Graphs associated with finite-dimensional Zinbiel algebras

Abstract

In this paper, we study the link between graphs and finite-dimensional Zinbiel algebras, determining which configurations are associated with those algebras. We analyze the properties of those graphs and the type of Zinbiel algebras associated to them. Moreover, we have designed and performed the implementation of an algorithm which constructs and draws the graph associated with a given Zinbiel algebra and, conversely, another procedure to test if a given graph is associated with some Zinbiel algebra. Finally, we apply our results and methods to study the isomorphism classes for each configuration associated with these algebras providing a new method to classify them.