Abstract
References
- [1] F. Ammar, Z. Ejbehi and A. Makhlouf, Cohomology and deformations of Homalgebras, J. Lie Theory 21(4), 813–836, 2011.
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-Yang–Baxter equation Hom-Nijenhuis operator
References
- [1] F. Ammar, Z. Ejbehi and A. Makhlouf, Cohomology and deformations of Homalgebras, J. Lie Theory 21(4), 813–836, 2011.
Details
| Primary Language | English |
|---|---|
| Subjects | Algebra and Number Theory, Algebraic and Differential Geometry, Category Theory, K Theory, Homological Algebra, Operator Algebras and Functional Analysis |
| Journal Section | Research Article |
| Authors | |
| Submission Date | September 18, 2024 |
| Acceptance Date | June 3, 2025 |
| Early Pub Date | June 24, 2025 |
| Published in Issue | Year 2026 Issue: Advanced Online Publication |