Yau-type ternary Hom-Lie bialgebras

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 D. Yau. 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 algebra is also considered.

3-Hom–Lie Yang–Baxter Equation and 3-Hom–Lie Bialgebras

“…In [10], Liu, Chen and Ma described the representations and module-extensions of 3-Hom-Lie algebras. In [11], Abdaoui, Mabrouk, Makhlouf and Massoud introduced and studied 3-Hom-Lie bialgebras, which are a ternary version of Hom-Lie bialgebras introduced by Yau. In [12], Ben Hassine, Chtioui and Mabrouk introduced the notion of 3-Hom-L-dendriform algebras which is the dendriform version of 3-Hom-Lie-algebras and studied their properties, the authors introduced the classical Yang-Baxter equation and Manin triples for 3-Lie algebras in [13,14]. Recently, we introduced the notion of 3-Hom-Lie-Rinehart algebras and systematically described a cohomology complex by considering coefficient modules in [15].…”