Commun. Korean Math. Soc. 2024; 39(1): 11-30
Online first article January 29, 2024 Printed January 31, 2024
https://doi.org/10.4134/CKMS.c230055
Copyright © The Korean Mathematical Society.
Issam Bartouli, Imed Basdouri, Gaith Chaabane, Mohamed Fadous, Jean Lerbet
Universite d'\'Evry Val d'Essonne; University of Gafsa; University of Sfax; University of Sfax; Universite d'\'Evry Val d'Essonne
3-Lie algebras are in close relationships with many fields. In this paper we are concerned with the study of 3-Hom-Lie super algebras, the concepts of 3-Hom-Lie coalgebras and how they make a 3-Hom-Lie superbialgebras, we study the structures of such categories of algebras and the relationships between each others. We study a super twisted 3-ary version of the Yang-Baxter equation, called the super 3-Lie classical Hom-Yang-Baxter equation (3-Lie CHYBE), which is a general form of 3-Lie classical Yang-Baxter equation and prove that the superbialgebras induced by the solutions of the super 3-Lie CHYBE induce the coboundary local cocycle 3-Hom-Lie superbialgebras.
Keywords: Bialgebras, Yang-Baxter equations, Lie bialgebras, Lie coalgebras, Hom-Lie and related algebras, representation, central extension, double extension
MSC numbers: 16T10, 16T25, 17B62, 17B61
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