Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 12 (2016), 014, 18 pages      arXiv:1507.04061      https://doi.org/10.3842/SIGMA.2016.014

Hom-Big Brackets: Theory and Applications

Liqiang Cai and Yunhe Sheng
Department of Mathematics, Jilin University, Changchun 130012, Jilin, China

Received July 16, 2015, in final form February 02, 2016; Published online February 05, 2016

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.

Key words: hom-Lie algebras; hom-Nijenhuis-Richardson brackets; hom-big brackets; hom-Lie bialgebras; hom-Nijenhuis operators; hom-$\mathcal O$-operators.

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