Title Finite-dimensional Zinbiel algebras and combinatorial structures
Authors CEBALLOS GONZÁLEZ, MANUEL, Nunez, Juan , Tenorio, Angel F.
External publication No
Scope Article
Nature Científica
JCR Quartile 3
SJR Quartile 3
JCR Impact 0.6
SJR Impact 0.333
Web https://www.scopus.com/inward/record.uri?eid=2-s2.0-85140360956&doi=10.2478%2fauom-2022-0035&partnerID=40&md5=7f6b18a54320b6f468423d3846ddf638
Publication date 01/09/2022
ISI 000867466900005
Scopus Id 2-s2.0-85140360956
DOI 10.2478/auom-2022-0035
Abstract 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.
Keywords Graph; combinatorial structure; Zinbiel algebra; algorithm; complexity
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