Hom-Big Brackets: Theory and Applications

In this paper, we introduce the notion of hom-big brackets, which is a generalization of Kosmann–Schwarzbach's big brackets. We show that it gives rise to a graded hom-Lie algebra. Thus, it is a useful tool to study hom-structures. In particular, we use it to describe hom-Lie bialgebras and hom-Nijenhuis operators.