A new approach to hom-Lie bialgebras

Abstract

In this paper, we introduce a new definition of a hom-Lie bialgebra, which is equivalent to a Manin triple of hom-Lie algebras. We also introduce a notion of an $\mathcal{O}$-operator and then construct solutions of the classical hom-Yang-Baxter equation in terms of $\mathcal{O}$-operators and hom-left-symmetric algebras.

References in corpus (6)

• Deformations of Lie Algebras using $\sigma$-derivations
• Representations of hom-Lie algebras
• Hom-algebras and homology
• Representations and Cohomology of n-ary multiplicative Hom-Nambu-Lie algebras
• The classical Hom-Yang-Baxter equation and Hom-Lie bialgebras
• Infinitesimal Hom-bialgebras and Hom-Lie bialgebras