Cohomology and deformations of compatible Hom-Lie algebras
arXiv:2202.03137 · doi:10.1016/j.geomphys.2023.104951
Abstract
In this paper, we consider compatible Hom-Lie algebras as a twisted version of compatible Lie algebras. Compatible Hom-Lie algebras are characterized as Maurer-Cartan elements in a suitable bidifferential graded Lie algebra. We also define a cohomology theory for compatible Hom-Lie algebras generalizing the recent work of Liu, Sheng and Bai. As applications of cohomology, we study abelian extensions and deformations of compatible Hom-Lie algebras.
17pages; comments are welcome