Hom-Big Brackets: Theory and Applications

[摘要] 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.

[关键词] hom-Lie algebras;hom-Nijenhuis–Richardson brackets;hom-big brackets;homLie bialgebras;hom-Nijenhuis operators;hom-O-operators