Hom-Big Brackets: Theory and Applications

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.

References in corpus (1)

• Notes on Formal Deformations of Hom-associative and Hom-Lie Algebras

Cited by in corpus (9)

• On Hom-Gerstenhaber algebras and Hom-Lie algebroids
• Hom-Lie Algebras and Hom-Lie Groups, Integration and Differentiation
• A complement on representations of Hom-Lie algebras
• Twisted O-operators on 3-Lie algebras and 3-NS-Lie algebras
• Hom-Lie superalgebra structures on exceptional simple Lie superalgebras of vector fields
• Equivalent description of Hom-Lie algebroids
• Hom-Lie groups of a class of Hom-Lie algebra
• Generalized representations of 3-Hom-Lie algebras
• Derivation Hom-Lie 2-algebras and non-abelian extensions of Hom-Lie algebras