Authors: ELKADRI ABDAOUI, SAMI MABROUK, ABDENACER MAKHLOUF, SONIA MASSOUD
Abstract: The purpose of this paper is to introduce and study $3$-Hom-Lie bialgebras, which are a ternary version of Hom-Lie bialgebras introduced by Yau (2015). We provide their properties, some key constructions and their 3-dimensional classification. Moreover we discuss their representation theory and their generalized derivations and coderivations. Furthermore, a more generalized notion called generalized $3$-Hom-Lie bialgebra is also considered.
Keywords: $3$-Hom-Lie bialgebra, multiplicative $3$-Hom-Lie bialgebra, extension, classification, representation, generalized derivation
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