Finite-dimensional Zinbiel algebras and combinatorial structures

In this paper, we study the link between finite-dimensional Zinbiel algebras and combinatorial structures or (pseudo)digraphs determining which configurations are associated with those algebras. Some properties of Zinbiel algebras that can be read from their associated combinatorial structures are s...

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Detalles Bibliográficos
Autores: Ceballos González, Manuel, Núñez-Valdés, Juan, Tenorio, Ángel F.
Tipo de recurso: artículo
Fecha de publicación:2022
País:España
Institución:Universidad Loyola Andalucía
Repositorio:Brújula
OAI Identifier:oai:repositorio.uloyola.es:20.500.12412/6932
Acceso en línea:https://hdl.handle.net/20.500.12412/6932
Access Level:acceso abierto
Palabra clave:Graph
Combinatorial structure
Zinbiel algebra
Algorithm
Complexity
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spelling Finite-dimensional Zinbiel algebras and combinatorial structuresCeballos González, ManuelNúñez-Valdés, JuanTenorio, Ángel F.GraphCombinatorial structureZinbiel algebraAlgorithmComplexityIn this paper, we study the link between finite-dimensional Zinbiel algebras and combinatorial structures or (pseudo)digraphs determining which configurations are associated with those algebras. Some properties of Zinbiel algebras that can be read from their associated combinatorial structures are studied. We also analyze the isomorphism classes for each configuration associated with these algebras providing a new method to classify them and we compare our results with the current classifications of 2- and 3-dimensional Zinbiel algebras. We also obtain the 3-vertices combinatorial structures associated with such algebras. In order to complement the theoretical study, we have designed and performed the implementation of an algorithm which constructs and draws the (pseudo)digraph associated with a given Zinbiel algebra and, conversely, another procedure to test if a given combinatorial structure is associated with some Zinbiel algebra.2022info:eu-repo/semantics/articlehttps://hdl.handle.net/20.500.12412/6932reponame:Brújulainstname:Universidad Loyola AndalucíaInglésUS-1262169; P20 01056; MTM2016- 75024-P; FEDERinfo:eu-repo/semantics/openAccessoai:repositorio.uloyola.es:20.500.12412/69322026-06-24T12:48:37Z
dc.title.none.fl_str_mv Finite-dimensional Zinbiel algebras and combinatorial structures
title Finite-dimensional Zinbiel algebras and combinatorial structures
spellingShingle Finite-dimensional Zinbiel algebras and combinatorial structures
Ceballos González, Manuel
Graph
Combinatorial structure
Zinbiel algebra
Algorithm
Complexity
title_short Finite-dimensional Zinbiel algebras and combinatorial structures
title_full Finite-dimensional Zinbiel algebras and combinatorial structures
title_fullStr Finite-dimensional Zinbiel algebras and combinatorial structures
title_full_unstemmed Finite-dimensional Zinbiel algebras and combinatorial structures
title_sort Finite-dimensional Zinbiel algebras and combinatorial structures
dc.creator.none.fl_str_mv Ceballos González, Manuel
Núñez-Valdés, Juan
Tenorio, Ángel F.
author Ceballos González, Manuel
author_facet Ceballos González, Manuel
Núñez-Valdés, Juan
Tenorio, Ángel F.
author_role author
author2 Núñez-Valdés, Juan
Tenorio, Ángel F.
author2_role author
author
dc.subject.none.fl_str_mv Graph
Combinatorial structure
Zinbiel algebra
Algorithm
Complexity
topic Graph
Combinatorial structure
Zinbiel algebra
Algorithm
Complexity
description In this paper, we study the link between finite-dimensional Zinbiel algebras and combinatorial structures or (pseudo)digraphs determining which configurations are associated with those algebras. Some properties of Zinbiel algebras that can be read from their associated combinatorial structures are studied. We also analyze the isomorphism classes for each configuration associated with these algebras providing a new method to classify them and we compare our results with the current classifications of 2- and 3-dimensional Zinbiel algebras. We also obtain the 3-vertices combinatorial structures associated with such algebras. In order to complement the theoretical study, we have designed and performed the implementation of an algorithm which constructs and draws the (pseudo)digraph associated with a given Zinbiel algebra and, conversely, another procedure to test if a given combinatorial structure is associated with some Zinbiel algebra.
publishDate 2022
dc.date.none.fl_str_mv 2022
dc.type.none.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/20.500.12412/6932
url https://hdl.handle.net/20.500.12412/6932
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv US-1262169; P20 01056; MTM2016- 75024-P; FEDER
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.source.none.fl_str_mv reponame:Brújula
instname:Universidad Loyola Andalucía
instname_str Universidad Loyola Andalucía
reponame_str Brújula
collection Brújula
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,812429

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