Cohomology and deformations of compatible Hom-Lie algebras

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.

arXiv comment17pages; comments are welcome

References in corpus (7)

• Deformations of Lie Algebras using $\sigma$-derivations
• Representations of hom-Lie algebras
• Character formulas for the operad of two compatible brackets and for the bihamiltonian operad
• Operads of compatible structures and weighted partitions
• Hom-Lie algebroids, Hom-Lie bialgebroids and Hom-Courant algebroids
• Maurer-Cartan characterizations and cohomologies of compatible Lie algebras
• Poisson-Nijenhuis groupoids