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.
📌 3 Key Takeaways
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Objective & Hypothesis:In this paper, we introduce the notions of matched pairs and Manin triple for compatible Hom-Lie algebras.
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Key Findings & Data: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.
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Conclusion & Impact: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.
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.
Chtioui, T., Atef, H., Mabrouk, S. (2026). A bialgebra theory for compatible Hom-Lie algebras. Hacettepe Journal of Mathematics and Statistics, Volume: 55 Issue: 1. https://doi.org/10.15672/hujms.1552307
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