Another approach to Hom-Lie bialgebras via Manin triples

Abstract

Abstract Motivated by the essential connection between Lie bialgebras and Manin triples, we introduce the notion of a Hom-Lie bialgebra with emphasis on its compatibility with a Manin triple of Hom-Lie algebras associated to a nondegenerate symmetric bilinear form. Then coboundary Hom-Lie bialgebras can be studied without a skew-symmetric condition of naturally leading to the classical Hom-Yang-Baxter equation whose solutions are used to construct coboundary Hom-Lie bialgebras, in particular on the double space of a Hom-Lie bialgebra. We also derive solutions of the classical Hom-Yang-Baxter equation from -operators and Hom-left-symmetric algebras.