Augmented, free and tensor generalized digroups

The concept of generalized digroup was proposed by Salazar-Díaz, Velásquez and Wills-Toro in their paper "Generalized digroups" as a non trivial extension of groups. In this way, many concepts and results given in the category of groups can be extended in a natural form to the category of generalized digroups. The aim of this paper is to present the construction of the free generalized digroup and study its properties. Although this construction is vastly di erent from the one given for the case of groups, we will use this concept, the classical construction for groups and the semidirect product to construct the tensor generalized digroup as well as the semidirect product of generalized digroups. Additionally, we give a new structural result for generalized digroups using compatible actions of groups and an equivariant map from a group set to the group corresponding to notions of associative dialgebras and augmented racks.

• Autores: Velásquez Ossa, Raúl Eduardo; Rodríguez Nieto, José Gregorio; Salazar Díaz, Olga Patricia
• Tipo de recurso: Article of investigation
• Fecha de publicación: 2019
• Institución: Universidad de Antioquia
• Repositorio: Repositorio UdeA
• Idioma: eng
• OAI Identifier: oai:bibliotecadigital.udea.edu.co:10495/46450
• Acceso en línea: https://hdl.handle.net/10495/46450
• Palabra clave: Group actions (Mathematics); Acciones grupales (Matemáticas); Teoria de los grupos; Groups, Theory of; Grupos de Lie; Lie groups; Álgebra; Algebra; http://id.loc.gov/authorities/subjects/sh85057471
• Rights: openAccess
• License: http://creativecommons.org/licenses/by/4.0/