A new approach to hom-Lie bialgebras

TL;DR

This paper introduces a new definition of hom-Lie bialgebras, establishes their equivalence to Manin triples, and constructs solutions to the classical hom-Yang-Baxter equation using $\

Contribution

It presents a novel definition of hom-Lie bialgebras and links them to Manin triples, also introducing $\

Findings

New hom-Lie bialgebra definition

Equivalence to Manin triples established

Solutions to hom-Yang-Baxter equation constructed

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.