A bialgebra theory for compatible Hom-Lie algebras

Year 2026, Volume: 55 Issue: 1, 85 - 107, 23.02.2026

Taoufik Chtioui , Hajjaji Atef , Sami Mabrouk

https://doi.org/10.15672/hujms.1552307

https://izlik.org/JA52GY67GC

Abstract

In this paper, we introduce the notions of matched pairs and Manin triple for compatible Hom-Lie algebras. Then, we give a bialgebra theory of compatible Hom-Lie algebras with emphasis on its compatibility with Manin triple of compatible Hom-Lie algebras associated to a nondegenerate symmetric bilinear form. Moreover, we study coboundary compatible Hom-Lie bialgebras. Finally, we investigate some properties of a representation of a Hom-Nijenhuis Hom-Lie algebra and introduce the notion of a Hom-Nijenhuis Hom-Lie coalgebra. Furthermore, a Hom-Nijenhuis Hom-Lie bialgebra can be established by a Hom-Nijenhuis Hom-Lie algebra and a Hom-Nijenhuis Hom-Lie coalgebra satisfying some compatible conditions.

Keywords

compatible Hom-Lie algebra , compatible Hom-Lie bialgebra , classical Hom-YangBaxter equation , Hom-Nijenhuis operator

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