Hom-Big Brackets: Theory and Applications

TL;DR

This paper introduces hom-big brackets, a generalization of big brackets, forming a graded hom-Lie algebra, and demonstrates their utility in studying hom-structures like hom-Lie bialgebras and hom-Nijenhuis operators.

Contribution

It defines hom-big brackets and shows they form a graded hom-Lie algebra, providing a new tool for analyzing hom-structures.

Findings

Hom-big brackets generalize big brackets.

Hom-big brackets form a graded hom-Lie algebra.

Application to hom-Lie bialgebras and hom-Nijenhuis operators.

Abstract

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.