Actions of internal groupoids in the category of Leibniz algebras

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Communications Faculty of Sciences University Ankara Series A1 Mathematics and Statistics
Volume:68 Issue:1
Actions of internal groupoids in the category of Leibniz algebras

Actions of internal groupoids in the category of Leibniz algebras

Authors : Tunçar ŞAHAN, Ayhan ERCİYES

Pages : 619-632

Doi:10.31801/cfsuasmas.453582

View : 46 | Download : 8

Publication Date : 2019-02-01

Article Type : Research Paper

Abstract :The aim of this paper is to characterize the notion of internal category insert ignore into journalissuearticles values(groupoid); in the category of Leibniz algebras and investigate some properties of well-known notions such as covering groupoids and groupoid operations insert ignore into journalissuearticles values(actions); in this category. Further, for a fixed internal groupoid G in the category of Leibniz algebras, we prove that the category of covering groupoids of G and the category of internal groupoid actions of G on Leibniz algebras are equivalent. Finally, we interpret the corresponding notion of covering groupoids in the category of crossed modules of Leibniz algebras.
Keywords : Leibniz algebra, groupoid action, covering

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