finally, we introduce and implement the algorithmic procedure used for our goals and devoted to decide if a given combinatorial structure is associated or not with a Leibniz algebra.

show abstract

Section: Algorithm To Decide If a Given Combinatorial Structure Is Asmentioning

confidence: 99%

Section: Definitionmentioning

confidence: 99%

See 1 more Smart Citation

(Pseudo)digraphs and Leibniz algebra isomorphisms

Ceballos

Núñez

Villalón

2018

Math Methods in App Sciences

Self Cite

View full text Add to dashboard Cite

show abstract

“…Indeed, with this approach, new alternative techniques raise to improve well‐known theories or find new ones. As an example of it, the reader can consult the research started in , where a mapping between Lie algebras and combinatorial structures was introduced in order to translate properties of Lie algebras into the language of graph theory and vice versa , research that was later extended to Leibniz algebras in . In an analogous way, several works concerning certain connection between the evolution algebras and graph theory can be found in .…”

Section: Introductionmentioning

confidence: 99%

Associating hub‐directed multigraphs to arrowhead matrices

Marrero

Valdés

Villar

2017

Math Methods in App Sciences

View full text Add to dashboard Cite

In this paper, we use the arrowhead matrices as a tool to study graph theory. More precisely, we deal with an interesting class of directed multigraphs, the hub‐directed multigraphs. We associate the arrowhead matrices with the adjacency matrices of a class of directed multigraph, and we obtain new properties of the second objects by using properties of the first ones. The hub‐directed multigraphs with potential use in applications are also defined. As main result, we show that a hub‐directed multigraph G(H) with adjacency matrix H∗ is a dominant hub‐directed multigraph if and only if H∗=CE, where C is the adjacency matrix of another directed multigraph and E is the adjacency matrix of a particular elementary dominant hub‐directed pseudo‐graph. Another decomposition of its Gram (arrowhead) matrix A=()H∗TH∗ is also given. Copyright © 2017 John Wiley & Sons, Ltd.

show abstract

Computation of isotopisms of algebras over finite fields by means of graph invariants

Falcón

Ganfornina

Núñez

et al. 2017

Journal of Computational and Applied Mathematics

View full text Add to dashboard Cite

In this paper we define a pair of faithful functors that map isomorphic and isotopic finite-dimensional algebras over finite fields to isomorphic graphs. These functors reduce the cost of computation that is usually required to determine whether two algebras are isomorphic. In order to illustrate their efficiency, we determine explicitly the classification of two-and threedimensional partial quasigroup rings.

show abstract

Algorithmic method to obtain combinatorial structures associated with Leibniz algebras

Cited by 3 publications

References 11 publications

(Pseudo)digraphs and Leibniz algebra isomorphisms

(Pseudo)digraphs and Leibniz algebra isomorphisms

Associating hub‐directed multigraphs to arrowhead matrices

Computation of isotopisms of algebras over finite fields by means of graph invariants

Contact Info

Product

Resources

About